##### Document Text Contents

Page 1

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 47 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [1]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. A T shaped object with dimensions shown in the figure, is lying on a smooth floor.

A force F is applied at a point P Parallel to AB, such that the object has only the

translational motion without rotation. Find the distance of P from to C.

(A)

2

2

l (B)

3

2

l

(C)

4

3

l (D) l

2. A circular disc of radius R is removed form a bigger circular disc of radius 2R, such that the circumference of the discs coincide.

The distance of centre of mass of the new disc is αR from the centre of the bigger disc. The value of is :

(A) 1/3 (B) 1/2 (C) 1/6 (D) 1/4

3. When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many rotations will it make

before coming to rest ? Assume constant resistive torque

(A) 24 (B) 36 (C) 18 (D) 12

4. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same

radius about a tangential axis in the plane of the ring is :

(A) 3 5 (B) 12 3 (C) 1 3 (D) 5 6

5. Four balls each of radius 10 cm and mass 1 kg, 2kg, 3kg and 4 kg are attached to the periphery

of massless plate of radius 1m. What is moment of inertia of the system about the centre of

plate ?

(A) 212 04. kg m (B) 210 04. kg m

(C) 211 50. kg m (D) 25 04. kg m

6. A solid sphere is rotating in free space. If the radius of sphere is increased keeping mass same which one of the following will not

be affected ?

(A) Angular velocity (B) Angular momentum(C) Moment of inertia (D) Rotational kinetic energy

7. A force of 200 N acts tangentially on the rim of a wheel 25cm in radius. Find the torque.

(A) 50 Nm (B) 150 Nm (C) 75 Nm (D) 39 Nm

8. A disc of moment of inertia 25kg m is acted upon by a constant torque of 40 Nm. Starting from rest the time taken by it to

acquire an angular velocity of 24 –1rads is :

(A) 3 s (B) 4 s (C) 2.5 s (D) 120 s

Page 2

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 48 HWT/Physics

9. A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 110ms . It then rolls up a smooth inclined plane of inclination

30 with the horizontal. The height attained by sphere before it stops is:

(A) 700 cm (B) 701 cm (C) 7.1 m (D) None of these

10. The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle is:

(A) g sin (B) 2 3/ g sin (C) 1 2/ g sin (D) 1 3/ g sin

Page 7

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 50 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [6]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. Two point objects of mass 1.5g and 2.5g respectively are at a distance of 16cm apart, the centre of gravity is at a distance x from

the object of mass 1.5g, where x is :

(A) 10 cm (B) 6 cm (C) 13 cm (D) 3 cm

2. A body A of mass M while falling vertically downwards under gravity breaks into two parts ; a body B of mass 1/3M and a body

C of mass 2/3M. The centre of mass of bodies B and C taken together shift compared to that of body A towards

(A) depends on height of breaking (B) does not shift

(C) body C (D) body B

3. A pulley of radius 2 m is rotating about its axis by a force F = (20t – 5t2) N (where t is measured in second) applied tangentially.

If the moment of inertia of the pulley about its axis of rotation is 210kgm , the number of rotations made by the pulley before its

direction of motion is reserved, is:

(A) more than 3 but less than 6 (B) more then 6 but less than 9

(C) more than 9 (D) less than 3

4. A thin wire of mass M and length L is bent to form a circular ring. The moment of inertia of this ring about its axis is:

(A) 2

2

1

4

ML

(B) 2

1

12

ML (C) 2

2

1

3

ML

(D) 2

2

1

ML

5. A boy and a man carry a uniform rod of length L, horizontally in such a way that boy gets 1/4th load. If the boy is at one end of the

rod, the distance of the man from the other end is:

(A)

3

L

(B)

4

L

(C)

2

3

L

(D)

3

4

L

6. A uniform rod AB of length l and mass m is free to rotate about point A. a horizontal

axis perpendicular to the rod passing through the end. The rod is rest in the

horizontal position. The initial angular acceleration of the rod will be:

