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Page 1
More than One Correct Options
Q 1. A mass m of radius r is rolling horizontally without any slip with a linear speed v. It then rolls up
to a height given by
2
3v
4g
(a) the body is identified to be a disc or a solid cylinder
(b) the body is a solid sphere
(c) moment of inertia of the body about instantaneous axis of rotation is
2
3
mr
2
(d) moment of inertia of the body about instantaneous axis of rotation is
2
7
mr
5
Q 2. Four identical rods each of mass m and length lare joined to form a rigid square frame. The frame
lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its
moment of inertia about
(a) the x-axis is
2
2
ml
3
(b) the z-axis is
2
4
ml
3
(c) an axis parallel to the z-axis and passing through a corner is
2
10
ml
3
(d) one side is
2
5
ml
3
Q 3. A uniform circular ring rolls without slipping on a horizontal surface. At any instant, its position is
as shown in the figure. Then
(a) section ABC has greater kinetic energy than section ADC
(b) section BC has greater kinetic energy than section CD
(c) section BC has the same kinetic energy as section DA
(d) the sections CD and DA have the same kinetic energy
Q 4. A cylinder of radius R is to roll without slipping between two planks as shown in the figure. Then
(a) angular velocity of the cylinder is
v
R
counter clockwise
(b) angular velocity of the cylinder is
2v
R
clockwise
(c) velocity of centre of mass of the cylinder is v towards left
Page 2
More than One Correct Options
Q 1. A mass m of radius r is rolling horizontally without any slip with a linear speed v. It then rolls up
to a height given by
2
3v
4g
(a) the body is identified to be a disc or a solid cylinder
(b) the body is a solid sphere
(c) moment of inertia of the body about instantaneous axis of rotation is
2
3
mr
2
(d) moment of inertia of the body about instantaneous axis of rotation is
2
7
mr
5
Q 2. Four identical rods each of mass m and length lare joined to form a rigid square frame. The frame
lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its
moment of inertia about
(a) the x-axis is
2
2
ml
3
(b) the z-axis is
2
4
ml
3
(c) an axis parallel to the z-axis and passing through a corner is
2
10
ml
3
(d) one side is
2
5
ml
3
Q 3. A uniform circular ring rolls without slipping on a horizontal surface. At any instant, its position is
as shown in the figure. Then
(a) section ABC has greater kinetic energy than section ADC
(b) section BC has greater kinetic energy than section CD
(c) section BC has the same kinetic energy as section DA
(d) the sections CD and DA have the same kinetic energy
Q 4. A cylinder of radius R is to roll without slipping between two planks as shown in the figure. Then
(a) angular velocity of the cylinder is
v
R
counter clockwise
(b) angular velocity of the cylinder is
2v
R
clockwise
(c) velocity of centre of mass of the cylinder is v towards left
(d) velocity of centre of mass of the cylinder is 2v towards right
Q 5. A uniform rod of mass m = 2 kg and length l = 0.5 m is sliding along two mutually perpendicular
smooth walls with the two ends P and Q having velocities v P = 4 m/s and vQ = 3 m/s as shown.
