Question

A uniform rod of mass M₁ is hinged at its upper end. A particle of mass M₂ moving horizontally strikes the rod at its mid point elastically. If the particle comes to rest after collision, the value of $\frac{M_{1}}{M_{2}}$ is –

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$

Answer 1

Answer: (A)

$\frac{3}{4}$

Answer 2

L_H = M₂v $\frac{L}{2}$ = $\frac{M_{1}L^{2}}{3}$ w

w = $\frac{3M_{2}v}{2M_{1}L}$ …(1)

for e = 1, v_CM = v = $\frac{\omega L}{2}$ …(2)

Ž $\frac{2v}{L}$ = $\frac{3M_{2}v}{2M_{1}L}$

Ž $\frac{M_{1}}{M_{2}}$ = $\frac{3}{4}$