(A)

2

3

g

l

(B)

2

l

mg

(C)

3

2

gl (D)

3

2

g

l

7. A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 1 kg – m2 and its

rate of rotation 2 rvs/s. The angular momentum is:

(A) 1.257 kg m2s–1 (B) 12.57 kg m2s–1 (C) 13.57 kg m2s–1 (D) 20 kg m2s–1

8. A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular

speed is ω . Its centre of mass rises to a maximum of

(A)

2 21

3

l

g

(B)

1

6

l

g

(C)

2 21

2

l

g

(D)

2 21

6

l

g

Page 8

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 51 HWT/Physics

9. A thin metal disc of radius of 0.25m and mass 2kg starts from rest and rolls down on an inclined plane. If its rotational kinetic

energy is 4 J at the foot of inclined plane, the linear velocity at the same point, is in 1ms .

(A) 2 (B) 2 2 (C) 2 3 (D) 3 2

10. An annular ring with inner and outer radii R1 and R2 is rotating with a uniform angular speed. The ratio of the forces experienced

by the two particles situated on the inner and outer parts of the ring, F1 / F2 is:

(A) 2

1

R

R

(B)

2

1

2

R

R

(C) 1 (D) 1

2

R

R

Page 13

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 56 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [9]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. Two particles of equal mass m go around a circle of

radius R under the action of their mutual gravitational

attraction. The speed of each particle with respect to

their centre of mass is:

(A)

Gm

R

(B)

4

Gm

R

(C)

3

GM

R

(D)

2

Gm

R

2. Two balls, each of radius R, equal mass and density are

placed in contact, then the force of gravitation between

them is proportional to:

(A)

2

1

F

R

(B) F R

(C) 4F R (D)

1

F

R

3. Imagine a new planet having the same density as that of

earth but it is 3 times bigger than the earth in size. If the

acceleration due to gravity on the surface of the earth in

size is g and that on the surface of the new planet is g ,

then:

(A) 2g g (B) 3g g

(C) 4g g (D) 5g g

4. If the earth stops rotating, the value of g at the equator

(A) increases (B) decreases

(C) no effect (D) None of these

5. The change in the value of g at a height h above the

surface of the earth is the same as at a depth d below the

surface of earth. When both d and h are much smaller

than the radius of earth, then which one of the following

is correct?

(A)

2

h

d (B)

3

2

h

d

(C) 2d h (D) d h

6. A thin uniform annular disc (see figure) of mass M has

outer radius 4R & inner radius 3R. The work required to

take a unit mass from point P on its axis to infinity is:

(A) 2 4 2 5

7

GM

R

(B) 2 4 2 5

7

GM

R

(C)

4

GM

R

(D) 2 2 1

5

GM

R

7. A planet in a distant solar system is 10 times more

massive than the earth and its radius is 10 times smaller.

Given that the escape velocity from the earth is

111kms , the escape velocity from the surface of the

planet would be:

(A) 11 1. kms (B) 111kms

(C) 1110 kms (D) 10 11. kms

8. The escape velocity of a projectile on the earth’s surface

is 11.2 1kms . A body is projected out with thrice this

speed. The speed of the body far away from the earth

will be:

(A) 122 4. kms (B) 131 7. kms

(C) 133 6. kms (D) None of these

9. A geostationary satellite is orbiting the earth at a height

of 6R above the surface of the earth; R being the radius

of the earth. What will be the time period of another

satellite at a height 2.5R from the surface of the earth?