Then
(a) The angular velocity of rod, ? = 10rad/s, counter clockwise
(b) The angular velocity of rod, ? = 5.0rad/s, counter clockwise
(c) The velocity of centre of mass of rod, vcm = 2.5 m/s
(d) The total kinetic energy of rod,
25
K
3
? joule
Q 6. A wheel is rolling without slipping on a horizontal plane with velocity v an acceleration a of
centre of mass as shown in figure. Acceleration at
(a) A is vertically upwards (b) B may be vertically downwards
(c) C cannot be horizontal (d) a point on the rim may be horizontal leftwards
Q 7. A uniform rod of length l and mass 2 m rests on a smooth horizontal table. A point mass m
moving horizontally at right angles to the rod with velocity v collides with one end of the rod and
sticks it. Then
(a) angular velocity of the system after collision is
v
l
(b) angular velocity of the system after collision is
v
2l
(c) the loss in kinetic energy of the system as a whole as a result of the collision is
2
mv
6
(d) the loss in kinetic energy of the system as a whole as a result of the collision is
2
7mv
24
Q 8. A nonuniform ball of radius R and radius of gyration about geometric centre =R/2, is kept on a
frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck
horizontally with a sharp impulse = J. The point of application of the impulse is at a height h
above the surface. Then
Page 3
More than One Correct Options
Q 1. A mass m of radius r is rolling horizontally without any slip with a linear speed v. It then rolls up
to a height given by
2
3v
4g
(a) the body is identified to be a disc or a solid cylinder
(b) the body is a solid sphere
(c) moment of inertia of the body about instantaneous axis of rotation is
2
3
mr
2
(d) moment of inertia of the body about instantaneous axis of rotation is
2
7
mr
5
Q 2. Four identical rods each of mass m and length lare joined to form a rigid square frame. The frame
lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its
moment of inertia about
(a) the x-axis is
2
2
ml
3
(b) the z-axis is
2
4
ml
3
(c) an axis parallel to the z-axis and passing through a corner is
2
10
ml
3
(d) one side is
2
5
ml
3
Q 3. A uniform circular ring rolls without slipping on a horizontal surface. At any instant, its position is
as shown in the figure. Then
(a) section ABC has greater kinetic energy than section ADC
(b) section BC has greater kinetic energy than section CD
(c) section BC has the same kinetic energy as section DA
(d) the sections CD and DA have the same kinetic energy
Q 4. A cylinder of radius R is to roll without slipping between two planks as shown in the figure. Then
(a) angular velocity of the cylinder is
v
R
counter clockwise
(b) angular velocity of the cylinder is
2v
R
clockwise
(c) velocity of centre of mass of the cylinder is v towards left
(d) velocity of centre of mass of the cylinder is 2v towards right
Q 5. A uniform rod of mass m = 2 kg and length l = 0.5 m is sliding along two mutually perpendicular
smooth walls with the two ends P and Q having velocities v P = 4 m/s and vQ = 3 m/s as shown.
Then
(a) The angular velocity of rod, ? = 10rad/s, counter clockwise
(b) The angular velocity of rod, ? = 5.0rad/s, counter clockwise
(c) The velocity of centre of mass of rod, vcm = 2.5 m/s
(d) The total kinetic energy of rod,
25
K
3
? joule
Q 6. A wheel is rolling without slipping on a horizontal plane with velocity v an acceleration a of
centre of mass as shown in figure. Acceleration at
(a) A is vertically upwards (b) B may be vertically downwards
(c) C cannot be horizontal (d) a point on the rim may be horizontal leftwards
Q 7. A uniform rod of length l and mass 2 m rests on a smooth horizontal table. A point mass m
moving horizontally at right angles to the rod with velocity v collides with one end of the rod and
sticks it. Then
(a) angular velocity of the system after collision is
v
l
(b) angular velocity of the system after collision is
v
2l
(c) the loss in kinetic energy of the system as a whole as a result of the collision is
2
mv
6
(d) the loss in kinetic energy of the system as a whole as a result of the collision is
2
7mv
24
Q 8. A nonuniform ball of radius R and radius of gyration about geometric centre =R/2, is kept on a
frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck
horizontally with a sharp impulse = J. The point of application of the impulse is at a height h
above the surface. Then
(a) the ball with slip on surface for all cases (b) the ball will roll purely if h = 5R/4
(c) the ball will roll purely if h = 3R/2 (d) there will be no rotation if h = R
Q 9. A hollow spherical ball is given an initial push up an incline of inclination angle ?.
The ball rolls
purely. Coefficient of static friction between ball and incline = ?. During its upwards journey
(a) friction acts up along the incline (b) (2 tan ?)/5
(c) friction acts down along the incline (d) (2 tan ?)/7
Q 10. A uniform disc of mass m and radius R rotates about a fixed vertical axis passing through its
centre with angular velocity ?. A particle of same mass m and having velocity of 2 ?R towards
centre of the disc collides with the disc moving horizontally and sticks to its rim.
(a) The angular velocity of the disc will become ?/3
(b) The angular velocity of the disc will become 5 ?/3
(c) The impulse on the particle due to disc is
37
mR
3
?
