Question

A dumbell consisting of two masses m each, connected by a light rigid rod of length , falls on two pads of equal height, one steel and the other brass through a height h. The co-efficients of restitution are e₁ and e₂ (e₁< e₂). To what maximum height will the centre of mass of the dumbell rise after bouncing off the pads?

• A. $\frac{h}{e_{1} + e_{2}}$
• B. (e₁+e₂)²$\frac{h}{4}$
• C. $\frac{e_{1}^{2} + e_{2}^{2}}{4}$
• D. $\frac{4h}{e_{1}^{2} + e_{2}^{2}}$

Answer 1

Answer: (B)

(e₁+e₂)²$\frac{h}{4}$

Answer 2

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

⇒ 0 = $\left\lbrack \frac{\left( e_{1} + e_{2} \right)}{2}\sqrt{2gh} \right\rbrack^{2} - 2gh^{'}$h′

= $\frac{\left( e_{1} + e_{2} \right)^{2}h}{4}$, Hence, (2) is the correct choice