(A) 6 2 h (B) 6 gR

(C) 6 3 h (D) 12h

10. A satellite is revolving around the earth with a kinetic

energy E. The minimum addition of kinetic energy

needed to make it escape from its orbit is:

(A) 2E (B) E (C) 2E / (D) E

Page 14

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 57 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [10]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of

mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital

velocity is:

(A)

GM

L

(B)

3

2

GM

L

(C)

3GM

L

(D)

2

3

GM

L

(E)

3

GM

L

2. A body is taken to a height of nR from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at

the altitude is:

(A) (n + 1)2 (B) (n + 1)–2 (C) (n + 1)–1 (D) (n + 1)

3. The height at which the acceleration due to gravity becomes g / 9 (where g = the acceleration due to gravity on the surface of the

earth) in terms of R, the radius of the earth, is:

(A) 2R (B)

3

R

(C)

2

R

(D) 2R

4. The acceleration due to gravity becomes

2

g

(g = acceleration due to gravity on the surface of the earth) at a height equal to:

(A) 4R (B) R / 4 (C) 2R (D) R / 2

5. Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the

gravitational field is zero is:

(A)

4Gm

r

(B)

6Gm

r

(C)

9Gm

r

(D) zero

6. The escape velocity from the earth is 11 kms–1. The escape velocity from a planet having twice the radius and same mean density

as that of earth is:

(A) 15 5. kms (B) 111 kms (C) 122kms (D) None of these

7. Energy required to move of a body of mass m from an orbit of radius 2 R to 3R if it is orbiting around a planet of mass M is:

(A) GMm/12R2 (B) GMm/3R2 (C) GMm/8R (D) GMm/6R

8. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R.

The ratio of their respective periods is:

(A) 4 : 1 (B) 1 : 8 (C) 8 : 1 (D) 1 : 4 (E) 1 : 2

9. A planet revolves around the sun in an elliptical orbit. The linear

speed of the planet will be maximum at

(A) D (B) B

(C) A (D) C

10. Two satellites A and B go round a planet in circular orbits having radii 4R and R, respectively. If the speed of satellite A is 3v,

then speed of satellite B is:

(A)

3

2

v

(B)

4

2

v

(C) 6v (D) 12v

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 47 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [1]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. A T shaped object with dimensions shown in the figure, is lying on a smooth floor.

A force F is applied at a point P Parallel to AB, such that the object has only the

translational motion without rotation. Find the distance of P from to C.

(A)

2

2

l (B)

3

2

l

(C)

4

3

l (D) l

2. A circular disc of radius R is removed form a bigger circular disc of radius 2R, such that the circumference of the discs coincide.

The distance of centre of mass of the new disc is αR from the centre of the bigger disc. The value of is :

(A) 1/3 (B) 1/2 (C) 1/6 (D) 1/4

3. When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many rotations will it make

before coming to rest ? Assume constant resistive torque

(A) 24 (B) 36 (C) 18 (D) 12

4. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same

radius about a tangential axis in the plane of the ring is :

(A) 3 5 (B) 12 3 (C) 1 3 (D) 5 6

5. Four balls each of radius 10 cm and mass 1 kg, 2kg, 3kg and 4 kg are attached to the periphery

of massless plate of radius 1m. What is moment of inertia of the system about the centre of

plate ?

(A) 212 04. kg m (B) 210 04. kg m

(C) 211 50. kg m (D) 25 04. kg m

6. A solid sphere is rotating in free space. If the radius of sphere is increased keeping mass same which one of the following will not

be affected ?

(A) Angular velocity (B) Angular momentum(C) Moment of inertia (D) Rotational kinetic energy

7. A force of 200 N acts tangentially on the rim of a wheel 25cm in radius. Find the torque.

(A) 50 Nm (B) 150 Nm (C) 75 Nm (D) 39 Nm

8. A disc of moment of inertia 25kg m is acted upon by a constant torque of 40 Nm. Starting from rest the time taken by it to

acquire an angular velocity of 24 –1rads is :

(A) 3 s (B) 4 s (C) 2.5 s (D) 120 s

Page 2

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 48 HWT/Physics

9. A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 110ms . It then rolls up a smooth inclined plane of inclination

30 with the horizontal. The height attained by sphere before it stops is:

