A small ball strikes a stationary uniform rod, which is free to rotate at one end, in gravity free space. The ball does not stick to the rod. The rod will rotate about

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the point about which the moment of inertia of the rod plus ball’ is minimum

the point of impact on the ball on the rod

its centre of mass of the rod.

the centre of mass of ‘rod plus ball’

answer is A.

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Detailed Solution

Force of impact N acts on the rod at end B. If N is shifted to the centre of mass C of the rod, it produce translation. A torque

T = N x 1/2 is produced w.r.t. centre of rod. The combined translational and rotation effect can be understood as shown in last fig. Hence, under the action of N, the centre of mass of the rod moves along the line of action of N and under the action of $τ$ the rod rotates about centre of mass of the rod.

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