JEE Main > Motion of System of Particles and Rigid Body

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 popular teachers.


Q 1.    

Correct4

Incorrect-1

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

Explanation

Q 2.    

Correct4

Incorrect-1

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



Q 3.    

Correct4

Incorrect-1

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

Q 4.    

Correct4

Incorrect-1

Moment of inertia of a circular wire of mass {tex} M {/tex} and radius {tex} R {/tex} about its diameter is

{tex} M R ^ { 2 } / 2 {/tex}

B

{tex} M R ^ { 2 } {/tex}

C

{tex} 2 M R ^ { 2 } {/tex}

D

{tex} M R ^ { 2 } / 4 {/tex}

Explanation



Q 5.    

Correct4

Incorrect-1

A particle of Mass {tex}m{/tex} moves along line PC 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 l {/tex}

C

{tex} m v r {/tex}

Zero

Explanation

Q 6.    

Correct4

Incorrect-1

A circular disc {tex} X {/tex} of radius {tex} R {/tex} is made from an iron plate of thickness {tex} t , {/tex} and another disc {tex} Y {/tex} of radius {tex} 4 R {/tex} is made from an iron plate of thickness t/4. Then the relation between the moment of inertia {tex} I _ { X } {/tex} and {tex} I _ { Y } {/tex} is

A

{tex} I _ { Y } = 32 I _ { X } {/tex}

B

{tex} I _ { Y } = 16 I _ { X } {/tex}

C

{tex} I _ { Y } = I _ { X } {/tex}

{tex} I _ { Y } = 64 I _ { X } {/tex}

Explanation



Q 7.    

Correct4

Incorrect-1

A particle performing uniform circular motion has angular momentum {tex} L . {/tex} If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

{tex} L / 4 {/tex}

B

{tex} 2 L {/tex}

C

{tex} 4 L {/tex}

D

{tex} L / 2 {/tex}

Explanation




Q 8.    

Correct4

Incorrect-1

Let {tex} \vec { F } {/tex} be the force acting on a particle having position vector {tex} \vec { r } {/tex} and {tex} \vec { T } {/tex} be the torque of this force about the origin. Then

A

{tex} \vec { r } \cdot \vec { T } = 0 {/tex} and {tex} \vec { F } \cdot \vec { T } \neq 0 {/tex}

B

{tex} \vec { r } \cdot \vec { T } \neq 0 {/tex} and {tex} \vec { F } \cdot \vec { T } = 0 {/tex}

C

{tex} \vec { r } \cdot \vec { T } \neq 0 {/tex} and {tex} \vec { F } \cdot \vec { T } \neq 0 {/tex}

{tex} \vec { r } \cdot \vec { T } = 0 {/tex} and {tex} \vec { F } \cdot \vec { T } = 0 {/tex}

Explanation


Q 9.    

Correct4

Incorrect-1

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

moment of inertia

angular momentum

C

angular velocity

D

rotational kinetic energy.

Explanation


Q 10.    

Correct4

Incorrect-1

One solid sphere {tex} A {/tex} and another hollow sphere {tex} B {/tex} are of same mass and same outer radii. Their moment of inertia about their diameters are respectively {tex} I _ { A } {/tex} and {tex} I _ { B } {/tex} such that

A

{tex} I _ { A } = I _ { B } {/tex}

B

{tex} I _ { A } > I _ { B } {/tex}

{tex} I _ { A } < I _ { B } {/tex}

D

{tex} I _ { A } / I _ { B } = d _ { A } / d _ { B } {/tex} (where {tex}d _ { A }{/tex} and {tex}d _ { B }{/tex} are their densities. )

Explanation


Q 11.    

