# JEE Main

Explore popular questions from Laws of Motion for JEE Main. This collection covers Laws of Motion previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Laws of Motion

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Q 1. With what acceleration {tex}a{/tex} should the box of Fig. descend so that the block of mass {tex} M {/tex} exerts a force {tex} M g / 4 {/tex} on the floor of the box? A

{tex} g / 4 {/tex}

B

{tex} g / 2 {/tex}

{tex}3 g / 4 {/tex}

D

{tex}4 g {/tex}

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Q 2. A body of mass {tex}2 \mathrm{kg} {/tex} moves vertically downwards with an acceleration {tex} a = 19.6 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} The force acting on the body simultaneously with the force of gravity is {tex} \left( g = 9.8 \mathrm { m } / \mathrm { s } ^ { 2 } , \text { neglect air resistance) } \right. {/tex}

{tex}19.6 \mathrm { N } {/tex}

B

{tex}19.2 \mathrm { N } {/tex}

C

{tex}59.2 \mathrm { N } {/tex}

D

{tex}58.8 \mathrm { N } {/tex}

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Q 3. Two blocks, each having a mass M, rest on frictionless surface as shown in the Fig. If the pulleys are light and frictionless, and M on the incline is allowed to move down, then the tension in the string will be A

{tex} \frac { 2 } { 3 } M g \sin \theta {/tex}

B

{tex} \frac { 3 } { 2 } M g \sin \theta {/tex}

{tex} \frac { M g \sin \theta } { 2 } {/tex}

D

{tex}2 M g \sin \theta {/tex}

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Q 4. A string of length {tex} L {/tex} and mass {tex} M {/tex} are lying on a horizontal table. A force {tex} F {/tex} is applied at one of its ends. Tension in the string at a distance {tex} x {/tex} from the ends at which force is applied is

A

Zero

B

{tex} F {/tex}

{tex} F ( L - x ) / L {/tex}

D

{tex} F ( L - x ) / M {/tex}

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Q 5. A body of mass {tex} m {/tex} is kept stationary on a rough inclined plane of inclination {tex} \theta {/tex} . The magnitude of force acting on the body by the inclined plane is

{tex} m g {/tex}

B

{tex} m g \sin \theta {/tex}

C

{tex} m g \cos \theta {/tex}

D

{tex} m g \sqrt { 1 + \cos ^ { 2 } \theta } {/tex}

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Q 6. In the arrangement shown in Fig, there is a friction force between the blocks of masses m and 2 m.Block of mass 2m is kept on a smooth horizontal plane. The mass of the suspended block is m. If block A is stationary with respect to block of mass 2m. The minimum value of co-efficient of friction between m and 2m is A

{tex}1 / 2 {/tex}

B

{tex}1 / \sqrt { 2 } {/tex}

{tex}1 / 4 {/tex}

D

{tex}1 / 3 {/tex}

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Q 7. A metre scale is moving with uniform velocity. This implies

A

the force acting on the scale is zero, but a torque about the centre of mass can act on the scale.

the force acting on the scale is zero and the torque acting about centre of mass of the scale is also zero.

C

the total force acting on it need not be zero but the torque on it is zero.

D

neither the force nor the torque needs to be zero.

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Q 8. A body with mass {tex}5 \mathrm { kg } {/tex} is acted upon by a force {tex} F = ( - 3 \hat { i } + 4 \hat { j } ) N . {/tex} If its initial velocity at {tex} t = 0 {/tex} is {tex} v = ( 6 \hat { i } - 12 \hat { j } ) \mathrm { ms } ^ { - 1 } {/tex} , the time at which it will just have a velocity along the {tex} y {/tex} -axis is

A

Never

10{tex} \mathrm { s } {/tex}

C

2s

D

15s

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Q 9. Two masses {tex} 8 \mathrm { kg } {/tex} and {tex} 12 \mathrm { kg } {/tex} are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the tension the string when the masses are released.

