NEET > Motion of System of Particles and Rigid Body

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


Q 1.    

Correct4

Incorrect-1

From a solid sphere of mass {tex} \mathrm { M } {/tex} and radius {tex} \mathrm { R } , {/tex} a cube of maximum possible volume is cut. Moment of inertia of cube
about an axis passing through its center and perpendicular to one of its faces is :

{tex} \frac { 4 \mathrm { MR } ^ { 2 } } { 9 \sqrt { 3 } \pi } {/tex}

B

{tex} \frac { 4 \mathrm { MR } ^ { 2 } } { 3 \sqrt { 3 } \pi } {/tex}

C

{tex} \frac { \mathrm { MR } ^ { 2 } } { 32 \sqrt { 2 } \pi } {/tex}

D

{tex} \frac { \mathrm { MR } ^ { 2 } } { 16 \sqrt { 2 } \pi } {/tex}

Explanation

Q 2.    

Correct4

Incorrect-1

A hollow sphere is held suspended. Sand is now poured into it in stages.
The centre of mass of the

A

rises continuously

B

remains unchanged in the process

C

first rises and then falls to the original position

first falls and then rises to the original position

Explanation

Q 3.    

Correct4

Incorrect-1

A body {tex} A {/tex} of mass {tex} M {/tex} while falling vertically downwards under gravity breaks into two parts; a body {tex} B {/tex} of mass {tex} \frac { 1 } { 3 } M {/tex}
and a body {tex} C {/tex} of mass {tex} \frac { 2 } { 3 } M {/tex} . The centre of mass of bodies {tex} B {/tex} and {tex} C {/tex} taken together shifts compared to that of body {tex} A {/tex} towards

does not shift

B

depends on height of breaking

C

body {tex} B {/tex}

D

body {tex} C {/tex}

Explanation

Q 4.    

Correct4

Incorrect-1

From a uniform wire, two circular loops are made (i) {tex} \mathrm { P } {/tex} of radius {tex} \mathrm { r } {/tex} and (ii) {tex} \mathrm { Q } {/tex} of radius nr. If the moment of inertia of {tex} \mathrm { Q } {/tex}
about an axis passing through its centre and perpendicular to its plane is 8 times that of {tex} \mathrm { P } {/tex} about a similar axis, the value of {tex} \mathrm { n } {/tex} is (diameter of the wire is very much smaller than {tex} \mathrm { r } {/tex} or {tex} \mathrm { nr } {/tex} )

A

8

B

6

C

4

2

Explanation





Q 5.    

Correct4

Incorrect-1

A billiard ball of mass {tex} m {/tex} and radius {tex} r , {/tex} when hit in a horizontal direction by a cue at a height {tex} h {/tex} above its centre, acquired a
linear velocity {tex} v _ { 0 } . {/tex} The angular velocity {tex} \omega _ { 0 } {/tex} acquired by the ball is

A

{tex} \frac { 5 v _ { 0 } r ^ { 2 } } { 2 h } {/tex}

B

{tex} \frac { 2 v _ { 0 } r ^ { 2 } } { 5 h } {/tex}

C

{tex} \frac { 2 v _ { 0 } h } { 5 r ^ { 2 } } {/tex}

{tex} \frac { 5 v _ { 0 } h } { 2 r ^ { 2 } } {/tex}

Explanation



Q 6.    

Correct4

Incorrect-1

Three bricks each of length Land mass {tex} \mathrm { M } {/tex} are arranged as shown frrom the wall. The distance of the centre of mass of the system from the wall is

A

{tex} \mathrm { L } / 4 {/tex}

B

{tex} \mathrm { L} / 2 {/tex}

C

{tex} ( 3 / 2 ) \mathrm { L } {/tex}

{tex} ( 11 / 12 ) \mathrm { L } {/tex}

Explanation



Q 7.    