(A) 700 cm (B) 701 cm (C) 7.1 m (D) None of these

10. The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle is:

(A) g sin (B) 2 3/ g sin (C) 1 2/ g sin (D) 1 3/ g sin

Page 7

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 50 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [6]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. Two point objects of mass 1.5g and 2.5g respectively are at a distance of 16cm apart, the centre of gravity is at a distance x from

the object of mass 1.5g, where x is :

(A) 10 cm (B) 6 cm (C) 13 cm (D) 3 cm

2. A body A of mass M while falling vertically downwards under gravity breaks into two parts ; a body B of mass 1/3M and a body

C of mass 2/3M. The centre of mass of bodies B and C taken together shift compared to that of body A towards

(A) depends on height of breaking (B) does not shift

(C) body C (D) body B

3. A pulley of radius 2 m is rotating about its axis by a force F = (20t – 5t2) N (where t is measured in second) applied tangentially.

If the moment of inertia of the pulley about its axis of rotation is 210kgm , the number of rotations made by the pulley before its

direction of motion is reserved, is:

(A) more than 3 but less than 6 (B) more then 6 but less than 9

(C) more than 9 (D) less than 3

4. A thin wire of mass M and length L is bent to form a circular ring. The moment of inertia of this ring about its axis is:

(A) 2

2

1

4

ML

(B) 2

1

12

ML (C) 2

2

1

3

ML

(D) 2

2

1

ML

5. A boy and a man carry a uniform rod of length L, horizontally in such a way that boy gets 1/4th load. If the boy is at one end of the

rod, the distance of the man from the other end is:

(A)

3

L

(B)

4

L

(C)

2

3

L

(D)

3

4

L

6. A uniform rod AB of length l and mass m is free to rotate about point A. a horizontal

axis perpendicular to the rod passing through the end. The rod is rest in the

horizontal position. The initial angular acceleration of the rod will be:

(A)

2

3

g

l

(B)

2

l

mg

(C)

3

2

gl (D)

3

2

g

l

7. A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 1 kg – m2 and its

rate of rotation 2 rvs/s. The angular momentum is:

(A) 1.257 kg m2s–1 (B) 12.57 kg m2s–1 (C) 13.57 kg m2s–1 (D) 20 kg m2s–1

8. A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular

speed is ω . Its centre of mass rises to a maximum of

(A)

2 21

3

l

g

(B)

1

6

l

g

(C)

2 21

2

l

g

(D)

2 21

6

l

g

Page 8

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 51 HWT/Physics

9. A thin metal disc of radius of 0.25m and mass 2kg starts from rest and rolls down on an inclined plane. If its rotational kinetic

energy is 4 J at the foot of inclined plane, the linear velocity at the same point, is in 1ms .

(A) 2 (B) 2 2 (C) 2 3 (D) 3 2

10. An annular ring with inner and outer radii R1 and R2 is rotating with a uniform angular speed. The ratio of the forces experienced

by the two particles situated on the inner and outer parts of the ring, F1 / F2 is:

(A) 2

1

R

R

(B)

2

1

2

R

R

(C) 1 (D) 1

2

R

R

Page 13

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 56 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [9]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. Two particles of equal mass m go around a circle of

radius R under the action of their mutual gravitational

attraction. The speed of each particle with respect to

their centre of mass is:

(A)

Gm

R

(B)

4

Gm

R

(C)

3

GM

R

(D)

2

Gm

R

2. Two balls, each of radius R, equal mass and density are

placed in contact, then the force of gravitation between

them is proportional to:

(A)

2

1

F

R

(B) F R

(C) 4F R (D)

1

F

R

3. Imagine a new planet having the same density as that of

earth but it is 3 times bigger than the earth in size. If the

acceleration due to gravity on the surface of the earth in

size is g and that on the surface of the new planet is g ,

then:

(A) 2g g (B) 3g g

(C) 4g g (D) 5g g

4. If the earth stops rotating, the value of g at the equator

(A) increases (B) decreases

(C) no effect (D) None of these

5. The change in the value of g at a height h above the

surface of the earth is the same as at a depth d below the

surface of earth. When both d and h are much smaller

than the radius of earth, then which one of the following

is correct?