96{tex} \mathrm { N } {/tex}

B

80{tex} \mathrm { N } {/tex}

C

100{tex} \mathrm { N } {/tex}

D

None of these

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Q 10. At a curved path of the road, the roadbed is raised a little on the side away from the center of the curved path. The slope of the roadbed is given by

A

{tex} \tan ^ { - 1 } \frac { v ^ { 2 } g } { r } {/tex}

B

{tex} \tan ^ { - 1 } \frac { r g } { v ^ { 2 } } {/tex}

C

{tex} \tan ^ { - 1 } \frac { r } { g v ^ { 2 } } {/tex}

{tex} \tan ^ { - 1 } \frac { v ^ { 2 } } { r g } {/tex}

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Q 11. For a particle rotating in a vertical circle with uniform speed, the maximum and minimum tension in the string are in the ratio {tex} 5 : 3 {/tex} . If the radius of vertical circle is {tex} 2 \mathrm { m } , {/tex} the speed of revolving body is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}

A

{tex} \sqrt { 5 } \mathrm { m } / \mathrm { s } {/tex}

{tex}4 \sqrt { 5 } \mathrm { m } / \mathrm { s } {/tex}

C

{tex}5 \mathrm { m } / \mathrm { s } {/tex}

D

{tex}10 \mathrm { m } / \mathrm { s } {/tex}

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Q 12. A particle of mass {tex} 0.1 \mathrm { kg } {/tex} is whirled at the end of a string in a vertical circle of radius {tex}1.0 \mathrm { m } {/tex} at a constant speed of {tex} 5 \mathrm { m } / \mathrm { s } . {/tex} The tension in the string at the highest point of its path is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}

A

0.5{tex} \mathrm { N } {/tex}

B

1.0{tex} \mathrm { N } {/tex}

1.5{tex} \mathrm { N } {/tex}

D

2.0{tex} \mathrm { N } {/tex}

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Q 13. A motor car is traveling at {tex} 60 \mathrm { m } / \mathrm { s } {/tex} on a circular road of radius {tex} 1200 \mathrm { m } . {/tex} It is increasing its speed at the rate of {tex} 4 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} The acceleration of the car is

A

3{tex} \mathrm { ms } ^ { - 2 } {/tex}

B

4{tex} \mathrm { ms } ^ { - 2 } {/tex}

5{tex} \mathrm { ms } ^ { - 2 } {/tex}

D

7{tex} \mathrm { ms } ^ { - 2 } {/tex}

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Q 14. A 2{tex} \mathrm { kg } {/tex} stone at the end of a string 1{tex} \mathrm { m } {/tex} long is whirled in a vertical circle at a constant speed. The speed of the stone is 4{tex} \mathrm { m } / \mathrm { s } {/tex} . The tension in the string will be 52{tex} \mathrm { N } {/tex} , when the stone is

A

at the top of the circle

at the bottom of the circle

C

halfway down

D

none of the above

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Q 15. A particle is moving with a constant angular acceleration of 4 {tex} \mathrm { rad } / \mathrm { s } ^ { 2 } {/tex} in a circular path. At {tex} t = 0 {/tex} , particle was at rest. Find the time at which the magnitudes of centripetal acceleration and tangential acceleration are equal.

A

{tex}1s{/tex}

B

{tex}2s{/tex}

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

D

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

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Q 16. A particle is rotating in a circle of radius {tex} R {/tex} with constant angular velocity {tex} \omega {/tex} . Its average velocity during {tex} t {/tex} seconds after start of motion is

{tex} \frac { 2 R } { t } \sin \left( \frac { \omega t } { 2 } \right) {/tex}

B

{tex} \frac { 2 R } { t } \cos \left( \frac { \omega t } { 2 } \right) {/tex}

C

{tex} \frac { R } { t } \sin \left( \frac { \omega t } { 2 } \right) {/tex}

D

{tex} \frac { R } { t } \cos \left( \frac { \omega t } { 2 } \right) {/tex}

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Q 17. A particle is moving along the circular path with a speed {tex} v {/tex} and tangential acceleration is {tex} g {/tex} at an instant. If the radius of the circular path be {tex} r , {/tex} then the net acceleration of the particle at that instant is

A

{tex} \frac { v ^ { 2 } } { r } + g {/tex}

B

{tex} \frac { v ^ { 2 } } { r ^ { 2 } } + g ^ { 2 } {/tex}

{tex} \left[ \frac { v ^ { 4 } } { r ^ { 2 } } + g ^ { 2 } \right] ^ { \frac { 1 } { 2 } } {/tex}

D

{tex} \left[ \frac { v ^ { 2 } } { r } + g ^ { 2 } \right] ^ { \frac { 1 } { 2 } } {/tex}

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Q 18. The angular velocity of a wheel increases from 1200 rpm to 4500 rpm in 10s. The number of revolutions made during this time is

A

950

475

C

237.5

D

118.75

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Q 19. The body moves along a path PQR from P to R shown as a dashed line in Fig. When the particle is at Q, its speed is decreasing.The acceleration of the particle at Q is best represented by the vector A

{tex} A {/tex}

B

{tex} B {/tex}

{tex} C {/tex}

D

{tex} D {/tex}

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