Two steel ball of equal diameter are connected by a rigid bar of negligible weight as shown and are dropped in the horizontal position from height h above the heavy steel and brass base plates. If the coefficient of restitution between the ball and steel base is $$0.6$$ and that between the other ball and the brass base is $$0.4$$. The angular velocity of the bar immediately after rebound is. (Assume$$ the two impacts are $$simultaneous).

Question

Infinity Learn · Accepted Answer

If v is the velocity by which balls strike the bases then their velocities after collision are $$0.6$$ v and $$0.4$$ v as shown 'u' is velocity of COM just after collision and ω in angular velocity acquired by the rod.For end A:  $$0.6v$$ $$=$$ $$u+l2$$.ω$$---------(i)For$$ end B: $$0.4v$$ $$=$$ $$u-l2$$.ω$$--------(ii)Solving$$ (i) and (ii), we $$get0.2v$$ $$=$$ ωl    ⇒ $$3$$ω $$=$$ $$v5lNow$$ using [$$v2-u2+2aS$$]$$v2$$ $$=$$ $$0+2$$×$$10$$×$$0.2$$ $$=$$ $$4$$ ⇒v $$=$$ $$2$$ $$m/s$$ω $$=$$ $$25$$×$$1$$ $$=$$ $$25rad/$$$$sec$$

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