## Monday, October 12, 2009

### IIT JEE Physics Final Revision Set 49

An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5.0 µF and the resulting LC circuit is set oscillating at its natural frequency. Let Q denote the instantaneous charge on the capacitor and I the current in the circuit. It is found that the maximum value of Q is 200 µC.
1. When Q = 100 µC, what is the value of |dI/dt|?
2. When Q = 200 µC, what is the value of I?
3. Find the maximum value of I.
4 When I is equal to one-half its maximum value, what is the value of |Q|?

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N0 nuclei of the element.

5. Calculate the number N of nuclei of A at time t.
6. If α = 2N0λ, calculate the number of nuclei of A after one half life of A, and also the limiting value of N as t → ∞.

Source 1998 JEE

### IIT JEE Physics Final Revision Set 48

A conducting sphere S1 of radius r is attached to an insulating handle. Another conducting sphere S2 of radius R is mounted on an insulating stand S2 is initially uncharged.
S1 is given a charge Q brought into contact with S2 and removed. This procedure is repeated n times.

1. Find the electrostatic energy of S2after n such contacts with S1.
2. What is the limiting valve of this energy as n →∞ ?

3. A particle of mass m and charge q is moving in a region where uniform constant electric and magnetic fields E and B are present. E and B are parallel to each other. At time t = 0, the velocity v0 of the particle is perpendicular to E (Assume that its speed is always << c, the speed of light in vacuum). Find the velocity v of the particle at time t. [You must express your answer in terms of t, q, m, the vectors v0, E an B and their magnitudes v0, E and B.

Suorce 1998 JEE

### IIT JEE Physics Final Revision Set 47

The air column in a pipe closed at one end is made to vibrate in its second overtone by tuning fork of frequency 440Hz The speed of sound in air is 330 m/s. End corrections may be neglected. Let P0 denote the mean pressure at any point in the pipe, and ΔP0 the maximum amplitude of pressure variation.

1. Find the length L of the air column.
2. What is the amplitude of pressure variation at the middle of the column?
3. What are the maximum and minimum pressures at the open end of the pipe?
4. What are the maximum and minimum pressures at the closed end of the pipe?

5. A solid body X of heat capacity C is kept in a an atmosphere whose temperature is TA = 300 K. At time t = 0, the temperature of X is T0 = 400 K. It cools according to Newton’s law of cooling. At time t1 its temperature is found to be 350 K.
At this time (t1) the body X is connected to a large body Y at atmospheric temperature TA through a conducting rod of length L, cross-sectional area A and thermal conductivity K. The heat capacity of Y is so large that any variation in its temperature may be neglected. The cross-sectional area A of the connecting rod is small compared to the surface area of X. Find the temperature of X at time t = 3t1.

Source: 1998 JEE

### IIT JEE Physics Final Revision Set 46

1. The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately:
(A) 540 nm (B) 400 nm
(C) 310 nm (D) 220 nm

2. X-rays are produced in an X-ray tube operating at a given accelerating voltage. The wavelength of the continuous X-rays has values from :
(A) 0 to ∞
(B) λmin to ∞ where λmin > 0
(C) 0 to λmax where λmax < ∞
(D)λmin to λmax where 0 < λmin < λmax < ∞

3. A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is U(x) = k |x|³ where k is a positive constant. If the amplitude of oscillation is a, then its time period T is :

(A) proportional to 1/√a
(B) proportional of a
(C) proportional to √a
(D) proportional to a³

Paragraph for 4 and 5

A particle of mass 10-2 Kg is moving along the positive x-axis under the influence of a force F(x) = – (k/2x²) where k = 10-2 Nm². At time t = 0 it is at x = 1.0 m and its velocity is v = 0:

4. Find its velocity when it reaches x = 0.5 m
5. Find the time at which it reaches x = 0.25 m

Source 1998 JEE

### IIT JEE Physics Final Revision Set 45

Questions may have more than one correct answer

1. A non-conducting slid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its centre :
(A) increases as r increases for r < R
(B) decreases as r increases for 0 < r < ∞
(C) decreases as r increases for R < r < ∞
(D) is discontinuous at r = R

2. A transverse sinusoidal wave of amplitude a, wavelength l and frequency f is travelling on a stretched string. The maximum speed of any point on the string is v/10, where v is the speed of propagation of the wave. If a = 10^–3 m and v = 10 m/s, then λ and f are given by :
(A) λ = 2π × 10^–2 m,f = 10³ Hz/2π (B)λ = 10^–3 m, f = 10³ Hz/2π
(C) λ = 2π × 10^–2 m, f = 104 Hz (D)λ = 10^–3 m, f = 104 Hz

3. A black body is at a temperature of 2880 K. The energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wein constant, b = 2.88 × 10^6 nm–K. Then :
(A) U1 = 0 (B) U3= 0
(C) U1 > U2 (D) U2 > U1

4. The SI unit of the inductance, the henry can be written as:
(A) Weber/ampere (B) Volt-second/ampere
(C) Joule/(ampere)² (D) ohm-second

5. Two very long straight parallel wires carry steady currents I and –I respectively. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is :

(A) (μ° Iqv) / 2πd (B) (μ° Iqv) / πd
(C) (2μ° Iqv) / πd (D) 0

1998 JEE

### IIT JEE Physics Final Revision Set 44

1. A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth.
(A) The acceleration of S is always directed towards the centre of the earth.
(B) The angular momentum of S about the centre of the earth changes in direction, but its magnitude remain constant
(C) the total mechanical energy of S varies periodically with time
(D) The linear momentum of S remains constant in magnitude

2. The torque r on a body about a given point is found to be equal to A × L where A is a constant vector and L is the angular momentum of the body about that point. From this it follows that:
(A) (dL)/dt is perpendicular to L at all instants of time.
(B) the component of L in the direction of A does not change with time.
(C) the magnitude of L does not change with time.
(D) L does not change with time.

3. In a p-n junction diode not connected to any circuit :
(A) the potential is the same everywhere
(B) the p-type side is at a higher potential than the n-type side
(C) there is an electric field at the junction directed from the n-side to the p-type side.
(D) there is an electric field at the junction directed from the p-type side to the n-type side.

4. During the melting of a slab of ice at 273K at atmospheric pressure :
(A) positive work is done by the ice-water system on the atmosphere.
(B) positive work is done on the ice-water system by the atmosphere.
(C) the internal energy of the ice-water system increases.
(D) the internal energy of the ice-water system decreases.

5. A spherical surface of radius of curvature R, separates air) refractive index 1.0) from glass (refractive index 1.5). The centre of curvature is in the glass. A point object P placed in air is found to have a real image Q in the glass. The line PQ cuts the surface at a point O and PO = OQ. The distance PO is equal to :
(A) 5R (B) 3R
(C) 2R (D) 1.5R

Source: 1998 JEE

### IIT JEE Physics Final Revision Set 43

1. A charge + q is fixed at each of the points x = x0, x = 3x0, x = 5x0 ….∞ on the x-axis and a charge – q is fixed at each of the points x = 2x0, x = 4x0, x = 6x0 …. ∞. Here x0 is a positive constant. Take the electric potential at a point due to a charge Q at a distance r from it to be Q/4πε0r.

Then the potential at the origin due to the above system of charges is :

(A) 0 (B) q / (8πε0x0 (ln 2))
(C) (q (ln 2))/(4πε0x0) (D) ∞

2. Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle θ with AB. The moment of inertia of the plate about the axis CD is then equal to :

(A) I (B) I sin²θ..
(C) I cos²θ (D) I cos²(θ/2)

3. A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement (s) from the following :
(A) the entire rod is at the same electric potential
(B) there is an electric field in the rod
(C) the electric potential is highest at the centre of the rod and decreases towards its ends.
(D) the electric potential is lowest at the centre of the rod and increases towards its ends.

4. A positively charged thin metal ring of radius R is fixed in the xy plane with its centre at the origin O. A negatively charged particle P is released from rest at the point (0, 0, z0) where z0 < 0. Then the motion of P is :
(A) period for all values of z0 satisfying 0 < z0 < ∞
(B) simple harmonic for all values of z0 satisfying 0 < z0 < R
(C) approximately simple harmonic provided z0 < < R
(D) such that P crosses 0 and continues to move along the negative z-axis towards z = – ∞.