(d) The impulse on the particle due to disc is 2m ?R
Q 11. The end B of the rod AB which makes angle ? with the floor is being pulled with a constant
velocity v0 as shown. The length of the rod is l.
(a) At ? = 37 ?
velocity of end A is
0
4
v
3
downwards
(b) At ? = 37 ? angular velocity of rod is
0
5v
3l
(c) Angular velocity of rod is constant
(d) Velocity of end A is constant
Answers
1. (a,c) 2. (all) 3. (a,b,d) 4. (a,b) 5. (a,c,d) 6. (all) 7. (a,c) 8. (b,d) 9. (a,b) 10. (a,c) 11. (a,b)
Solutions
1.
Page 4
More than One Correct Options
Q 1. A mass m of radius r is rolling horizontally without any slip with a linear speed v. It then rolls up
to a height given by
2
3v
4g
(a) the body is identified to be a disc or a solid cylinder
(b) the body is a solid sphere
(c) moment of inertia of the body about instantaneous axis of rotation is
2
3
mr
2
(d) moment of inertia of the body about instantaneous axis of rotation is
2
7
mr
5
Q 2. Four identical rods each of mass m and length lare joined to form a rigid square frame. The frame
lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its
moment of inertia about
(a) the x-axis is
2
2
ml
3
(b) the z-axis is
2
4
ml
3
(c) an axis parallel to the z-axis and passing through a corner is
2
10
ml
3
(d) one side is
2
5
ml
3
Q 3. A uniform circular ring rolls without slipping on a horizontal surface. At any instant, its position is
as shown in the figure. Then
(a) section ABC has greater kinetic energy than section ADC
(b) section BC has greater kinetic energy than section CD
(c) section BC has the same kinetic energy as section DA
(d) the sections CD and DA have the same kinetic energy
Q 4. A cylinder of radius R is to roll without slipping between two planks as shown in the figure. Then
(a) angular velocity of the cylinder is
v
R
counter clockwise
(b) angular velocity of the cylinder is
2v
R
clockwise
(c) velocity of centre of mass of the cylinder is v towards left
(d) velocity of centre of mass of the cylinder is 2v towards right
Q 5. A uniform rod of mass m = 2 kg and length l = 0.5 m is sliding along two mutually perpendicular
smooth walls with the two ends P and Q having velocities v P = 4 m/s and vQ = 3 m/s as shown.
Then
(a) The angular velocity of rod, ? = 10rad/s, counter clockwise
(b) The angular velocity of rod, ? = 5.0rad/s, counter clockwise
(c) The velocity of centre of mass of rod, vcm = 2.5 m/s
(d) The total kinetic energy of rod,
25
K
3
? joule
Q 6. A wheel is rolling without slipping on a horizontal plane with velocity v an acceleration a of
centre of mass as shown in figure. Acceleration at
(a) A is vertically upwards (b) B may be vertically downwards
(c) C cannot be horizontal (d) a point on the rim may be horizontal leftwards
Q 7. A uniform rod of length l and mass 2 m rests on a smooth horizontal table. A point mass m
moving horizontally at right angles to the rod with velocity v collides with one end of the rod and
sticks it. Then
(a) angular velocity of the system after collision is
v
l
(b) angular velocity of the system after collision is
v
2l
(c) the loss in kinetic energy of the system as a whole as a result of the collision is
2
mv
6
(d) the loss in kinetic energy of the system as a whole as a result of the collision is
2
7mv
24
Q 8. A nonuniform ball of radius R and radius of gyration about geometric centre =R/2, is kept on a
frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck
horizontally with a sharp impulse = J. The point of application of the impulse is at a height h
above the surface. Then
(a) the ball with slip on surface for all cases (b) the ball will roll purely if h = 5R/4
(c) the ball will roll purely if h = 3R/2 (d) there will be no rotation if h = R
Q 9. A hollow spherical ball is given an initial push up an incline of inclination angle ?.
The ball rolls
purely. Coefficient of static friction between ball and incline = ?. During its upwards journey
(a) friction acts up along the incline (b) (2 tan ?)/5
(c) friction acts down along the incline (d) (2 tan ?)/7
Q 10. A uniform disc of mass m and radius R rotates about a fixed vertical axis passing through its
centre with angular velocity ?. A particle of same mass m and having velocity of 2 ?R towards
centre of the disc collides with the disc moving horizontally and sticks to its rim.