(A)

2

h

d (B)

3

2

h

d

(C) 2d h (D) d h

6. A thin uniform annular disc (see figure) of mass M has

outer radius 4R & inner radius 3R. The work required to

take a unit mass from point P on its axis to infinity is:

(A) 2 4 2 5

7

GM

R

(B) 2 4 2 5

7

GM

R

(C)

4

GM

R

(D) 2 2 1

5

GM

R

7. A planet in a distant solar system is 10 times more

massive than the earth and its radius is 10 times smaller.

Given that the escape velocity from the earth is

111kms , the escape velocity from the surface of the

planet would be:

(A) 11 1. kms (B) 111kms

(C) 1110 kms (D) 10 11. kms

8. The escape velocity of a projectile on the earth’s surface

is 11.2 1kms . A body is projected out with thrice this

speed. The speed of the body far away from the earth

will be:

(A) 122 4. kms (B) 131 7. kms

(C) 133 6. kms (D) None of these

9. A geostationary satellite is orbiting the earth at a height

of 6R above the surface of the earth; R being the radius

of the earth. What will be the time period of another

satellite at a height 2.5R from the surface of the earth?

(A) 6 2 h (B) 6 gR

(C) 6 3 h (D) 12h

10. A satellite is revolving around the earth with a kinetic

energy E. The minimum addition of kinetic energy

needed to make it escape from its orbit is:

(A) 2E (B) E (C) 2E / (D) E

Page 14

Vidyamandir Classes

VMC/System of Particles & Rotational Motion 57 HWT/Physics

DATE : IITJEE : MARKS :

10 TIME : 25 MINUTES

NAME : TEST CODE : RTM [10]

ROLL NO. START TIME : END TIME : TIME TAKEN:

STUDENT’S SIGNATURE : PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions.

Each question carries 1 mark. There is NO NEGATIVE marking.

Choose the correct alternative. Only one choice is correct.

1. Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of

mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital

velocity is:

(A)

GM

L

(B)

3

2

GM

L

(C)

3GM

L

(D)

2

3

GM

L

(E)

3

GM

L

2. A body is taken to a height of nR from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at

the altitude is:

(A) (n + 1)2 (B) (n + 1)–2 (C) (n + 1)–1 (D) (n + 1)

3. The height at which the acceleration due to gravity becomes g / 9 (where g = the acceleration due to gravity on the surface of the

earth) in terms of R, the radius of the earth, is:

(A) 2R (B)

3

R

(C)

2

R

(D) 2R

4. The acceleration due to gravity becomes

2

g

(g = acceleration due to gravity on the surface of the earth) at a height equal to:

(A) 4R (B) R / 4 (C) 2R (D) R / 2

5. Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the

gravitational field is zero is:

(A)

4Gm

r

(B)

6Gm

r

(C)

9Gm

r

(D) zero

6. The escape velocity from the earth is 11 kms–1. The escape velocity from a planet having twice the radius and same mean density

as that of earth is:

(A) 15 5. kms (B) 111 kms (C) 122kms (D) None of these

7. Energy required to move of a body of mass m from an orbit of radius 2 R to 3R if it is orbiting around a planet of mass M is:

(A) GMm/12R2 (B) GMm/3R2 (C) GMm/8R (D) GMm/6R

8. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 4R.

The ratio of their respective periods is:

(A) 4 : 1 (B) 1 : 8 (C) 8 : 1 (D) 1 : 4 (E) 1 : 2

9. A planet revolves around the sun in an elliptical orbit. The linear

speed of the planet will be maximum at

(A) D (B) B

(C) A (D) C

10. Two satellites A and B go round a planet in circular orbits having radii 4R and R, respectively. If the speed of satellite A is 3v,

then speed of satellite B is:

(A)

3

2

v

(B)

4

2

v

(C) 6v (D) 12v