5. A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let 0 be the pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be:
(A) real and will remain at C
(B) real and located at a point between C and ∞
(C) virtual and located at a point between C and 0
(D) real and located at a point between C and 0

Source: 1998 JEE paper

### IIT JEE Physics Final Revision Set 42

1. The half life of 131I is 8 days. Given a sample of 131I at time t = 0, we can assert that:
(A) no nucleus will decay before t = 4 days
(B) no nucleus will decay before t = 8 days
(C) all nuclei will decay before t = 16 days
(D) a given nucleus may decay at any time after t = 0

2. Two identical containers A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The mass of the gas in A is mA and that in B is mB. The gas in each cylinder is now allowed to expand isothermally to the same final volume 2V. The changes in the pressure in A and B are found to be DP and 1.5 DP respectively. Then :
(A) 4 mA = 9mB (B) 2mA = 3mB
(C) 3mA = 2mB (D) 9mA= 4mB

3. A given quantity of an ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of the gas is:
(A) 2/3 P (B) P
(C) 3/2 P (D) 2P

4. Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is:
(A) 30 K (B) 18K
(C) 50 K (D) 42 K

5. A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let 0 be the pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be:
(A) real and will remain at C
(B) real and located at a point between C and µ
(C) virtual and located at a point between C and 0
(D) real and located at a point between C and 0

Source 1998 JEE

### IIT JEE Physics Final Revision Set 41

1. The electron in a hydrogen atom makes a transition n1 ®n2 where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of n1 and n2 are :
(A) n1 = 4, n2 = 2 (B)n1 = 8, n2 = 2
(C) n1 = 8, n2 = 1 (D) n1 = 6, n2 = 3

2.A dielectric slab of thickness d is inserted in a parallel late capacitor whose negative plate is at x = 0 and positive plate is at x = 3d. The slab iis equidistant from the plates. The capacitor is given some charge. As x goes from 0 to 3d:
(A) the magnitude of the electric field remains the same
(B) the direction of the electric field remains the same
(C) the electric potential increases continuously
(D) the electric potential increases at first, then decreases and again increases.

3.The (x, y) coordinated of the corners of a square plate are (0, 0), (L, 0), (L, L) and (0, L). The edges of the plate are clamped and transverse standing waves re set up in it. If u (x, y) denotes the displacements of the plate at the point (x, y) at some instant of time, the possible expression (s) for u is (are) (a = positive constant):
(A) a cos (π x/2L) cos (π y/2L)
(B) a sin (π x/L) sin (π y/L)
(C) a sin (π x/L) sin (2π y/L)
(D) a cos (2π x/L) sin (π y/L)

4. A force F= K(y î + x ĵ) (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particle is:
(A) –2Ka² (B) 2Ka²
(C) –Ka² (D) Ka²

5. A small square loop of wire of side l is placed inside a large square loop of wire of side L(L >> l). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to :
(A) l/L (B) I²/L
(C) L/l (D) L²/l.

JEE 1998

### IIT JEE Physics Final Revision Set 40

1. Let v, vrms and vp respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecule is m. Then :

(A) no molecule can have a energy greater then √2 Vrms
(B) no molecule can have speed less thenVp/√2
(C) Vp is l.t. V is l.t. Vrms
(D) the average kinetic energy of a molecule is 3/4 mvp²

2. A string of length 0.4 ma and mass 10-2 Kg is tightly clamped at its ends. The tension in the string is 1.6N. Identical wave pulses are produced at one end at equal intervals of time Dt. The minimum value of Dt, which allows constructive interference between successive pulses, is :
(A) 0.05s (B) 0.10 s
(C) 0.20 s
(D) 0.40 s

3.A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence 450. The ray undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value(s) of n from the following :
(A) 1.3 (B) 1.4
(C) 1.5 (D) 1.6

4. Let mp be the mass of proton, mn the mass of neutron. M1 the mass of 20/10 Ne nucleus and M2 the mass of 40/20 Ca nucleus. Then :
(A) M2 = 2M1 (B) M2 > 2M1
(C) M2 < 2M1 (D) M1 < 10 (mn + mp)

5. A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is:
(A) 0 (B) π /2
(C) π (D) 2π

Source. 1998 JEE

### IIT JEE Physics Final Revision Set 39

1. 1. A transistor is used in common emitter mode as an amplifier, then :
(A)the base emitter junction is forward biased
(B)the base emitter junction is reverse biased
(C)the input signal is connected in series with the voltage applied to bias the base emitter junction.
(D)the input signal is connected in series with the voltage applied to bias the base collector junction.

2. Water from a tap emerges vertically downwards with an initial speed of 1.0 m/s. The cross-sectional area of tap is 10^–4 m². Assume that the pressure is constant throughout the stream of water and that the flow is steady, the cross-sectional area of stream 0.15 m below the tap is :
(A) 5.0 × 10^–4 m² (B) 1.0 × 10^–4 m²
(C) 5.0 × 10^–5 m² (D) 2.0 × 10^–5 m²

3. A real image of a distant object is formed by a planoconvex lens on its principal axis. Spherical aberration:
(A) is absent
(B) is smaller if the curved surface of the lens faces the object
(C) is smaller if the plane surface of the lens faces the object
(D) is the same whichever side of the lens faces the object

4. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to per N2 molecule is:
(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) depends on the moment of inertia of the two molecules.

5.Two particles, each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is :
(A) q/2m (B) q/m
(C) 2q/m
(D) q/πm

Source: JEE 1998

### IIT JEE Physics Final Revision Set 38

1. A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice.

[Take atmospheric pressure = 1.0 × 10^5 N/m², density of water = 1000 kg/m³ and g = 10 m/s². Neglect any effect of surface tension.]

2. A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.

3. A metal rod AB of length 10x has its one end A in ice at 0°C and the other end B in water at 100°C. If a
point P on the rod is maintained at 400°C, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of λx from the ice end A, find the value of λ.
[Neglect any heat loss to the surrounding.]

Source: 2009 JEE paper 2

4. The moment of inertia of a uniform disc about its diameter is I. Then the moment of inertia about an axis passng through its centre and perpendicular to its plane is 2I. State true or false.

5. A particle executes a linear simple harmonic motion of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points located at 12.5 cm on either side of equilibrium position?

a. 2.5 s b. 1.5 sec c. 0.5 sec d. 3.0 sec

4 and 5 (non JEE)

### IIT JEE Physics Final Revision Set 37

1. A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance.
Then -

(A) the intensity of the sound heard at the first resonance was more than that at the second resonance
(B) the prongs of the tuning fork were kept in a horizontal plane above the resonance tube
(C) the amplitude of vibration of the ends of the prongs is typically around 1 cm
(D) the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air.

2. Column II gives certain systems undergoing a process. Column I suggests changes in some of the
parameters related to the system. Match the statements in Column I to the appropriate process(es) from
Column II.

Column I
(A) The energy of the system is increased
(B) Mechanical energy is provided to the system, which is converted into energy of random motion of its parts
(C) Internal energy of the system is converted into its mechanical energy
(D) Mass of the system is decreased

Column II

(p) System : A capacitor, initially uncharged
Process : It is connected to a battery

(q) System : A gas in an adiabatic container fitted with an adiabatic piston
Process : The gas is compressed by pushing the piston

(r) System : A gas in a rigid container
Process : The gas gets cooled due to colder atmosphere surrounding it

(s) System : A heavy nucleus, initially at rest
Process : The nucleus fissions into two fragments of nearly equal masses and some
neutrons are emitted
(t) System : A resistive wire loop
Process : The loop is placed in a time varying magnetic field perpendicular to its plane

3. A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = κr^a, where κ
and a are constants and r is the distance from its centre. If the electric field at r = R/2 is (1/8) times that at r = R, find the value of a.(in integer values)

4. A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x,
PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k = (μ0I/48πx), find the value of k (answer is to be in integers)

5.Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m². The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio nB/nA, where nA and nB are the number of moles of air in bubbles
A and B, respectively. [Neglect the effect of gravity.]

Source: 2009 JEE paper 2

### IIT JEE Physics Final Revision Set 36

When a particle is restricted to move along x-axis between x = 0 and x = a, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a. The wavelength of this standing wave is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as E = p²/2m. Thus, the energy of the particle can be denoted by a quantum number 'n' taking values 1, 2, 3, . . . . . (n = 1, called the ground state) corresponding to the number of loops in standing wave.
Use the model described above to answer the following three questions for a particle moving in the line x = 0 to x = a.

Take h = 6.6 × 10^–34 J-s and e = 1.6 × 10^–19 C.

