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