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  4. A uniform rod of mass m and length L is at rest on a smooth horizontal surface. A ball of mass m, moving with velocity v0, hits the rod perpendicularly at its one end and sticks to it. The angular velocity of rod after collision is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-6hbtfddrwsm4auxe.jpg />

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Q. A uniform rod of mass $m$ and length $L$ is at rest on a smooth horizontal surface. A ball of mass $m,$ moving with velocity $v_{0},$ hits the rod perpendicularly at its one end and sticks to it. The angular velocity of rod after collision is
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NTA AbhyasNTA Abhyas 2022

Solution:

$mv_{0}\times \left(\frac{L}{4}\right)=\left(\frac{7}{48} \, m \, L^{2} + m \times \frac{L^{2}}{16}\right)\times \omega $
$\Rightarrow \omega =\frac{6 \, v_{0}}{5 \, L}$