1. The allowed energy for the particle for a particular value of n is proportional to -
(A) a^(–2) (B) a^(–3/2) (C) a^(–1) (D) a^2

2. If the mass of the particle is m = 1.0 × 10^–30 kg and a = 6.6 nm, the energy of the particle
in its ground state is closest to -
(A) 0.8 meV (B) 8 meV (C) 80 meV (D) 800 meV

3. The speed of the particle, that can take discrete values, is proportional to -
(A) n^(–3/2) (B) n^(–1) (C) n^(1/2) (D) n

Source: JEE 2009 paper 1

4. A piece of wire is bent in the shape of a parabola y = kx² (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is –

a. a/gk b. a/2gk c. a/4gk d. 2a/gk

5.Under the influence of the Coulomb field of charge +Q, a charge –q is moving around it in an elliptical
orbital. Find out the correct statement(s).
(A) The angular momentum of the charge – q is constant
(B) The linear momentum of the charge –q is constant
(C) The angular velocity of the charge –q is constant
(D) The linear speed of the charge –q is constant

Source: JEE 2009 paper 2

### IIT JEE Physics Final Revision Set 35

1. If the resultant of all the external forces acting on a system of particles is zero, then from
an inertial frame, one can surely say that
(A) linear momentum of the system does not change in time
(B) kinetic energy of the system does not change in time
(C) angular momentum of the system does not change in time
(D) potential energy of the system does not change in time

2. A student performed the experiment of determination of focal length of a concave mirror
by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror
used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets
of (u, v) values recorded by the student (in cm) are : (42, 56), (48, 48), (60, 40), (66, 33),
(78, 39). The data set(s) that cannot come from experiment and is(are) incorrectly
recorded, is (are)
(A) (42, 56)
(B) (48, 48)
(C) (66, 33)
(D) (78, 39)

3. Cv and Cp denote the molar specific heat capacities of a gas at constant volume and
constant pressure, respectively. Then
(A) Cp – Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas
(B) Cp + Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas
(C) Cp / Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas
(D) Cp . Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas

Paragraph for Question Nos. 4 to 6

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, ²1H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is ²1H + ²1H → 32He + n + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of ²1H 1 nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core
are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t0 before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt0 is called Lawson number. In one of the
criteria, a reactor is termed successful if Lawson number is greater than 5 × 1014 s/cm3.

It may be helpful to use the following.
Boltzmann constant k = 8.6 × 10-5 eV/K;

e²/πε0 = 1.44 × 10-9 eVm.

4. In the core of nuclear fusion reactor, the gas becomes plasma because of –
(A) Strong nuclear force acting between the deuterons
(B) Coulomb force acting between the deuterons
(C) Coulomb force acting between deuteron-electron pairs
(D) the high temperature maintained inside the reactor core

5. Assume that two deuteron nuclei in the core of fusion reactor at temperature T are
moving towards each other, each with kinetic energy 1.5 kT, when the separation
between them is large enough to neglect Coulomb potential energy. Also neglect any
interaction from other particles in the core. The minimum temperature T required for
them to reach a separation of 4 × 10-15 m is in the range –

a. 1.0 × 1009 K is l.t. T is l.t. 2.0 × 109 K
b. 3.0 × 1009 K is l.t. T is l.t. 4.0 × 109 K
c. 2.0 × 1009 K is l.t. T is l.t. 3.0 × 109 K
d. 4.0 × 1009 K is l.t. T is l.t. 5.0 × 109 K

6. Results of calculations for four different designs of a fusion reactor using D-D reaction
are given below. Which of these is most promising based on Lawson criterion ?
(A) deuteron density = 2.0 × 10^12 cm–3, confinement time = 5.0 × 10^–3 s
(B) deuteron density = 8.0 × 10^14 cm–3, confinement time = 9.0 × 10^–1 s
(C) deuteron density = 4.0 × 10^23 cm–3, confinement time = 1.0 × 10^–11 s
(D) deuteron density = 1.0 × 10^24 cm–3, confinement time = 4.0 × 10^–12 s

JEE 2009 paper 1

### IIT JEE Physics Final Revision Set 34

1. STATEMENT-1
For an observer looking out through the window of a fast moving train, the nearby objects appear to move
in the opposite direction to the train, while the distant object appear to be stationary.

and
STATEMENT-2
If the observer and the object are moving at velocities V1 and V2 respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is V2-V1.

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for
STATEMENT-1
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True.

(Source: 2008 JEE paper 2)

2. The term that correct for the attractive forces present in a real gas in the van der Waals equation is -
(A) nb (B)an²/V²

(C)-an²/V² (D) – nb

3. A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The
coefficient of friction between them is √3 . The inclination θ of this inclined plane from the horizontal plane is gradually increased from 0º. Then

(A) at θ = 30º, the block will start sliding down the plane
(B) the block will remain at rest on the plane up to certain θ and then it will topple
(C) at θ = 60º, the block will start sliding down the plane and continue to do so at higher angles
(D) at θ = 60º, the block will start sliding down the plane and on further increasing θ, it will topple at certain θ

4. Three concentric metallic spherical shells of radii R, 2R, 3R are given charges Q1, Q2, Q3 respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q1 : Q2 : Q3 is-

(A) 1 : 2 : 3 (B) 1 : 3 : 5 (C) 1 : 4 : 9 (D) 1 : 8 : 18

5. A ball is dropped from a height of 20 m above the surface of water in a lake. The
refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is
looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the
fish sees the speed of ball as-
(A) 9 m/s (B) 12 m/s (C) 16 m/s (D) 21.33 m/s

Source: JEE 2009 paper 1

### IIT JEE Physics Final Revision Set 33

1. A vibrating string of certain length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension
of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is

(A) 344 (B) 336 (C) 117.3 (D) 109.3

2. A radio active sample S1 having an activity of 5μCi has twice the number of nuclei as another sample S2 which has an activity of 10μCi. The half lives of S1 and S2 can be

(A) 20 years and 5 years, respectively
(B) 20 years and 10 years, respectively
(C) 10 years each
(D) 5 years each

3. STATEMENT - 1
It is easier to pull a heavy object than to push it on a level ground.
and
STATEMENT - 2
The magnitude of frictional force depends on the nature of the two surfaces in contact.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for
STATEMENT-1
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True.

4. STATEMENT-1
For practical purposes the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT-2
The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by Q/4πε0R

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for
STATEMENT-1
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True.

5. STATEMENT-1
The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a
core inside the coil.
and
STATEMENT-2
Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for
STATEMENT-1
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True.

Source: 2008 JEE Paper 2

### IIT JEE Physics Final Revision Set 32

1. STATEMENT -1
In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown
resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at
the same point as before by decreasing the value of the standard resistance.
and
STATEMENT-2
Resistance of a metal increases with increase in temperature.
(A) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is a correct explanation for
STATEMENT -1
(B) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is NOT a correct explanation
for STATEMENT -1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True

2. STATEMENT – 1
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical
dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same
height. The hollow cylinder will reach the bottom of the inclined plane first.
and
STATEMENT – 2
By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical
when they reach the bottom of the incline.
(A) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is a correct explanation for
STATEMENT -1
(B) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is NOT a correct explanation
for STATEMENT -1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True

3. STATEMENT – 1
The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when
held vertically up, but tends to narrow down when held vertically down.
and
STATEMENT – 2
In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.
(A) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is a correct explanation for
STATEMENT -1
(B) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is NOT a correct explanation for STATEMENT -1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True

Paragraph
In a mixture of H and He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

4. The quantum number n of the state finally populated in He+ ions is
(A) 2 (B) 3 (C) 4 (D) 5

5. The wavelength of light emitted in the visible region by He+ ions after collisions with H atoms is
(A) 6.5 × 10-7 m (B) 5.6 × 10-7 m
(C) 4.8 × 10-7 m (D) 4.0 × 10-7 m

6. The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is

a. 1/4 b. 1/2 c. 1 d. 2

### IIT JEE Physics Final Revision Set 31

1. An ideal gas is expanding such that PT2 = constant. The coefficient of volume expansion of the gas is

a. 1/T b. 2/T c. 3/T d. 4/T

2. Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60º). In the position of minimum deviation, the angle of refraction will be

(A) 30º for both the colours (B) greater for the violet colour
(C) greater for the red colour (D) equal but not 30º for both the colours

3. Which one of following statements is Wrong in the context of X-rays generated from a X- ray tube ?
(A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases
(B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target
(C) Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube
(D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube

4. In a Young’s double slit experiment, the separation between the two slits is d and the wavelength of the light is λ. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).

(A) If d = λ, the screen will contain only one maximum
(B) If λ < d < 2λ, at least one more maximum (besides the central maximum) will be observed on the
screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the
intensities of the observed dark and bright fringes will increase
(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase

5.STATEMENT – 1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT – 2
An object moving around the Earth under the influence of Earth’s gravitational force is in a state of
‘free-fall’.
(A) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is a correct explanation for
STATEMENT -1
(B) STATEMENT – 1 is True, STATEMENT- 2 is True; STATEMENT -2 is NOT a correct explanation
for STATEMENT -1
(C) STATEMENT-1 is True, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 is True

Source JEE 2008 Paper 1

### IIT JEE Physics Final Revision Set 30

Paragraph
A cylinder of mass 1 kg is given heat of 20000J at atmospheric pressure. If initially temperature of cylinder is 20°C.

1.Find final temperature of the cylinder.
2. Find the work done by the cylinder.
3 Find the change in internal energy of the cylinder.
(Given that Specific heat of cylinder= 400 J kg-1 0C-1, Coefficient of volume expansion
= 9 × 10-5 °C-1, Atmospheric pressure = 105 N/m2 and Density of cylinder = 9000 kg/m³)

Paragraph
In a moving coil galvanometer, torque on the coil can be expressed as τ = ki, where i is current through the wire and k is constant. The rectangular coil of the galvanometer having numbers of turns N, area A and moment of inertia I is placed in magnetic field B.