Correct4

Incorrect-1

Four point masses, each of value {tex} m , {/tex} are placed at the corners of a square {tex} A B C D {/tex} of side {tex} \ell {/tex} . The moment of inertia of this system about an axis passing through {tex} A {/tex} and parallel to {tex} B D {/tex} is

A

2{tex} m l ^ { 2 } {/tex}

B

{tex} \sqrt { 3 } m \ell ^ { 2 } {/tex}

3{tex} m \ell ^ { 2 } {/tex}

D

{tex} m \ell ^ { 2 } {/tex}

Explanation



Q 8.    

Correct4

Incorrect-1

A loop of radiusr and mass m 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 zero. What will be the velocity of the centre of the hoop when it ceases to slip?

A

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

B

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

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

D

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

Explanation

Q 9.    

Correct4

Incorrect-1

Two masses {tex} m _ { 1 } {/tex} and {tex} m _ { 2 } {/tex} are connected by a massless spring of spring constant {tex} k {/tex} and unstretched length {tex} \ell . {/tex} The masses are placed on a frictionless straight channel, which are consider our {tex} x {/tex} -axis. They are initially at {tex} x = 0 {/tex} and {tex} x = \ell {/tex}
respectively. At {tex} t = 0 , {/tex} a velocity {tex} v _ { 0 } {/tex} is suddenly imparted to the first particle. At a later time {tex} t , {/tex} the centre of mass of the two masses is at:

A

{tex} x = \frac { m _ { 2 } \ell } { m _ { 1 } + m _ { 2 } } {/tex}

B

{tex} x = \frac { m _ { 1 } \ell } { m _ { 1 } + m _ { 2 } } + \frac { m _ { 2 } v _ { 0 } t } { m _ { 1 } + m _ { 2 } } {/tex}

C

{tex} x = \frac { m _ { 2 } \ell } { m _ { 1 } + m _ { 1 } } + \frac { m _ { 2 } v _ { 0 } t } { m _ { 1 } + m _ { 2 } } {/tex}

{tex} x = \frac { m _ { 2 } \ell } { m _ { 1 } + m _ { 2 } } + \frac { m _ { 1 } v _ { 0 } t } { m _ { 1 } + m _ { 2 } } {/tex}

Explanation



Q 10.    

Correct4

Incorrect-1

A body of mass 1.5{tex} \mathrm { kg } {/tex} rotating about an axis with angular velocity of 0.3{tex} \mathrm { rad } \mathrm { s } ^ { - 1 } {/tex} has the angular momentum of 1.8{tex} \mathrm { kg } {/tex} {tex} \mathrm { m } ^ { 2 } \mathrm { s } ^ { - 1 } . {/tex} The radius of gyration of the body about an axis is

2{tex} \mathrm { m } {/tex}

B

1.2{tex} \mathrm { m } {/tex}

C

0.2{tex} \mathrm { m } {/tex}

D

1.6{tex} \mathrm { m } {/tex}

Explanation

Q 11.    

Correct4

Incorrect-1

If {tex} \overrightarrow { \mathrm { F } } {/tex} is the force acting on a particle having position vector {tex} \overrightarrow { \mathrm { r } } {/tex} and {tex} \vec { \tau } {/tex} be the torque of this force about the origin, then:

A

{tex} \overrightarrow { \mathrm { r } } \cdot \vec { \tau } > 0 {/tex} and {tex} \overrightarrow { \mathrm { F } } \cdot \vec { \tau } < 0 {/tex}

{tex} \overrightarrow { \mathrm { r } } \cdot \vec { \tau } = 0 {/tex} and {tex} \overrightarrow { \mathrm { F } } \cdot \vec { \tau } = 0 {/tex}

C

{tex} \overrightarrow { \mathrm { r } } \cdot \vec { \tau } = 0 {/tex} and {tex} \overrightarrow { \mathrm { F } } \cdot \vec { \tau } \neq 0 {/tex}

D

{tex} \overrightarrow { \mathrm { r } } , \vec { \tau } \neq 0 {/tex} and {tex} \overrightarrow { \mathrm { F } } , \vec { \tau } = 0 {/tex}

Explanation

Q 12.    