(a) The angular velocity of the disc will become ?/3
(b) The angular velocity of the disc will become 5 ?/3
(c) The impulse on the particle due to disc is
37
mR
3
?
(d) The impulse on the particle due to disc is 2m ?R
Q 11. The end B of the rod AB which makes angle ? with the floor is being pulled with a constant
velocity v0 as shown. The length of the rod is l.
(a) At ? = 37 ?
velocity of end A is
0
4
v
3
downwards
(b) At ? = 37 ? angular velocity of rod is
0
5v
3l
(c) Angular velocity of rod is constant
(d) Velocity of end A is constant
Answers
1. (a,c) 2. (all) 3. (a,b,d) 4. (a,b) 5. (a,c,d) 6. (all) 7. (a,c) 8. (b,d) 9. (a,b) 10. (a,c) 11. (a,b)
Solutions
1.
Disc or cylinder I0 = I CM + mR
2
2.
3.
Resultant velocity of particles in region ABC is greater than that in CDA.
So,(KE)ABC>(KE)CDA
Similarly, vBC > v CD ? K BC >K CD
and vCD = vDA ? K CD =KDA
Page 5
More than One Correct Options
Q 1. A mass m of radius r is rolling horizontally without any slip with a linear speed v. It then rolls up
to a height given by
2
3v
4g
(a) the body is identified to be a disc or a solid cylinder
(b) the body is a solid sphere
(c) moment of inertia of the body about instantaneous axis of rotation is
2
3
mr
2
(d) moment of inertia of the body about instantaneous axis of rotation is
2
7
mr
5
Q 2. Four identical rods each of mass m and length lare joined to form a rigid square frame. The frame
lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its
moment of inertia about
(a) the x-axis is
2
2
ml
3
(b) the z-axis is
2
4
ml
3
(c) an axis parallel to the z-axis and passing through a corner is
2
10
ml
3
(d) one side is
2
5
ml
3
Q 3. A uniform circular ring rolls without slipping on a horizontal surface. At any instant, its position is
as shown in the figure. Then
(a) section ABC has greater kinetic energy than section ADC
(b) section BC has greater kinetic energy than section CD
(c) section BC has the same kinetic energy as section DA
(d) the sections CD and DA have the same kinetic energy
Q 4. A cylinder of radius R is to roll without slipping between two planks as shown in the figure. Then
(a) angular velocity of the cylinder is
v
R
counter clockwise
(b) angular velocity of the cylinder is
2v
R
clockwise
(c) velocity of centre of mass of the cylinder is v towards left
(d) velocity of centre of mass of the cylinder is 2v towards right
Q 5. A uniform rod of mass m = 2 kg and length l = 0.5 m is sliding along two mutually perpendicular
smooth walls with the two ends P and Q having velocities v P = 4 m/s and vQ = 3 m/s as shown.
Then
(a) The angular velocity of rod, ? = 10rad/s, counter clockwise
(b) The angular velocity of rod, ? = 5.0rad/s, counter clockwise
(c) The velocity of centre of mass of rod, vcm = 2.5 m/s
(d) The total kinetic energy of rod,
25
K
3
? joule
Q 6. A wheel is rolling without slipping on a horizontal plane with velocity v an acceleration a of
centre of mass as shown in figure. Acceleration at
(a) A is vertically upwards (b) B may be vertically downwards
(c) C cannot be horizontal (d) a point on the rim may be horizontal leftwards
Q 7. A uniform rod of length l and mass 2 m rests on a smooth horizontal table. A point mass m
moving horizontally at right angles to the rod with velocity v collides with one end of the rod and
sticks it. Then
(a) angular velocity of the system after collision is
v
l
(b) angular velocity of the system after collision is
v
2l
(c) the loss in kinetic energy of the system as a whole as a result of the collision is
2
mv
6
(d) the loss in kinetic energy of the system as a whole as a result of the collision is
2
7mv
24
Q 8. A nonuniform ball of radius R and radius of gyration about geometric centre =R/2, is kept on a
frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck
horizontally with a sharp impulse = J. The point of application of the impulse is at a height h
above the surface. Then
(a) the ball with slip on surface for all cases (b) the ball will roll purely if h = 5R/4
(c) the ball will roll purely if h = 3R/2 (d) there will be no rotation if h = R
Q 9. A hollow spherical ball is given an initial push up an incline of inclination angle ?.
