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Motion of System of Particles and Rigid Body

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Q 1. A cubical block of side {tex} L {/tex} rests on a rough horizontal surface with coefficient of friction {tex} \mu {/tex}. A horizontal force {tex} F {/tex} is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

A

infinitesimal

B

{tex} \mathrm { mg } / 4 {/tex}

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

D

{tex} \mathrm { mg } ( 1 - \mu ) {/tex}

Explanation

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Q 2. A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved?

centre of the circle

B

on the circumference of the circle.

C

inside the circle

D

outside the circle.

Explanation

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Q 3. A particle is confined to rotate in a circular path decreasing linear speed, then which of the following is correct?

A

{tex} \vec { L } {/tex} (angular momentum) is conserved about the centre

only direction of angular momentum {tex} \vec { L } {/tex} is conserved

C

It spirals towards the centre

D

its acceleration is towards the centre.

Explanation

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Q 4. A small mass {tex} m {/tex} is attached to a massless string whose other end is fixed at {tex} P {/tex} as shown in the figure. The mass is undergoing circular motion in the {tex} x - y {/tex} plane with centre at {tex} O {/tex} and constant angular speed {tex} \omega . {/tex} If the angular momentum of the system, calculated about {tex} O {/tex} and {tex} P {/tex} are denoted by {tex} \vec { L } _ { O } {/tex} and {tex} \vec { L } _ { P } {/tex} respectively, then

A

{tex} \vec { L } _ { O } {/tex} and {tex} \vec { L } _ { P } {/tex} do not vary with time

B

{tex} \vec { L } _ { O } {/tex} varies with time while {tex} \vec { L } _ { P } {/tex} remains constant

{tex} \vec { L } _ { O } {/tex} remains constant while {tex} \vec { L } _ { P } {/tex} varies with time

D

{tex} \vec { L } _ { O } {/tex} and {tex} \vec { L } _ { P } {/tex} both vary with time

Explanation