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Laws of Motion

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Q 1. A ship of mass {tex} 3 \times 10 ^ { 7 } \mathrm { kg } {/tex} initially at rest, is pulled by a force of {tex} 5 \times 10 ^ { 4 } \mathrm { N } {/tex} through a distance of {tex} 3 \mathrm { m } {/tex}. Assuming that the resistance due to water is negligible, the speed of the ship is

{tex} 1.5 \mathrm { m } / \mathrm { sec } {/tex}

{tex} 60 \mathrm { m } / \mathrm { sec } {/tex}

{tex} 0.1 \mathrm { m } / \mathrm { sec } {/tex}

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

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Q 2. A block of mass {tex} 2 \mathrm { kg } {/tex} rests on a rough inclined plane making an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal. The coefficient of static friction between the block and the plane is {tex} 0.7 . {/tex} The frictional force on the block is

{tex} 9.8 \mathrm { N } {/tex}

{tex} 0.7 \times 9.8 \times \sqrt { 3 } \mathrm { N } {/tex}

{tex} 9.8 \times \sqrt { 3 } \mathrm { N } {/tex}

{tex} 0.7 \times 9.8 \mathrm { N } {/tex}

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Q 3. A block of mass {tex}0.1{/tex} is held against a wall applying a horizontal force of {tex} 5 \mathrm { N } {/tex} on the block. If the coefficient of friction between the block and the wall is {tex} 0.5 , {/tex} the magnitude of the frictional force acting on the block is:

{tex} 2.5 \mathrm { N } {/tex}

{tex} 0.98 \mathrm { N } {/tex}

{tex} 4.9 \mathrm { N } {/tex}

{tex} 0.49 \mathrm { N } {/tex}

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Q 4. A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

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Q 5. An insect crawls up a hemispherical surface very slowly (see fig.). The coefficient of friction between the insect and the surface is {tex} 1 / 3 . {/tex} If the line joining the center of the hemispherical surface to the insect makes an angle {tex} \alpha {/tex} with the vertical, the maximum possible value of {tex} \alpha {/tex} is given by

{tex} \cot \alpha = 3 {/tex}

{tex} \tan \alpha = 3 {/tex}

{tex} \sec \alpha = 3 {/tex}

{tex} \cosec \alpha = 3 {/tex}

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Q 6. A string of negligible mass going over a damped pulley of mass {tex} m {/tex} supports a block of mass {tex} M {/tex} as shown in the figure. The force on the pulley by the clamp is given by

{tex} \sqrt { 2 } \mathrm { Mg } {/tex}

{tex} \sqrt { 2 } \mathrm { mg } {/tex}

{tex} \sqrt { ( M + m ) ^ { 2 } + m ^ { 2 } } g {/tex}

{tex} \sqrt { ( M + m ) ^ { 2 } + M ^ { 2 } } g {/tex}

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Q 7. What is the maximum value of the force {tex} F {/tex} such that the block shown in the arrangement, does not move?

{tex} 20 \mathrm { N } {/tex}

{tex} 10 \mathrm { N } {/tex}

{tex} 12 \mathrm { N } {/tex}

{tex} 15 \mathrm { N } {/tex}

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Q 8. A block {tex} P {/tex} of mass {tex} m {/tex} is placed on a horizontal frictionless plane. A second block of same mass {tex} m {/tex} is placed on it and is connected to a spring of spring constant {tex} k , {/tex} the two blocks are pulled by distance {tex} A . {/tex} Block {tex} Q {/tex} oscillates without slipping. What is the maximum value of frictional force between the two blocks.

{tex} k A / 2 {/tex}

{tex} k A {/tex}

{tex} \mu _ { S } \mathrm { mg } {/tex}

zero

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