Question

Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = MV is imparted to the body at one of its ends what would be it angular velocity?

A. `v//l`
B. `2v//l`
C. `v//2l`
D. None

Answer 1

Correct Answer - A
In uniform circular motion theonly force acting on the particle is centripetal (towards centre). Torque of this force aboit thecentre is zero. Hence angular momentum about centre remain conserved. Let `omega` be the angular velocity of the rod. Applying angular impulse = change in angular momentum about centre of mas of the system.
`J. (l)/(2) = I_(C) omega`
:. `(Mv) ((l)/(2)) = (2) 2 xx M(l//2)^(2) omega`
`omega = (v)/(2)`.
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