Correct4

Incorrect-1

The moment of inertia of a uniform semicircular disc of mass {tex} M {/tex} and radius {tex} r {/tex} about a line perpendicular to the plane of the disc through the center is

A

{tex} M r ^ { 2 } {/tex}

{tex} \frac { 1 } { 2 } M r ^ { 2 } {/tex}

C

{tex} \frac { 1 } { 4 } M r ^ { 2 } {/tex}

D

{tex} \frac { 2 } { 5 } M r ^ { 2 } {/tex}

Explanation


Q 12.    

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 body {tex} C {/tex} of mass {tex} \frac { 2 } { 3 } M {/tex}. The center of mass of bodies {tex} B {/tex} and {tex} C {/tex} taken together shifts compared to that of body {tex} A {/tex} towards

A

body {tex} C {/tex}

B

body {tex} B {/tex}

C

depends on height of breaking

does not shift

Explanation


Q 13.    

Correct4

Incorrect-1

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


Q 14.    

Correct4

Incorrect-1

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?

A

{tex} d {/tex}

B

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

C

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

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

Explanation


Q 15.    

Correct4

Incorrect-1

A force of {tex} - F \hat { k } {/tex} acts on {tex} O , {/tex} the origin of the coordinate system. The torque about the point {tex} ( 1 , - 1 ) {/tex} is

A

{tex} - F ( \hat { i } - \hat { j } ) {/tex}

B

{tex} F ( \hat { i } - \hat { j } ) {/tex}

C

{tex} - F ( \hat { i } + \hat { j } ) {/tex}

{tex} F ( \hat { i } + \hat { j } ) {/tex}

Explanation


Q 16.    

Correct4

Incorrect-1

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


Q 17.    

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} l {/tex}. The moment of inertia of this system about an axis through {tex} A {/tex} and parallel to {tex} B D {/tex} is

A

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

B

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

C

{tex} \sqrt { 3 } \mathrm { m } l ^ { 2 } {/tex}

{tex} 3 m l ^ { 2 } {/tex}

Explanation


Q 18.    

Correct4

Incorrect-1

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 {tex} \theta {/tex} with the horizontal. Then its acceleration is

A

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

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

C

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

D

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

Explanation


Q 19.    

Correct4

Incorrect-1

Angular momentum of the particle rotating with a central force is constant due to

A

constant torque

B

constant force

C

constant linear momentum

zero torque

Explanation


Q 20.    

Correct4

Incorrect-1

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

A

{tex} I _ { A C } = \sqrt { 2 } I _ { E F } {/tex}

B

{tex} \sqrt { 2 } I _ { A C } = I _ { E F } {/tex}

C

{tex} I _ { A D } = 3 I _ { E F } {/tex}

{tex} I _ { A C } = I _ { E F } {/tex}

Explanation


Q 21.    

Correct4

Incorrect-1

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

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

B

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

C

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

D

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

Explanation


Q 22.    

Correct4

Incorrect-1

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 ( x / L ) ^ { n } {/tex} where {tex} n {/tex} can be zero or any positive number. If the position {tex} x _ {CM} {/tex} of the centre of mass of the rod is plotted against {tex} n , {/tex} which of the following graphs best approximates the dependence of {tex} x _ { \mathrm { CM } } {/tex} on {tex} n ? {/tex}

A

C

D

Explanation



Q 23.    

Correct4

Incorrect-1

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 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


Q 24.    

Correct4

Incorrect-1

The minimum velocity (in {tex} \mathrm { ms } ^ { - 1 } {/tex} ) with which a car driver must traverse a flat curve of radius {tex} 150 \mathrm { m } {/tex} and coefficient of friction
0.6 to avoid skidding is

A

60

30

C

15

D

25

Explanation

Q 25.    

Correct4

Incorrect-1

A cylinder of height {tex} 20 \mathrm { m } {/tex} is completely filled with water. The velocity of efflux of water {tex} \left( \mathrm { in }\, \mathrm { ms } ^ { - 1 } \right) {/tex} through a small hole on
the side wall of the cylinder near its bottom is

A

10

20

C

25.5

D

5

Explanation