A uniform rod of mass M is hinged at its upper end. A particle of mass m moving horizontally strikes the rod at its mid point elastically. If the particle comes to rest after collision find the value of M/m

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answer is A.

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Detailed Solution

Let $ω$ is angular velocity of rod just after collision

from angular momentum conservation,

$mv \frac{L}{2} = \frac{{ML}^{2}}{3} ω \Rightarrow ω = \frac{3 mv}{2 ML}$

From coefficient of restitution equation, $1 = \frac{\frac{ωL}{2}}{v} \Rightarrow ω = \frac{2 v}{L}$

From the above two equations, $\frac{M}{m} = \frac{3}{4}$

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