The ball rolls
purely. Coefficient of static friction between ball and incline = ?. During its upwards journey
(a) friction acts up along the incline (b) (2 tan ?)/5
(c) friction acts down along the incline (d) (2 tan ?)/7
Q 10. A uniform disc of mass m and radius R rotates about a fixed vertical axis passing through its
centre with angular velocity ?. A particle of same mass m and having velocity of 2 ?R towards
centre of the disc collides with the disc moving horizontally and sticks to its rim.
(a) The angular velocity of the disc will become ?/3
(b) The angular velocity of the disc will become 5 ?/3
(c) The impulse on the particle due to disc is
37
mR
3
?
(d) The impulse on the particle due to disc is 2m ?R
Q 11. The end B of the rod AB which makes angle ? with the floor is being pulled with a constant
velocity v0 as shown. The length of the rod is l.
(a) At ? = 37 ?
velocity of end A is
0
4
v
3
downwards
(b) At ? = 37 ? angular velocity of rod is
0
5v
3l
(c) Angular velocity of rod is constant
(d) Velocity of end A is constant
Answers
1. (a,c) 2. (all) 3. (a,b,d) 4. (a,b) 5. (a,c,d) 6. (all) 7. (a,c) 8. (b,d) 9. (a,b) 10. (a,c) 11. (a,b)
Solutions
1.
Disc or cylinder I0 = I CM + mR
2
2.
3.
Resultant velocity of particles in region ABC is greater than that in CDA.
So,(KE)ABC>(KE)CDA
Similarly, vBC > v CD ? K BC >K CD
and vCD = vDA ? K CD =KDA
4.
u - R ? = v
u + R ? = 3v
? u=2v and R ? = v
5.
6.
Net acceleration at A is vertical, at B it may be vertical, at C it cannot be horizontal and at E it
may be horizontal leftward.
7.
Read More
FAQs on DC Pandey Solutions (JEE Advance): Mechanics of Rotational Motion- 2 - DC Pandey Solutions for JEE Physics
| 1. What are the conditions for rotational equilibrium? |  |
Ans. In order to have rotational equilibrium, two conditions must be satisfied:
- The net torque acting on the system must be zero.
- The net force acting on the system must be zero.
| 2. How can we calculate the moment of inertia of a rigid body? | |
Ans. The moment of inertia of a rigid body can be calculated using the formula:
I = ∫r²dm
where I is the moment of inertia, r is the perpendicular distance of an infinitesimally small mass element from the axis of rotation, and dm is the mass element.
| 3. What is the difference between angular velocity and angular acceleration? | |
Ans. Angular velocity is a vector quantity that describes the rate of change of angular displacement with respect to time. It is measured in radians per second (rad/s).
Angular acceleration, on the other hand, is the rate of change of angular velocity with respect to time. It is also a vector quantity and is measured in radians per second squared (rad/s²).
| 4. Can you explain the concept of torque? | |
Ans. Torque is the rotational equivalent of force. It is the measure of the tendency of a force to rotate an object about an axis. Mathematically, torque is calculated as the product of force and the perpendicular distance from the axis of rotation to the line of action of the force. It is given by the formula:
τ = r × F
where τ is the torque, r is the lever arm or the perpendicular distance, and F is the force.
| 5. What is the relationship between linear velocity and angular velocity? | |
Ans. The relationship between linear velocity (v) and angular velocity (ω) can be given by the formula:
v = ω × r
where v is the linear velocity, ω is the angular velocity, and r is the distance from the axis of rotation to the point of interest. This formula shows that linear velocity is directly proportional to the angular velocity and the distance from the axis of rotation.
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The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
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The content of DC Pandey Solutions (JEE Advance): Mechanics of Rotational Motion- 2 is prepared as per the latest JEE syllabus.
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