A dumbell consisting of two masses m each, connected by a light rigid rod of length ℓ, falls on two pads of equal height, one steel and the other brass through a height h= 64m. The co-efficients of restitution are e1 =1/2 and e2 = 1. If maximum height reached by the centre of mass of the dumbell, after bouncing off the pads is H meter, then write \frac{H}{6} in answer.

Engineering

Physics

Acceleration

Center of Mass

Collision

Question

A dumbell consisting of two masses m each, connected by a light rigid rod of length ℓ, falls on two pads of equal height, one steel and the other brass through a height h= 64m. The co-efficients of restitution are e₁ =1/2 and e₂ = 1. If maximum height reached by the centre of mass of the dumbell, after bouncing off the pads is H meter, then write $\frac{H}{6}$ in answer.

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The centre of mass of the system after collision will move up with velocity at $\frac{(e_{1} + e_{2}) \sqrt{2 gh}}{2}$

$\Rightarrow 0 = {[\frac{(e_{1} + e_{2})}{2} \sqrt{2 gh}]}^{2} - 2 {gh}^{'}$

$h^{'} = \frac{{(e_{1} + e_{2})}^{2} h}{4} = 36$