Question

A rod of length falls on two metal pads of same height from a height h. The coefficients of restitution of the metal pads are e₁ and e₂ (e₁> e₂). The angular velocity of the rod after it recoils is

• A. $\frac{e_{1}}{e_{2}}\mathcal{l}\sqrt{2gh}$
• B. $\frac{e_{1} + 1}{e_{2} + 1}\sqrt{2gh}$
• C. $\frac{e_{1} - e_{2}}{\mathcal{l}}\sqrt{2gh}$
• D. $\frac{e_{1} + 1}{e_{2} - 1}\sqrt{2gh}$

Answer 1

Answer: (C)

$\frac{e_{1} - e_{2}}{\mathcal{l}}\sqrt{2gh}$

Answer 2

After collision, the end A moves with a linear velocity of e₁$\sqrt{2gh}$. Whereas end B moves with a velocity of e₂$\sqrt{2gh}$.

∴ The relative velocity between the ends is

e₁$\sqrt{2gh}$ − e₂$\sqrt{2gh}$.

⇒ The angular velocity = $\frac{e_{1} - e_{2}}{\mathcal{l}}\sqrt{2gh}$