Consider a body shown in figure consisting of two identical balls each of mass M connected by a light rigid rod. An impulse J = Mv is imparted to the body at one of its end, what would be its angular velocity?

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$\frac{v}{L}$

$\frac{2 v}{L}$

$\frac{v}{3 L}$

$\frac{v}{4 L}$

answer is A.

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Detailed Solution

About centre of mass of the system

$\begin{array}{l} J \times \frac{L}{2} = 2 (\frac{{ML}^{2}}{4}) \times ω \Rightarrow MV \frac{L}{2} = 2 (\frac{{ML}^{2}}{4}) \times ω \\ \Rightarrow ω = \frac{v}{L} \end{array}$

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