Rotation 5 Question 23
35. A rod of length $L$ and mass $M$ is hinged at point $O$. A small bullet of mass $m$ hits the rod as shown in the figure. The bullet gets embedded in the rod. Find angular velocity of the system just after impact.
(2005, 2M)
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Answer:
Correct Answer: 35. $\frac{3 m v}{L(3 m+M)}$
Solution:
- Angular momentum of the system about an axis perpendicular to plane of paper and passing through $O$ will remain conserved.
$$ \begin{aligned} & L _i=L _f \\ & \therefore \quad m v L=I \omega=m L^{2}+\frac{M L^{2}}{3} \omega \\ & \therefore \quad \omega=\frac{3 m v}{L(3 m+M)} \end{aligned} $$