4. Find k in terms of given parameters N, I, A and B.
5. Find the torsional constant of the spring, if a current i0 produces a deflection of π/2 in the coil.
6. the maximum angle through which coil is deflected, if charge Q is passed through the coil almost instantaneously. (Ignore the damping in mechanical oscillations)

Source 2005 JEE Mains

### IIT JEE Physics Final Revision Set 29

1. A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is 3 m/s and maximum transverse acceleration is 90 m/s². If the wave velocity is 20 m/s then find the waveform.

2. A cylinder of mass m and radius R rolls down an inclined plane of inclination θ. Calculate the linear acceleration of the axis of cylinder.

3. A long solenoid of radius a and number of turns per unit length n is enclosed by cylindrical shell of radius R, thickness d (d is very small compared to R) and length L. A variable current i = i0sin ωt flows through the coil. If the resistivity of the material of cylindrical shell is ρ, find the induced current in the shell.

Paragraph:
Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is (14)1/3.

4. Find atomic number of the nucleus.
5. Find the frequency of Kα line of the X−ray produced. (R = 1.1 × 107 m-1 and c = 3 ×108 m/s)

Source 2005 JEE Main

### IIT JEE Physics Final Revision Set 28

1. A whistling train approaches a junction. An observer standing at junction observes the frequency to be 2.2 KHz and 1.8 KHz of the approaching and the receding train. Find the speed of the train (speed of sound = 300 m/s)

2. A conducting liquid bubble of radius a and thickness t (t <
3. The potential energy of a particle of mass m is given by
V (x) = E0 when 0 is l.t. or = x is l.t. or = 1
V (x) = 0 when x>1
λ1 and λ2 are the de−Broglie wavelengths of the particle, when 0 ≤ x ≤ 1 and x > 1 respectively. If the total energy of particle is 2E0, find λ1/λ2.

4. A U tube is rotated about one of it’s limbs
with an angular velocity ω. Find the difference
in height H of the liquid (density ρ) level,
where diameter of the tube d << L.

5. The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and first division of vernier scale coincides with the main scale. Mass of the cube is 2.736 g. Find the density of the cube in appropriate significant figures.

Source 2005 JEE Mains

### IIT JEE Physics Final Revision Set 27

1. A spherical ball of radius R, is floating in a liquid with half of its volume submerged in the liquid. Now the ball is displaced vertically by small distance inside the liquid. Find the frequency of oscillation of ball.
----
Paragraph:
A point object is moving with velocity 0.01 m/s on principal axis towards a convex lens of focal length 0.3m. When object is at a distance of 0.4 m from the lens, find

2. rate of change of position of the image, and
3. rate of change of lateral magnification of image.

4. A cubical block is floating inside a bath. The temperature of system
is increased by small temperature ΔT. It was found that the depth
of submerged portion of cube does not change. Find the relation
between coefficient of linear expansion (α) of the cube and volume
expansion of liquid (γ).

5. In a Young’s double slit experiment light consisting of two wavelengths λ1 = 500 nm and λ2 = 700 nm is incident normally on the slits. Find the distance from the central maxima where the maximas due to two wavelengths coincide for the first time after central maxima. (Given D/d = 1000) where D is the distance between the slits and the screen and d is the separation between the slits.

Source: 2004 Mains

### IIT JEE Physics Final Revision Set 26

1. The age of a rock containing lead and uranium is equal to 1.5 × 109 yrs. The uranium is decaying into lead with half life equal to 4.5 × 109 yrs. Find the ratio of lead to uranium present in the rock, assuming initially no lead was present in the rock. (Given 21/3 = 1.259)

2. An inductor of inductance (L) equal to 35 mH
and resistance (R) equal to 11 Ω are connected
in series to an AC source. The rms voltage of
a.c. source is 220 volts and frequency is 50 Hz.
Find the peak value of current in the circuit.

Two identical blocks A and B are placed on a rough inclined plane of
inclination 45°. The coefficient of friction between block A and incline is
0.2 and that of between B and incline is 0.3. The initial separation between
the two blocks is √2 m. The two blocks are released from rest, then find

3. the time after which front faces of both blocks come in same line
4. the distance moved by each block for attaining above position.

5. In a photoelectric setup, the radiations from the Balmer series of hydrogen atom are incident on a metal
surface of work function 2eV. The wavelength of incident radiations lies between 450 nm to 700 nm. Find
the maximum kinetic energy of photoelectron emitted.
(Given hc/e = 1242 eV-nm).

Source 2004 jee main

## Sunday, October 11, 2009

### IIT JEE Physics Final Revision Set 25

1. In Searle’s apparatus diameter of the wire was measured 0.05 cm by screw gauge of least count 0.001 cm.The length of wire was measured 110 cm by meter scale of least count 0.1 cm. An external load of 50 N was applied. The extension in length of wire was measured 0.125 cm by micrometer of least count 0.001 cm. Find the maximum possible error in measurement of young’s modulus.

2. Two infinitely large sheets having charge densities σ1 and σ2
respectively (σ1 > σ2) are placed near each other separated by
distance ‘d’. A charge ‘Q’ is placed in between two plates such that
there is no effect on charge distribution on plates. Now this charge
is moved at an angle of 45° with the horizontal towards plate having
charge density σ2 by distance ‘a’ (a is l.t. d). Find the work done by
electric field in the process.

3. An α -particle and a proton are accelerated from rest through same potential difference and both enter into a uniform perpendicular magnetic field. Find the ratio of their radii of curvature.

4. A small ball of radius ‘r’ is falling in a viscous liquid under gravity. Find the dependency of rate of heat produced in terms of radius ‘r’ after the drop attains terminal velocity.

5. A screw gauge of pitch 1mm has a circular scale divided into 100 divisions. The diameter of a wire is to be measured by above said screw gauge. The main scale reading is 1mm and 47th circular division coincides with main scale. Find the curved surface area of wire in true significant figures. (Given the length of wire
is equal to 5.6 cm and there is no zero-error in the screw gauge.)

Source: 2004 JEE mains

### IIT JEE Physics Final Revision Set 21

1. Two litre of water at initial temperature of 27° C is heated by a heater of power 1 kW. If the lid of kettle is opened, then heat is lost at the constant rate of 160 J/s. Find the time required to raise the temperature of water to 77° C with the lid open (Specific heat of water 4.2 kJ/kg)

(A) 5 min 40 sec (B) 14 min 20 sec
(C) 8 min 20 sec (D) 16 min 10 sec

2. Ideal gas is contained in a thermally insulated and rigid container and it is heated through a resistance 100Ω by
passing a current of 1A for five minutes, then change in internal energy of the gas is
(A) 0 kJ (B) 30 kJ
(C) 10 kJ (D) 20 kJ

Source: JEE screening 2005

3. Consider the spectral line resulting from the transition n=2 → n=1 in the atoms and ions given below. The shortest wave length is produced by

a. hydrogen atom
b. singly ionized helium
c. deuterium atom
d. doubly ionized lithium

4. State true or false
A beam of white light passing through a hollow prism gives no spectrum

5. State true or false
A charged particle enters a region of uniform magnetic fieldat an angle of 85°C to the magnetic lines of force. The path of the particle is circle.

Source: 1983 JEE paper

### IIT JEE Physics Final Revision Set 20

1. An open organ pipe resonated with frequency ‘f1’ and 2nd harmonic. Now one end is closed and the frequency is slowly increased then it resonates with frequency f2 and nth harmonic then

(a) n = 3, f2 = (3/4)f1
(b) n = 5, f2 = (3/4)f1
(c) n = 3, f2 = (5/4)f1
(d) n = 5, f2 = (5/4)f1

2. Temperature of a gas is 20°C and pressure is changed from 1.01×105 Pa to 1.165×105 Pa . If volume is decreased isothermally by 10%. Bulk modulus of gas is
(A) 1.55× 105 (B) 0.155× 105
(C) 1.4× 105 (D) 1.01×105

3. A galvanometer with resistance 100Ω is converted to ammeter with a resistance of 0.1Ω. The galvanometer shows full scale deflection with a current of 100 µA. Then the minimum current in the circuit for full scale deflection of galvanometer will be

(A) 100.1mA (B) 10.01mA
(C) 1.001mA (D) 0.1001mA

4. One calorie is defined as the heat required to raise the temperature of 1 gm of water by 1°C in a certain interval of temperature and at certain pressure. The temperature interval and pressure is

(A) 13.5° C to 14.5° C & 76 mm of Hg (B) 6.5° C to 7.5° C & 76 mm of Hg
(C) 14.5° C to 15.5° C & 760 mm of Hg (D) 98.5° C to 99.5° C & 760 mm of Hg

5. If a star converts all of its Helium into oxygen nucleus, find the amount of energy released per nucleus of
oxygen. He = 4.0026 amu, O = 15.9994 amu
(A) 7.26 MeV (B) 7 MeV
(C) 10.24 MeV (D) 5.12 MeV

Source: 2005 JEE screening

### IIT JEE Physics Final Revision Set 19

1. In a resonance tube with tuning fork of frequency 512Hz, first resonance occurs at water level equal to 30.3 cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is
(A) 51.2 cm/s (B) 102.4 cm/s
(C) 204.8 cm/s (D) 153.6 cm/s

2. A thin concave and a thin convex lens are in contact. The ratio of the magnitude of power of two lenses is 2/3
and focal length of combination is 30cm, then the focal length of individual lenses are
(A) – 15 cm, 10 cm (B) – 75 cm, 50 cm
(C) 75 cm, - 50 cm (D) 75 cm, 50 cm

3. Which of the following process does not occur through convection
(A) Boiling of water (B) Land breeze and Sea breeze
(C) Circulation of air around furnace (D) Heating of glass bulb through filament

4. In YDSE, an electron beam is used to obtain interference pattern. If speed of electron is increased then
(A) no interference pattern will be observed.
(B) distance between two consecutive fringes will increase.
(C) distance between two consecutive fringes will decrease.
(D) distance between two consecutive fringes remains same.

