# JEE Main

Explore popular questions from Motion of System of Particles and Rigid Body for JEE Main. This collection covers Motion of System of Particles and Rigid Body previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Motion of System of Particles and Rigid Body

Correct Marks 4

Incorrectly Marks -1

Q 1. The initial angular velocity Of a circular disc Of mass M is. Then two small spheres Of mass {tex}m{/tex} are attached gently to diametrically opposite points on the edge Of the disc. What is the final angular velocity Of the disc?

A

{tex} \left( \frac { M + m } { M } \right) \omega _ { 1 } {/tex}

B

{tex} \left( \frac { M + m } { m } \right) \omega _ { 1 } {/tex}

{tex} \left( \frac { M } { M + 4 m } \right) \omega _ { 1 } {/tex}

D

{tex} \left( \frac { M } { M + 2 m } \right) \omega _ { 1 } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 2. A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

A

Solid sphere

B

Hollow sphere

C

Ring

All same

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 3. A particle of mass {tex} m {/tex} moves along line {tex} P C {/tex} with velocity {tex} v {/tex} as shown. What is the angular momentum of the particle about {tex} P ? {/tex}

A

{tex} m v L {/tex}

B

{tex} m v \ell {/tex}

C

{tex} m v r {/tex}

Zero

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 4. A particle performing uniform circular motion has angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

{tex} \frac { L } { 4 } {/tex}

B

{tex}2 L {/tex}

C

{tex} 4L {/tex}

D

{tex} \frac { L } { 2 } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 5. A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

A

Angular velocity

Angular momentum

C

Moment of inertia

D

Rotational kinetic energy

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 6. An annular ring with inner and outer radii {tex} R _ { 1 } {/tex} and {tex} R _ { 2 } {/tex} is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by two particles situated on the inner and outer parts of the ring is

{tex} \frac { R _ { 1 } } { R _ { 2 } } {/tex}

B

1

C

{tex} \left( \frac { R _ { 1 } } { R _ { 2 } } \right) ^ { 2 } {/tex}

D

{tex} \frac { R _ { 2 } } { R _ { 1 } } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 7. Consider a two particle system with particles having masses {tex} m _ { 1 } {/tex} and {tex} m _ { 2 } . {/tex} If the first particle is pushed towards the centre of mass through a distance {tex} d , {/tex} by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

{tex} \frac { m _ { 1 } } { m _ { 2 } }d {/tex}

B

{tex} d {/tex}

C

{tex} \frac { m _ { 2 } } { m _ { 1 } } d {/tex}

D

{tex} \frac { m _ { 1 } } { m _ { 1 } + m _ { 2 } } d {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 8. A thin circular ring of mass {tex} m {/tex} and radius {tex} R {/tex} is rotating about its axis with a constant angular velocity {tex} \omega {/tex} . Two objects each of mass {tex} M {/tex} are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity of

A

{tex} \frac { \omega m } { m + M } {/tex}

{tex} \frac { \omega m } { m + 2 M } {/tex}

C

{tex} \frac { \omega ( m + 2 M ) } { m } {/tex}

D

{tex} \frac { \omega ( m - 2 M ) } { m + 2 M } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 9. A circular disc of radius {tex} R {/tex} is removed from a bigger circular disc of radius 2{tex} R {/tex} such that the circumferences of the discs coincide. The centre of mass of the new disc is {tex} \frac{a }{R} {/tex} from the centre of the bigger disc. The value of {tex} a {/tex} is

A

{tex} \frac { 1 } { 2 } {/tex}

B

{tex} \frac { 1 } { 6 } {/tex}

C

{tex} \frac { 1 } { 4 } {/tex}

{tex} \frac { 1 } { 3 } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 10. A round uniform body of radius {tex} R , {/tex} mass {tex} m {/tex} and moment of inertia {tex} I {/tex} rolls down (without slipping) an inclined plane making an angle with the horizontal. Then its acceleration is

A

{tex} \frac { g \sin \theta } { 1 + \frac { m R ^ { 2 } } { I } } {/tex}

B

{tex} \frac { g \sin \theta } { 1 - \frac { I } { m R ^ { 2 } } } {/tex}

C

{tex} \frac { g \sin \theta } { 1 - \frac { m R ^ { 2 } } { I } } {/tex}

{tex} \frac { g \sin \theta } { 1 + \frac { I } { m R } } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 11. The angular momentum of a particle rotating with a central force is constant due to

A

constant linear momentum.

zero torque.

