Question

A thin rod of mass m and length l is hinged at one end point which is at a distance h (h <l) above the horizontal surface. The rod is released from rest from the horizontal position. If e is the co-efficient of restitution, the angular velocity of rod just after collision will be (h = 1m, l = 2m, e = 1) –

• A. $\frac{3\sqrt{3g}}{8}$
• B. $\frac{6\sqrt{3g}}{8}$
• C. $\frac{5\sqrt{3g}}{8}$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

mg × $\frac{\mathcal{l}}{2}$ sin 30ŗ = $\frac{1}{2}$ × $\frac{m\mathcal{l}^{2}}{3}$ w²

w = $\sqrt{\frac{3g}{2\mathcal{l}}}$ = $\sqrt{\frac{3g}{4}}$= $\frac{\sqrt{3g}}{2}$

e = $\frac{\omega\mathcal{l}\cos 30^{0}}{\omega'\mathcal{l}\cos 30^{0}}$

w' = w =$\frac{\sqrt{3g}}{2}$