Question 20 of 130

Consider a uniform rod of mass $M=4m$ and length $l$ pivoted about its centre. A mass $m$ moving with velocity $v$ making angle $\theta =\dfrac{\pi }{4}$ to the rod’s long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:

A$\dfrac{3}{7\sqrt{2}}\dfrac{v}{l}$B$\dfrac{3}{7}\dfrac{v}{l}$C$\dfrac{3\sqrt{2}}{7}\dfrac{v}{l}$D$\dfrac{4}{7}\dfrac{v}{l}$

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Answer: (C) $\dfrac{3\sqrt{2}}{7}\dfrac{v}{l}$

${L}_{oi}={L}_{of}$
$\dfrac{mV}{\sqrt{2}}\times \dfrac{L}{2}=\left[\dfrac{4m{L}^{2}}{12}+\dfrac{m{L}^{2}}{4}\right]\times \omega$
$\omega =\dfrac{6V}{7\sqrt{2}L}=\dfrac{3\sqrt{2}V}{7L}$