5. A spherical body of area A and emissivity e = 0.6 is kept inside a perfectly black body. Total heat radiated by the body at temperature T
(A) 0.4 e AT4 (B) 0.8eAT4
(C) 0.6 eAT4 (D) 1.0eAT4

source 2005 JEE screening

### IIT JEE Physics Final Revision Set 18

1. T1 is the time period of simple pendulum. The point of suspension moves vertically upwards according to y =kt², where k = 1 m/s². New time period is T2, then T1²/T2² = ? ( g = 10 m/s²)

(A) 4/5 (B) 6/5
(C) 5/6 (D) 1

2.Which of the following does not have the same dimension?
(A) Electric flux, Electric field, Electric dipole moment
(B) Pressure, stress, Young’s modulus
(C) Electromotive force, Potential difference, Electric voltage.
(D) Heat, Potential energy, Work done

3. A capacitor (C = 4.0 µF) is connected through a resistor (R = 2.5 MΩ) across a battery of negligible internal resistance of voltage 12 volts. The time after which the potential difference across the capacitor becomes three
times to that of resistor is (ln 2 = 0.693)

(A) 13.86 sec. (B) 6.48 sec.
(C) 3.24 sec. (D) 20.52 sec.

4. A photon of energy 10.2 eV collides inelastically with a Hydrogen atom in ground state. After a certain time
interval of few micro seconds another photon of energy 15.0 eV collides inelastically with the same hydrogen
atom, then the observation made by a suitable detector is
(A) 1 photon with energy 10.2 eV and an electron with energy 1.4 eV
(B) 2 photon with energy 10.2 eV
(C) 2 photon with energy 1.4 eV
(D) one photon with energy 3.4 eV and 1 electron with energy 1.4 eV

5. In a resonance tube with tuning fork of frequency 512Hz, first resonance occurs at water level equal to
30.3 cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is
(A) 51.2 cm/s (B) 102.4 cm/s
(C) 204.8 cm/s (D) 153.6 cm/s

Source: 2005 JEE screening

### IIT JEE Physics Final Revision Set 17

1. In Young’s double slit experiment the angular position of a point on the central maxima whose intensity is one fourth of maximum intensity
(A) sin-1(λ/d) (B)sin-1(λ/2d)
(C)sin-1(λ/3d) (D)sin-1(λ/4d)

2. Ratio of area of hole to beaker is 0.1. Height of liquid in beaker is 3m, and hole is at the height of 52.5 cm from the bottom of beaker, find the square of the velocity of liquid coming out from the hole
(A) 50 (m/s)² (B) 50.5 (m/s)²
(C) 51 (m/s)² (D) 42 (m/s)²

3. A cylindrical conducting rod is kept with its axis along positive z-axis, where a uniform magnetic field exists
parallel to z-axis. The current induced in the cylinder is
(A) zero (B) clockwise as seen from +z axis
(C) anti-clockwise as seen from +z axis (D) opposite to the direction of magnetic field.

4. A particle is confined to rotate in a circular path with decreasing linear speed, then which of the following is correct?
(A) L(angular momentum) is conserved about the centre.
(B) only direction of angular momentum L is conserved.
(C) It spirals towards the centre.
(D) its acceleration is towards the centre.

5. The atomic number (Z) of an element whose kα wavelength is λ is 11. The atomic number of an element whose
kα wavelength is 4λ is equal to
(A) 6 (B) 11
(C) 44 (D) 4

Source 2005 JEE screening

### IIT JEE Physics Final Revision Set 16

1. Match items in column 1 with items in column 2
Column 1
(A) Nuclear fusion
B) Nuclear fission
(C) β-decay
(D) Exothermic nuclear reaction

Column 2

(P) Converts some matter into energy

(Q) Generally possible for nuclei with low atomic number

(R) Generally possible for nuclei with higher atomic number

(S) Essentially proceeds by weak nuclear forces

2. A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths fe and f0,
respectively. Then: match items in column 1 with column 2

Column 1

(A) Intensity of light received by lens
(B) Angular magnification
(C) Length of telescope
(D) Sharpness of image

Column 2

(Q) Dispersion of lens

(R) focal length f0, fe
(D) Sharpness of image

3. Match colmns 1 and 2
(A) Dielectric ring uniformly charged
(B) Dielectric ring uniformly charged rotating
with angular velocity ω
(C) Constant current in ring i0.
(D) i = i0cos ωt

Column 2

(P) Time independent electrostatic field out of system
(Q) Magnetic field
(R) Induced electric field
(S) Magnetic moment

Source: 2006 JEE

### IIT JEE Physics Final Revision Set 15

Two waves y1 = A cos( 0.5 πx − 100 πt)
and y2 = A cos( 0.46 πx − 92 πt) are travelling in a pipe placed along x-axis.

1. Find the number of times
intensity is maximum in time interval of 1 sec.
(A) 4 (B) 6
(C) 8 (D) 10

2. Find wave velocity of louder sound
(A) 100 m/s (B) 192 m/s
(C) 200 m/s (D) 96 m/s

3. Find the number of times y1+ y2 = 0 at x = 0 in 1 sec
(A) 100 (B) 46
(C) 192 (D) 96

4.In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final
temperature of the mixture.
Given, L(fusion) = 80 cal/g = 336 J/g, L(vaporization) = 540 cal/g = 2268 J/g,
S(ice) = 2100 J/kg K = 0.5 cal/gK and S(water) = 4200 J/kg K = 1 cal /gK

5. In hydrogen-like atom (z = 11), "n"th line of Lyman series has wavelength λ equal to the de-Broglie’s wavelength of electron in the level from which it originated. What is the value of n?

Source: JEE 2006

### IIT JEE Physics Final Revision Set 13

1. STATEMENT-1 The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume. because

STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

2. STATEMENT-1 If there is no external torque on a body about its center of mass, then the velocity of the centre of mass remains constant. because STATEMENT-2 The linear momentum of an isolated system remains constant.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle. Assume that the sound of whistle is composed of components varying in frequency from f1 = 800 Hz to f2 = 1120 Hz. The spread in the frequency (highest frequency – lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s.

3. The speed of sound of the whistle is
(A) 340 m/s for passengers in A and 310 m/s for passengers in B
(B) 360 m/s for passengers in A and 310 m/s for passengers in B
(C) 310 m/s for passengers in A and 360 m/s for passengers in B
(D) 340 m/s for passengers in both the trains

4. The spread of frequency as observed by the passengers in train B is
(A) 310 Hz (B) 330 Hz (C) 350 Hz (D) 290 Hz

5. Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II.

Column 1

A. Bimetallic strip
(B) Steam engine
(C) Incandescent lamp
(D) Electric fuse

Column 2
(p) Radiation from a hot body

(q) Energy conversion

(r) Melting
(s) Thermal expansion of solids

Source: JEE 2007 paper 2

### IIT JEE Physics Final Revision Set 12

1.Column 1 gives certain situations in which a straight metallic wire of resistance R is used and
column 2 gives some resulting effects. Match column 1 itmes with column 2 items.

Column 1
a. A charged capacitor is connected to
the ends of the wire

b. The wire is moved perpendicular to
its length with a constant velocity in
a uniform magnetic field
perpendicular to the plane of motion

c. The wire is placed in a constant
electric field that has direction along
the length of the wire

d. A battery of constant emf is
connected to the ends of the wire

Column 2

p. A constant current flows through the wire
q. Thermal energy is generated in the wire
r. A constant potential difference develops
between the ends of the wire
s. Charges of constant magnitude appear
at the ends of the wire

(Source: 2007 paper 1)

2. A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 3v²/4g with respect to the initial position.The object is

(A) ring (B) solid sphere (C) hollow sphere (D) disc

3. In the experiment to determine the speed of sound using a resonance column, (A) prongs of the tuning fork are kept in a vertical plane (B) prongs of the tuning fork are kept in a horizontal plane (C) in one of the two resonance observed, the length of the resonating air column is close to the wavelength of sound in air (D) in one of the two resonance observed, the length of the resonating air column is close to half of the wavelength of sound in air

4. Positive and negative point charges of equal magnitude are kept at [0,0,a/2] and [0,0,-a/2], respectively. The work done by the electric field when another positive point charge is moved from (-a,0,0) to (0,a,0) is

(A) positive (B) negative (C) zero (D) depends on the path connecting the initial and final positions

5.

