Two spherical bodies of mass M and 5M and radii R and 2R released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is:

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Important Questions on Motion of System of Particles and Rigid Body

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 5 - Motion of System of Particles and Rigid Body>AIPMT - 25th July 2015>Q 30

An automobile moves on a road with a speed of

54 k m h^{- 1}

. The radius of its wheels is

0.45 m

and the moment of inertia of the wheel about its axis of rotation is

3 k g m^{2}

. If the vehicle is brought to rest in

15 s

, the magnitude of average torque transmitted by its brakes to the wheel is:

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 5 - Motion of System of Particles and Rigid Body>AIPMT - 25th July 2015>Q 31

Point masses $m_{1}$ and $m_{2}$ are placed at the opposite ends of rigid rod of length $L$ , and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $L$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $ω_{0}$ is minimum, is given by:
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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 5 - Motion of System of Particles and Rigid Body>AIPMT - 25th July 2015>Q 32

A force

\vec{F} = α \hat{i} + 3 \hat{j} + 6 \hat{k}

is acting at a point

\vec{r} = 2 \hat{i} - 6 \hat{j} - 12 \hat{k}

. The value of

α

for which angular momentum about origin is conserved is:

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 5 - Motion of System of Particles and Rigid Body>AIPMT - 4th May 2014>Q 34

A solid cylinder of mass

50 k g

and radius

0.5 m

is free to rotate about horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of