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
Sunday, October 11, 2009
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
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.
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)
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)
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)
Answer: b
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)
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)
Answer: b
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)
answer: c
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
Answer (b)
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
Answer: ( c )
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)
Answer: true
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.
Answer: true
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)
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)
answer: c
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
Answer (b)
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
Answer: ( c )
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)
Answer: true
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.
Answer: true
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)
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