STATEMENT-1
Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.

STATEMENT-2
For every action there is an equal and opposite reaction.

A) Statement-1 is True, Statement-2 is True; Statement
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

Source: 2007 Physics paper 2

### IIT JEE Physics Final Revision Set 11

1. STATEMENT-1 : In an elastic collision
between two bodies, the relative speed of
the bodies after collision is equal to the
relative speed before the collision.
Because
STATEMENt-2 : In an elastic collision,
the linear momentum of the system is
conserved.

a. Statement-1 is True, Statement-2 is
True; Statement-2 is a correct
explanation for Statement-1.
b. Statement-1 is True, Statement-2 is
True; Statement-2 is NOT a correct
explanation for Statement-1.
c. Statement-1 is True, Statement-2 is
False.
d. Statement-1 is False, Statement-2 is
True.

Two discs A and B are mounted coaxially on a
vertical axle. The discs have moments of inertia
I and 2I respectively about the common axis.
Disc A is imparted an initial angular velocity 2ω
using the entire potential energy of a spring
compressed by a distance x1 . Disc B is
imparted an angular velocity w by a spring
having the same spring constant and constant
and compressed by a distance x2 . Both the
discs rotate in the clockwise direction.

2. The ratio of x1 /x2 is
a. 2 b. 1/2 c. √2 d. 1/√2

3. When disc B is brought in contact with
disc A, they acquire a common angular
velocity in time t. The average frictional
torque on one disc by the other during
this period is

a. 2Iω/3t b. 9Iω/2t c. 9Iω/4t s. 3Iω/2t

4. The loss of kinetic energy during the
above process is

a. Iω²/2 b. Iω²/3 c. Iω²/4 d. Iω²/6

5. Match column 1 items with column 2 items

Column 1

a. Transition
between two
atomic energy
levels

b. Electron
emission from
a material

c. Mosley’s law

d. Change of
photon
energy into
kinetic
energy of
electrons

Column 2

p. Characteristic Xrays
q. Photoelectric
effect
r. Hydrogen
spectrum
d.β-decay

Source: 2007 JEE paper 1

### IIT JEE Physics Final Revision Set 10

1. Consider a neutral conducting sphere. A
positive point charge is placed outside
the sphere. The net charge on the sphere
is then,
1. Negative and distributed uniformly
over the surface of the sphere.
2. Negative and appears only at the point
on the sphere closest to the point charge
3. Negative and distributed nonuniformly
over the entire surface of the
sphere
4. Zero

2. STATEMENT – 1
The formula connecting u, v and f for a
spherical mirror is valid only for mirrors
whose sizes are very small compared to
because
STATEMENT-2
Laws of reflection are strictly valid for
plane surfaces, but not for large
spherical surfaces.
a. Statement-I is true, Statement-2 is
True ; Statement-2 is a correct
explanation for Statement-I
b. Statement-1 is true, Statement-2 is
True ; Statement-2 is NOT a correct
explanation for Statement-I.
c. Statement-1 is True, Statement-2 is
False.
d. Statement-1 is False, Statement-2 is
True.

3.STATEMENT-1: If the accelerating
potential in an X-ray tube is increased,
the wavelengths of the characteristic Xrays
do not change. Because
STATEMENT-2 : When an electron
beam strikes the target in an X-ray tube,
part of the kinetic energy is converted
into X-ray energy.
a. Statement-1 is True, Statement-2 is
True; Statement-2 is a correct
explanation for Statement-1.
b. Statement-1 is True, Statement-2 is
True; Statement-2 is NOT a correct
explanation for Statement-1.
c. Statement-1 is True, Statement-2 is
False.
d. Statement-1 is False, Staement-2 is
True.

4. STATEMENT-1 : A block of mass m
starts moving on a rough horizontal
surface with a velocity v. It stops due to
friction between the block and the
surface after moving through a certain
distance. The surface is now tilted to an
angle of 30° with the horizontal and the
same block is made to go up on the
surface with the same initial velocity v.
The decrease in the mechanical energy
in the second situation is smaller than
that in the first situation. Because
STATEMENT-2 : The coefficient of
friction between the block and the
surface decreases with the increase in
the angle of inclination.
a. Statement-1 is True, Statement-2 is
True ; Statement-2 is a correct
explanation for statement-1.
b. Statement-1 is True, Statement-2 is
True; Statement-2 is NOT a correct
explanation for statement-1.
c. Statement-1 is True, Statement-2 is
False.
d. Statement-1 is False, Statement-2 is
True.

Source: 2007 JEE paper 1

### IIT JEE Physics Final Revision Set 9

1. A long, hollow conducting cylinder is
kept coaxially inside another long,
hollow conducting cylinder of longer
radius. Both the cylinders are initially
electrically neutral.

a. A potential difference appears between
the two cylinders when a charge density
to the inner cylinder.
b. A potential difference appears between
the two cylinders when a charge density
is given to the outer cylinder.
c. No potential difference appears
between the two cylinders when a
uniform line charge is kept along the
axis of the cylinders.
d. No potential difference appears
between the two cylinders when same
charge density is given to both the
cylinders.

2. In an experiment to determine the focal
length (f) of a concave mirror by the u-v
method, a student places the object pin
A on the principal axis at a distance x
from the pole P. The student looks at the
pin and its inverted image from a
distance keeping his/her eye in line with
PA. When the student shifts his/her eye
towards left, the image appears to the
right of the object pin. Then,

a. x is l.t. f b. f is l.t. x is l.t. 2f
c. x = 2f d. x > 2f

3.The largest wavelength in the ultraviolet
region of the hydrogen spectrum is 122
nm. The smallest wavelength in the
infrared region of the hydrogen spectrum
(to the nearest integer) is
a. 802 nm b. 823 nm
c. 1882 nm d. 1648 nm

4. A resistance of 2Ω is connected across
one gap of a metre-bridge (the length of
the wire is 100 cm) and an unknown
resistance, greater than 2Ω , is
connected across the other gap. When
these resistance are interchanged, the
balance point shifts by 20 cm. Neglecting
any corrections, the unknown resistance
is
a. 3Ω b. 4Ω
c. 5Ω d. 6Ω

5. A ray of light traveling in water is
incident on its surface open to air. The
angle of incidence is θ, which is less
than the critical angle. Then there will be
1. Only a reflected ray and no refracted
ray
2. Only a refracted ray and no reflected
ray
3. A reflected ray and a refracted ray and
the angle between them would be less
than 180° – 2θ
4. A reflected ray and a refracted ray and
the angle between them would be greater
than
180° – 2θ .

Source 2007 Paper 1

### IIT JEE Physics Final Revision Set 8

One mole of a diatomic ideal gas (y = 1.4) is taken through a cyclic process starting from point A. The process A→B is an adiabatic compression. B→C is isobaric expansion, C→D an adiabatic expansion and D→A is isochoric. The volume ratios are VA/VB = 16 and VC/VD = 2 and the temperature at A is TA = 300 K.

1. Calculate the temperature of the gas at the point B and D

2. Find the efficiency of the cycle.

3. The average translational kinetic energy of O2 (molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of N2 (molar mass 28) molecules in eV at the same temperature is:
(A) 0.0015 (B) 0.003
(C) 0.048 (D) 0.768

4. A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be:
(A) 225 (B) 450
(C) 900 (D) 1800

5. A proton, a deuteron and an α-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp, rd and rα denote respectively the radii of the trajectories of these particles, then:
(A) rα = rp is l.t. rd (B) rα > rd > rp
(C) rα = rd is l.t. rp (D) rp = rd = rα

Source 1997 JEE

### IIT JEE Physics Final Revision Set 7

1. The resolving power of an electron microscope is higher than that of an optical microscope because the wavelength of electron is ---- than the wavelength of visible light.

2. In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in a quantum state n is _______.

3. Five point charges, each of value +q, are placed on five vertices of a regular hexagon of side L. The magnitude of the force on a point charge of value -q placed at the centre of the hexagon is _______ netwtons.

4. A ray of light undergoes deviation of 30° when incident on an equilateral prism of refractive index √2. The angle made by the ray inside the prism with the base of the prism is ______ .

5. A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the track is

a. zero b. 45° c. 30° d. 60°

Source 1992 JEE

### IIT JEE Physics Final Revision Set 6

Two thin circular discs of mass 2 Kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. The axis of the rod is along the perpendicular to the planes of the disk through their centres. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of motion of the truck. Its friction with the floor of the truck is large enough so that the object can roll on the truck without slipping. Take x-axis as the direction of motion of the truck and z-axis as the vertically upwards direction. If the truck has an acceleration 9 m/s2, calculate:

1. the force of friction on each disk.
2. the magnitude and direction of the frictional torque acting on each disk about the centre of mass O of the object.
3. Express the torque in the vector form in terms of unit vectors i, j and k in x, y and z directions.