Correct4

Incorrect-1

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

A

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

B

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

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

D

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

Explanation





Q 13.    

Correct4

Incorrect-1

A wheel is rolling straight on ground without slipping. If the axis of the wheel has speed {tex} v {/tex} , the instantenous velocity of a point {tex} \mathrm { P } {/tex} on the rim, defined by angle {tex} \theta , {/tex} relative to the ground will be

A

{tex} v \cos \left( \frac { 1 } { 2 } \theta \right) {/tex}

2{tex} v \cos \left( \frac { 1 } { 2 } \theta \right) {/tex}

C

{tex} v ( 1 + \sin \theta ) {/tex}

D

{tex} \mathrm { v } ( 1 + \cos \theta ) {/tex}

Explanation

Q 14.    

Correct4

Incorrect-1

A solid sphere having mass {tex} m {/tex} and radius r rolls down an inclined plane. Then its kinetic energy is

A

{tex} \frac { 5 } { 7 } {/tex} rotational and {tex} \frac { 2 } { 7 } {/tex} translational

{tex} \frac { 2 } { 7 } {/tex} rotational and {tex} \frac { 5 } { 7 } {/tex} translational

C

{tex} \frac { 2 } { 5 } {/tex} rotational and {tex} \frac { 3 } { 5 } {/tex} translational

D

{tex} \frac { 1 } { 2 } {/tex} rotational and {tex} \frac { 1 } { 2 } {/tex} translational

Explanation

Q 15.    

Correct4

Incorrect-1

A ring of mass {tex} \mathrm { M } {/tex} and radius {tex} \mathrm { R } {/tex} is rotating about its axis with angular velocity {tex} \omega {/tex} . Two identical bodies each of mass {tex} \mathrm { m } {/tex} are
now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be:

A

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

B

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

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

D

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

Explanation



Q 16.    

Correct4

Incorrect-1

A certain bicycle can go up a gentle incline with constant speed when the frictional force of ground pushing the rear wheel is
{tex} \mathrm { F } _ { 2 } = 4 \mathrm { N } . {/tex} With what force {tex} \mathrm { F } _ { 1 } {/tex} must the chain pull on the sprocket wheel if {tex} \mathrm { R } _ { 1 } = 5 \mathrm { cm } {/tex} and {tex} \mathrm { R } _ { 2 } = 30 \mathrm { cm } ? {/tex}

A

4{tex} \mathrm { N } {/tex}

24{tex} \mathrm { N } {/tex}

C

140{tex} \mathrm { N } {/tex}

D

{tex} \frac { 35 } { 4 } \mathrm { N } {/tex}

Explanation

Q 17.    

Correct4

Incorrect-1

A wooden cube is placed on a rough horizontal table, a force is applied to the cube. Gradually the force is increased.
Whether the cube slides before toppling or topples before sliding is independent of:

A

the position of point of application of the force

B

the length of the edge of the cube

mass of the cube

D

Coefficient of friction between the cube and the table

Explanation



Q 18.    

Correct4

Incorrect-1

From a circular ring of mass {tex} \mathrm { M } {/tex} and radius {tex} \mathrm { R } , {/tex} an arc corresponding to a {tex} 90 ^ { \circ } {/tex} sector is removed. The moment of inertia of the ramaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is {tex} \mathrm { k } {/tex} times {tex} \mathrm { MR } ^ { 2 } {/tex} . Then the value of {tex} \mathrm { k } {/tex} is

{tex} 3/ 4 {/tex}

B

{tex} 7/ 8 {/tex}

C

{tex} 1/ 4 {/tex}

D

1

Explanation



Q 19.    

Correct4

Incorrect-1

A mass m moves in a circle on a smooth horizontal plane with velocity {tex} \mathrm { v } _ { 0 } {/tex} at at a radius {tex} \mathrm { R } _ { 0 } {/tex} . The mass is attached to string which passes through a smooth hole in the plane as shown.

