A thin rod of length L and mass M is held vertically with one end on floor and is allowed to fall. v

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6.System of Particles and Rotational Motion

hard

A thin rod of length $L$ and mass $M$ is held vertically with one end on the floor and is allowed to fall. Find the velocity of the other end when it hits the floor, assuming that the end on the floor does not slip

A

$\sqrt {\frac{{3g}}{L}} $

B

$\sqrt {3gL}$

C

$\sqrt {\frac{L}{{3g}}} $

D

$\sqrt {\frac{g}{{3L}}} $

Solution

Energy conservation $\operatorname{mg} \frac{\mathrm{L}}{2}=\frac{1}{2} \mathrm{I} \omega^{2}$

$\frac{\mathrm{mgL}}{2}=\frac{1}{2}\left(\frac{\mathrm{mL}^{2}}{3}\right) \omega^{2}$

$\omega=\sqrt{\frac{3 g}{L}}$

$\mathrm{V}=\mathrm{L} \omega=\sqrt{3 \mathrm{gL}}$

Standard 11

Physics

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