4. In the following column I lists some physical quantities and the column II gives approximate energy of them. Choose the appropriate value of energy from column II for each of the physical quantities in column I

Column I ------------- Column II
(i) Energy of thermal neutron---- (A) 0.025 eV
(ii) Energy of X-Ray ------------ (B) 0.5 eV
(iii) Binding energy per nucleon-- (C) 3 eV
(iv) Photoelectric threshold of a metal --- (D) 20 eV
------------------------------------------ (E) 10 keV
-------------------------------------------(F) 8 MeV

5. A band playing music at a frequency f is moving towards a wall at a speed Vb. A motorist is following the band with a speed Vm. If V is the speed of sound, obtain an expression for the beat frequency heard by the motorist.
Source JEE paper 1997

### IIT JEE Physics Final Revision Set 5

Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fasted photoelectrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV.

Find

1. the energy of the photons causing the photoelectric emission.
2. the quantum numbers of the two levels involved in the emission of these photons.
3. the change in the angular momentum of the electron in the hydrogen atom in the above transition.
4. the recoil speed of the emitting atom assuming it to be at rest before the transition. (Ionizatin potential of hydrogen is 13.6 eV.)

5.A plant observed by an astronomical refracting telescope having an objective of focal length 16 m and an eyepiece of focal length 2 cm.

a. The distance between the objective eye piece is 16.02 m.
b. The angular magnification of the planet is -800.
c. The image of the planet is inverted.
d. The objective is larger than the eyepiece.

Source; JEE 1992 paper

### IIT JEE Physics Final Revision Set 4

A cart is moving along x direction with a velocity of 4 m/s. A person on the cart throws a stone with a velocity of 6 m/s relative to himself. In the frame of reference of the cart the stone is thrown in y-z plane making an angle of 30° with vertical z axis. At the highest point of its trajectory the stone hits an object of equal mass hung vertically from branch of a tree by means of a string of length L.A completely inelastic collision occurs in which the stone gets embedded in the object.
Determine :
1. The speed of the combined mass immediately after the collision with respect to an observer on the ground.
2. The length L of the string such that the tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.

Two blocks of mass m1 = 10 Kg and m2 = 5 Kg connected to each other by a massless inextensible string of length 0.3 m are placed along a diameter of turn table. The coefficient of friction between the table and m1 is 0.5 while there is no friction between m2 and the table. The table is rotating with an angular velocity of 10 rad/s about a vertical axis passing through its centre O. The masses are placed along the diameter of the table on either side of the centre O such that the mass m1 is at a distant of 0.124 m from O. The masses are observed to be at rest with respect to an observer on the turn table.

3. Calculate the frictional force on m1.
4. What should be the minimum angular speed of the turn tale so that the masses will slip from this position.
5. How should the masses be placed with the string remaining taut so that there is no frictional force acting on the mass m1.

Source: 1997 JEE paper

## Saturday, September 5, 2009

### IIT-JEE-Physics-Revision Questions - Set 3

1. A laser beam λ = 666 nm has a power of 3 mW. Find the pressure exerted on a surface by this beam if the cross sectional area is 3 nm². Assume perfect reflection as normal incidence.

2. A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies between -0.85 eV and -0.544 eV (including both these values). Find the atomic number of the atom.

Take hc = 1240 eV-nm, ground state energy of hydrogen atom = -13.6 eV.

3. The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state is

(a) 2.82 ms-1
(b)4.178 ms-1
(c)8.356 ms-1
(d)6.817 ms-1

4. An electron makes transition inside a hydrogen atom. The orbital angular momentum of the electron may change by

(a) h/2π (b) h/π (c)h/4π (d)h/3π

Multiple options are possible

5. Nuclei of radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N0 nuclei of the element. Calculate the number N of nuclei of A at time t.

## Sunday, August 23, 2009

### IIT - JEE- Physics - Revision Questions - Set 2 - Past JEE Questions

1. A uniform rigid rod of mass M and length L is standing vertically along the y-axis on a smooth horizontal surface, with its lower end at the origin (0,0). A slight disturbance at t = 0 causes the lower end to slip on the smooth surface along the positive x-axis, and the rod starts falling.

What is the path followed by the centre of mass of the rod during its fall?

2. A hemispherical bowl of radius R = 0.1 m is rotating about its own axis (which is vertical), with an angular velocity ω. A particle of mass 10-2 kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl.

Obtain the relation between h and ω. What is minimum value of ω needed, in order to have a non-zero value of h?

3. A cylindrical solid of mass 10-2 and cross-sectional area 10-4 m2 is moving parallel to its axis (the x-axis) with a uniform speed of 103 m/s in the positive direction. At t = 0, its front face passes the dust particles of uniform density 10-3 kg/m3. When a dust particle collides with the face of the cylinder, it sticks to its surface. Assuming that the dimensions of the cylinder remain practically unchanged, and that the dimensions of the cylinder remain practically unchanged, and that the dust sticks only to the front face of the cylinder, find the x-coordinate of the front of the cylinder at t = 150 s.

4. A circular ring of radius R with uniform positive charge density λ per unit length is located in the y-z plane with its centre at the origin O. A particle of mass m and positive charge q is projected from the point P(R√3,0,0) on the positive x-axis directly towards O, with an initial speed v. Find the smallest (non-zero) value of the speed v such that the particle does not return to P.

5. Two radio stations broadcast their programmes at the same amplitude A, and at slightly different frequencies ω1 and ω2 respectively, where ω2 - ω1 = 10³ Hz. A detector receives the signals from the two stations simulataneously. It can only detect signals of intensity ≥2A². Find the time interval between successive maxima of the intensity of the signal received by the detector.

Source (1993 JEE paper)

## Saturday, August 22, 2009

### Past IIT JEE Questions - Collection 1 (For JEE 2010)

1. A ball of density d is dropped on to a horizontal solid surface. It bounces elastically from the surface and returns to its original position in time t1. Next, the ball is released and it falls through the same height before striking the surface of a liquid of density dL. What is the expression for the time t2 the ball takes to come back to the position from which it was released in terms of d, t1 and dL. d is less than dL.

2. A straight segment of a circuit with length L is carrying a current I (in the positive direction of x). It is placed between two infinitely long conductors in which current I is flowing in opposite directions are placed perpendicular to it. What is the expression for th force acting on the circuit segment?

3. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fasted photoelectrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV. Find the energy of the photons causing the photoelectric emission.

4. A charge of Q is uniformly distributed over a spherical volume of radius R. What is the expression for the energy of the system?

5. Light is incident at an angle α on one planar end of a trasparent cylindrical rod of refractive index n. Determine the least value of n so that the light enteriing the rod does not emerge from the curved surface of the rod irrespective of the value of α.

(Source: 1992 JEE paper)

## Saturday, May 16, 2009

### IIT JEE Level Revision Questions - 1. Introduction to physics

Past JEE Question

Which of the following choices does not represent the same dimensions of the mentioned physical quanties?

a. Heat, potential energy and work
b. Electric flux, electric field, and electric dipole moment
c. Pressure, stress, and Young's modulus
d. Potential difference, voltage, and electromotive force of a galvanic cell.

(JEE 2005 screening)

Revision question 1

Find dimensions of a) work done by a force b) linear momentum, c)kinetic energy

Past JEE question

In the expression P = (α²/β)e-αZ/kθ, P is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be

a. M¹L³T-2
b. M¹L²T-2
c. M¹L¹T-1
d. M°L²T-1

Value of k = Boltzmann constant = 1.38*10-23 J/K

(JEE 2004 screening)

### IIT JEE Level Revision Questions - 3. Rest and Motion: Kinematics

Past JEE question

A small block slides without friction down an inclinded plane starting from the rest. If Sn is the distance travelled form time t = n to t = n+1, then Sn/Sn+1 is

a. (2n-1)/2n
b. (2n+1)/(2n-3)
c. (2n+1)/(2n+3)
d. 2n/(2n+1)

(JEE 2004, Screening)

1982

1(ii)
A particle moving eastwards with a velocity 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is

a. zero
b. 1/SQRT(2) m/s² towards north-west
c. ½ m/s² toward north-west
d. ½ m/s² towards north

The average acceleration must have an westward component and northward component to make the velocity towards east as zero and to make velocity towards north as 5 m/s

Hence it will act in the direction of northwest.

Westward component of average acceleration = (0-5)/10 = -½ m/s²
Northward component of average of acceleration = (5-0)/10 = ½ m/s²

Hence magnitude of average acceleration = Sqrt( (-1/2) ²+(1/2) ²) = 1/SQRT(2)

1983

1(i)
A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in the direction.

a. due north
b. 30° east of north
c 30° west of north
d. 60° east of north

Since the man wants to reach the spot opposite to him, he has to swim to towards west of north to make use of water velocity in the direction west to east.

As he travels 10 metres/ per minute in that direction, he will have a moment of 5 metres/min in the west to east direction.