The tension in the string is increased gradually and finally m moves in a circle of radius {tex} \frac { \mathrm { R } _ { 0 } } { 2 } {/tex} . The final value of the kinetic energy is

A

{tex} \frac { 1 } { 4 } \mathrm { mv } _ { 0 } ^ { 2 } {/tex}

2{tex} \mathrm { mv } _ { 0 } ^ { 2 } {/tex}

C

{tex} \frac { 1 } { 2 } \mathrm { mv } _ { 0 } ^ { 2 } {/tex}

D

{tex} \mathrm { mv } _ { 0 } ^ { 2 } {/tex}

Explanation



Q 20.    

Correct4

Incorrect-1

A rod {tex} \mathrm { PQ } {/tex} of length L revolves in a horizontal plane about the axis {tex} \mathrm { YY } ^ { \prime } {/tex} . The angular velocity of the rod is {tex} \omega {/tex} . If {tex} \mathrm { A } {/tex} is the area of cross-section of the rod and {tex} \rho {/tex} be its density, its rotational kinetic energy is

A

{tex} \frac { 1 } { 3 } \mathrm { AL } ^ { 3 } \rho \omega ^ { 2 } {/tex}

B

{tex} \frac { 1 } { 2 } \mathrm { AL } ^ { 3 } \rho \omega ^ { 2 } {/tex}

{tex} \frac { 1 } { 24 } \mathrm { AL } ^ { 3 } \rho \omega ^ { 2 } {/tex}

D

{tex} \frac { 1 } { 18 } \mathrm { AL } ^ { 3 } \rho \omega ^ { 2 } {/tex}

Explanation





Q 21.    

Correct4

Incorrect-1

A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 10{tex} \mathrm { m } / \mathrm { s } {/tex} . It then rolls up a smooth inclined plane of inclination {tex} 30 ^ { \circ } {/tex} with the horizontal. The height attained by the sphere before it stops is

A

700{tex} \mathrm { cm } {/tex}

B

701{tex} \mathrm { cm } {/tex}

7.1{tex} \mathrm { m } {/tex}

D

70{tex} \mathrm { m } {/tex}

Explanation

Q 22.    

Correct4

Incorrect-1

A hollow smooth uniform sphere {tex} A {/tex} of mass {tex} \mathrm { m } {/tex} rolls without sliding on a smooth horizontal surface. It collides head on elastically with another stationary smooth solid sphere {tex} B {/tex} of
the same mass {tex} m {/tex} and same radius. The ratio of kinetic energy of {tex} B {/tex} to that of {tex} A {/tex} just after the collision is

A

{tex} 1 : 1 {/tex}

B

{tex} 2 : 3 {/tex}

{tex} 3 : 2 {/tex}

D

{tex} 4 : 3 {/tex}

Explanation

Q 23.    

Correct4

Incorrect-1

Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio of {tex} 1 : 3 . {/tex} The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio of

A

{tex} 1 : 3 {/tex}

{tex} 3 : 1 {/tex}

C

{tex} 1 : 9 {/tex}

D

{tex} 9 : 1 {/tex}

Explanation





Q 24.    

Correct4

Incorrect-1

A pulley fixed to the ceiling carries a string with blocks of mass {tex} \mathrm { m } {/tex} and 3{tex} \mathrm { m } {/tex} attached to its ends. The masses of string
and pulley are negligible. When the system is released, its centre of mass moves with what acceleration?

A

0

B

{tex} - g / 4 {/tex}

{tex} g / 2 {/tex}

D

{tex} - g / 2 {/tex}

Explanation





Q 25.    

Correct4

Incorrect-1

A ring of mass {tex} m {/tex} and radius {tex} R {/tex} has four particles each of mass {tex} m {/tex} attached to the ring as shown in figure. The centre of ring has a speed {tex} v _ { 0 } {/tex} . The kinetic energy of the system is

A

{tex} m v _ { 0 } ^ { 2 } {/tex}

B

3{tex} m v _ { 0 } ^ { 2 } {/tex}

5{tex} m v _ { 0 } ^ { 2 } {/tex}

D

6{tex} m v _ { 0 } ^ { 2 } {/tex}

Explanation