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Q.

A particle of mass m is attached to an end of a uniform rod of mass M = 2m and length ‘l’ which is suspended through its mid point by an inextensible string as shown. Initially the rod is in horizontal position and at rest. The system is released from this position. Just after the release.

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a

The angular acceleration of the system is 6g5l

b

The angular acceleration of the system is 2g5l

c

The tension in the string is 125  mg

d

The tension in the string is 25  mg

answer is A.

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Detailed Solution

The FBD of the rod and the ball are shown. Applying  τ=Iα about the C.M. of the rod, we have,  N(l2)=(Ml212)αWriting Newton’s II law in the vertical direction on the CM of the rod we have 2mg+N-T=0  and writing Newton’s II law in the vertical direction on the ball we have, mg−N=m(l2)α Solve these equations.α=6g5l and T=12mg5
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A particle of mass m is attached to an end of a uniform rod of mass M = 2m and length ‘l’ which is suspended through its mid point by an inextensible string as shown. Initially the rod is in horizontal position and at rest. The system is released from this position. Just after the release.