C

constant torque.

D

constant force.

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 12. For the given uniform square lamina {tex} A B C D , {/tex} whose centre is {tex} O {/tex} ,

A

{tex} I _ { \mathrm { AD } } = 3 I _ { \mathrm { EF } } {/tex}

{tex} I _ { \mathrm { AC } } = I _ { \mathrm { EF } } {/tex}

C

{tex} I _ { \mathrm { AC } } = \sqrt { 2 } I _ { \mathrm { EF } } {/tex}

D

{tex} \sqrt { 2 } I _ { \mathrm { AC } } = I _ { \mathrm { EF } } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 13. A thin rod of length {tex} L {/tex} is lying along the {tex} x {/tex} -axis with its ends at {tex} x = 0 {/tex} and {tex} x = L {/tex} . Its linear density (mass) length varies with {tex} x {/tex} as {tex} k \left( \frac { x } { L } \right) m , {/tex} where {tex} n {/tex} can be zero or any positive number. If the position {tex} x _ { \mathrm { CM } } {/tex} of the centre of mass of the rod is plotted against {tex} n , {/tex} which of the following graphs best approximates the depen- dence of {tex} x _ { \mathrm { CM } } {/tex} on {tex} n ? {/tex}

B

C

D

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 14. Consider a uniform square plate of side {tex} a {/tex} and mass {tex} m . {/tex} The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

A

{tex} \frac { 5 } { 6 } m a ^ { 2 } {/tex}

B

{tex} \frac { 1 } { 12 } m a ^ { 2 } {/tex}

C

{tex} \frac { 7 } { 12 } m a ^ { 2 } {/tex}

{tex} \frac { 2 } { 3 } m a ^ { 2 } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 15. A thin uniform rod of length {tex}\ell{/tex} and mass is swinging freely about a horizontal axis passing through its end.text Its maximum angular speed is {tex}\omega{/tex} Its centre of mass rises to a maximum height of

A

{tex} \frac { 1 } { 3 } \frac { \ell ^ { 2 } \omega ^ { 2 } } { g } {/tex}

B

{tex} \frac { 1 } { 6 } \frac { \ell \omega } { g } {/tex}

C

{tex} \frac { 1 } { 2 } \frac { \ell ^ { 2 } \omega ^ { 2 } } { g } {/tex}

{tex} \frac { 1 } { 6 } \frac { \ell ^ { 2 } \omega ^ { 2 } } { g } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 16. A point {tex} P {/tex} moves in counter-clockwise direction on a circular path as shown in Fig. The movement of {tex} P {/tex} is such that it sweeps out a length {tex} s = t ^ { 3 } + 5 , {/tex} where {tex} s {/tex} is in metres and {tex} t {/tex} is in seconds. The radius of the path is {tex} 20 \mathrm { m } . {/tex} The acceleration of {tex} P {/tex} when {tex} t = 2 {/tex} is nearly

A

{tex}13 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex}

B

{tex}12\, \mathrm { m } / \mathrm { s } ^ { 2 } {/tex}

C

{tex}7.2 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex}

{tex}14 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 17. For a particle in uniform circular motion, the acceler- ation {tex} \vec { a } {/tex} at a point {tex} P ( R , \theta ) {/tex} on the circle of radius {tex} R {/tex} is (here {tex} \theta {/tex} is measured from the {tex} x {/tex} -axis {tex} ) {/tex}

A

{tex} - \frac { v ^ { 2 } } { R } \cos \theta \hat { i } + \frac { v ^ { 2 } } { R } \sin \theta \hat { j } {/tex}

B

{tex} - \frac { v ^ { 2 } } { R } \sin \theta \hat { i } + \frac { v ^ { 2 } } { R } \cos \theta \hat { j } {/tex}

{tex} - \frac { v ^ { 2 } } { R } \cos \theta \hat { i } - \frac { v ^ { 2 } } { R } \sin \theta \hat { j } {/tex}