So angle is given by sin θ = 5/10 = ½
θ = 30°

4. State whether the statement is true or false
(i)
Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. (neglect air resistance)

Both the balls thrown vertically with the same speed will reach equal height irrespective of their masses. These would also pass through the point of projection in their downward motion with the same speed when subject to acceleration due to gravity.

1984

State whether the statement is true or false
3(a)
A projectile fired form the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.

At the top of the path, the vertical component of velocity is zero and the particle has only horizontal component. Hence the speed (the magnitude of the velocity) is minimum at the top of the path.

2004

A particle starts from rest. Its acceleration at the start is 10 m/s² and in 12 seconds the acceleration uniformly reduces to zero. The maximum speed of the particle will be

a. 20 m/s
b. 60 m/s
c. 550 m/s
d. 660 m/s

Revision question 1

A ball is dropped vertically from a height of d above the ground. It hits the ground and bounces up vertically to a height d/2. Neglecting the subsequent motion and air resistance, (a) what will be the shape of velocity versus distance diagram? (b)What will be the shape of velocity versus time diagram.

Options for A
Linear or curvilinear

Options for B
Linear or curvilinear

(Based on Past JEE questions JEE 2000, screening)

Revision Problem 2

An aeroplane has to go from a point A to another point B, 500 km away 30° east of north. A wind is blowing due north at a speed of 20 m/s. the air-speed of the plane is 150 m/s.

(a) Find the direction in which the pilot should head the plane to reach the point B.
(b) Find the time taken by the plane to go from A to B.

(Source: HC Verma, Prob. 49)

### IIT JEE Level Revision Questions - 6. Friction

Friction

1. fill blanks

A uniform cube of side ‘a’ and mass ‘m’ rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height of 3a/4 above the base. The minimum value of F for which the cube begins to tip about an edge is _______________ . (Assume that the cube does not slide)

2. A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is 0.6. If the acceleration of the truck is 5 m/s², the frictional force acting on the block is _________ .
(JEE 1984)

Reason: The horizontal force acting on the cube due to the acceleration of the truck is

F = ma = 1 kg * (5 m/s²) = 5 N

As the block is not moving, a frictional force of 5 N is acting on it.
We can verify that the static friction can go up to a maximum value of 1 kg *(10 m/s²)*0.6 = 6 N if we take g as approximately equal to 10 m/s².

Revision Question 1.

A 2 kg block is placed over a 4 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between blocks is 0.20. Find the acceleration of the two blocks if a horizontal force of 12 N is applied to (a) the upper block, 9b) the lower block. Take g = 10 m/s².

### IIT JEE Level Revision Questions - 7. Circular motion

Past JEE Questions

1. A thin circular ring of mass ‘M’ and radius ‘r’ is rotating about its axis with a constant angular velocity ω. Two objects, each of mass m, are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with an angular velocity

a. ω M/(M+m)
b. ω(M-2m)/(M+2m)
c. ω M/(M+2m)
d. ω (M+2m)/M

(1983)

2. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of the second satellite is larger than the first one by approximately.

a. 0.7%
b. 1%
c. 1.5%
d. 3.0%

(1995)

3. Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

a. 0.42 m from mass of 0.3 kg
b. 0.70 m from mass of 0.7 kg
c. 0.98 m from mass of 0.3 kg
d. 0.98 m from mass of 0.7 kg

(1995)

4. If the distance between the earth and the sun were half its present value, the number of days in a year would have been

a. 64.5
b. 129
c. 182.5
d. 730

Revision Questions

1. A circular road of radius r is banked for a speed of v = 40 km/hr. A car of mass m attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible.

a. The car cannot make a turn without skidding.
b. If the car turns at a speed less than 40 km/hr, it will slip down.
c. If the car turns at the correct speed of 40 km/hr, the force by the road on the car is equal to mv²/r.
d. If the car turns at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than mv²/r.

### IIT JEE Level Revision Questions - 8. Work and energy

Past JEE Questions

1. A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

a. t1/2
b. t3/4
c. t3/2
d. t2

(1984)

2. A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is:

a. MgL
b. MgL/3
c. MgL/9
d. MgL/18

(1985)

3. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:

a. its velocity is constant.
b. its acceleration is constant
c. its kinetic energy is constant
d. it moves in a circular path

(1987)

4. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with t as ac = k²rt² where k is a constant. The power delivered to the particle by the force acting on it is

a. 2 πmk²r²t
b. mk²r²t
c. (mk4r²t5)/3
d. zero

(1994)

5. Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

a. 0.42 m from mass of 0.3 kg
b. 0.7 m form mass of 0.7 kg
c. 0.98 m from mass of 0.3 kg
d. 0.98 m from mass of 0.7 kg

(1995)

6. A force F = -K(yi + xj) (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x axis to the point (a,0) and then parallel to the y axis to the point (a,a). The total work done by the force F on the particle is

a. -2Ka²
b. 2Ka²
c. -Ka²
d. Ka²

(1998)

7. An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. The maximum extension in the spring is

a. 4Mg/k
b. 2Mg/k
c. Mg/k
d. Mg/2k

(JEE 2002)

Solution

Change in gravitational energy = Energy stored in the spring

Mgx = ½ kx²

=> x = 2Mg/k

Revision Questions

1. A block of mass m moving at a speed v compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring. (Source HC Verma, prob. 44)

2. The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity of √(10gl) where l is the length of the pendulum. Find the tension in the string when
(a) the string is horizontal
(b) the bob is at its highest point and
(c) the string makes an angle of 60° with the upward vertical
(Source HC Verma Prob 53)

### IIT JEE Level Revision Questions - 9. Centre of mass, linear momentum, collision

Past JEE Questions

Centre of mass. Linear momentum collisions fill blanks

A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments, each of mass m, are found to move with a speed v, each in mutually perpendicular directions. The total energy released in the process of explosion is _________ .

1982
1(iv)
Two particles initially at rest move toward each other under a mutual force of attraction. At the instant when the speed of A is V and the speed of B is 2V, then the speed at the centre of the mass of the system is

a. zero
b. 1.5 V
c. V
d. 3 V

Velocity of centre of mass due to motion of particles due to internal forces is zero.

1986
1.(ii)
Multiple alternatives are correct. Find them

A ball hits the floor and rebounds after an inelastic collision. In this case:

a. The momentum of the ball just after the collision is the same as that just before the collision.
b. the mechanical energy of the ball remains the same in the collision.
c. the total momentum of the ball and the earth is conserved.
d. the total energy of the ball and the earth is conserved.

In an inelastic collision, momentum of the system is conserved. Also the total energy of the system is conserved. But total kinetic energy is not conserved.

1(iii)
A shell is fired from a cannon with a velocity V (m/s) at an angle θ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon and the speed (in m/s) of the other piece immediately after the explosion is:

At the highest point, the shell has only horizontal component of velocity. When the particle breaks into pieces, the momentum of the system is conserved. As one of the components retraces back its horizontal component at the time of explosion is V cos θ.
The systems momentum at the time of explosion is mV cos θ. The momentum of the piece that retraced the path is (m/2)V cos θ.

Therefore mV cos θ = -(m/2)V cos θ + (m/2)V’

(m/2)V’ = 3(m/2) V cos θ

V’ = 3 V cos θ.

1987
2(iii)
A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments, each of mass m, are found to move with a speed v, each in mutually perpendicular directions. The total energy released in the process of explosion is ---------------.

The momentum of the fragment with mass 2m has to be equal to the sum of momentums of the other two fragments.

As the magnitude of momentum of other two vectors is mv and the angle between them is 90°, the resultant vector will have the magnitude 2mv cos 45° .
2mv cos 45° = [2/SQRT(2)] mv

2mv’ = [2/SQRT(2)] mv
v’ = v [1/SQRT(2)]

So energy released in the explosion = sum kinetic energies of the three fragments

(½)mv² + (1/2)mv² +(1/2) 2m [(v(1/SQRT(2)] ²

mv²+mv²(1/2) = (3/2)mv²

1. A ball hits the floor and rebounds after an inelastic collision. In this case

a. the momentum of the ball just after the collision is the same as that just before the collision.
b. the mechanical energy of the ball remains the same in the collision.
c. the total momentum of the ball and the earth is conserved.
d. the total energy of the ball and the earth is conserved.

(More than one alternative may be correct)
JEE 1986

Answer ( c ) and (d)

Note: total kinetic energy is not conserved but total energy is conserved.

2. A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments, each of mass m, are found to move with a speed v, each in mutually perpendicular directions. The total energy released in the process of explosion is _________ .

(JEE 1987)

Solution;

As the two fragments went in mutual perpendicular directions with velocity v the resultant momentum

2mv cos 45° = 2mv(1/√2) = √2 mv

if the velocity of fragment with 2m mass is V

then 2 mV =/√2mv

V = v/√2

Hence energy released = ½ mv² + ½ mv² + ½ *2 m (v/√2) ²

= (3/2)mv²