D

{tex} \frac { v ^ { 2 } } { R } \hat { i } + \frac { v ^ { 2 } } { R } \hat { j } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 18. A small particle of mass {tex} m {/tex} is projected at an angle {tex} \theta {/tex} with the {tex} x {/tex} -axis with an initial velocity {tex} v _ { 0 } {/tex} in the {tex} x - y {/tex} plane as shown in Fig. At a time {tex} t < \left( v _ { 0 } \sin \theta / g \right) {/tex} the angular momentum of the particle is

A

{tex} - m g v _ { 0 } t ^ { 2 } \cos \theta \hat { j } {/tex}

B

{tex} m g v _ { 0 } t \cos \theta \hat { k } {/tex}

{tex} - \frac { 1 } { 2 } m g v _ { 0 } t ^ { 2 } \cos \theta \hat { k } {/tex}

D

{tex} \frac { 1 } { 2 } m g v _ { 0 } t ^ { 2 } \cos \theta \hat { i } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 19. A hoop of radius {tex} R {/tex} and mass {tex} m {/tex} rotating with an angular velocity {tex} \omega _ { 0 } {/tex} is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is is zero. What will be the velocity if the centre of the loop is ceases to slip?

A

{tex} \frac { r \omega _ { 0 } } { 3 } {/tex}

{tex} \frac { r \omega _ { 0 } } { 2 } {/tex}

C

{tex} r \omega _ { 0 } {/tex}

D

{tex} \frac { r \omega _ { 0 } } { 4 } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 20. A bob of mass {tex} m {/tex} attached to an inextensible string of length {tex} \ell {/tex} is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed {tex} \omega {/tex} rad/s about the vertical. About the point of suspension

A

Angular momentum is conserved.

B

Angular momentum changes in magnitude but not in direction.

Angular momentum changes in direction but not in magnitude.

D

Angular momentum changes both in direction and magnitude.

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 21. A thin circular ring of mass {tex} m {/tex} and radius {tex} R {/tex} is rotating about its axis with a constant angular velocity {tex} \omega {/tex}. Two objects each of mass {tex} M {/tex} are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity {tex} \omega ^ { \prime } = {/tex}

{tex} \frac { \omega m } { ( m + 2 M ) } {/tex}

B

{tex} \frac { \omega ( m + 2 M ) } { m } {/tex}

C

{tex} \frac { \omega ( m - 2 M ) } { ( m + 2 M ) } {/tex}

D

{tex} \frac { \omega m } { ( m + M ) } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 22. A {tex}T{/tex} shaped object with dimensions shown in the figure, is lying on a smooth floor. A force {tex}\overrightarrow{F}{/tex} is applied at the point {tex}P{/tex} parallel to {tex}AB{/tex}, such that the object has only the translational motion without rotation. Find the location of {tex}P{/tex} with respect to {tex}C{/tex}.

{tex} \frac { 4 } { 3 } l {/tex}

B

{tex} l {/tex}

C

{tex} \frac { 3 } { 4 } l {/tex}

D

{tex} \frac { 3 } { 2 } l {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 23. Initial angular velocity of a circular disc of mass {tex} M {/tex} is {tex} \omega _ { 1 } . {/tex} Then two small spheres of mass {tex} m {/tex} are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

A

{tex} \left( \frac { M + m } { M } \right) \omega _ { 1 } {/tex}

B

{tex} \left( \frac { M + m } { m } \right) \omega _ { 1 } {/tex}

{tex} \left( \frac { M } { M + 4 m } \right) \omega _ { 1 } {/tex}

D

{tex} \left( \frac { M } { M + 2 m } \right) \omega _ { 1 } {/tex}

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 24. A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

A

solid sphere

B

hollow sphere

C

ring

all same

##### Explanation

Correct Marks 4

Incorrectly Marks -1

Q 25. Two identical particles move towards each other with velocity {tex} 2 v {/tex} and {tex} v {/tex} respectively. The velocity of centre of mass is

A

{tex} { v } {/tex}

B

{tex} v / 3 {/tex}

{tex} v / 2 {/tex}

D

zero