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  4. There is a rod of length l and mass m It is hinged at one end to the ceiling. The period of small oscillations is

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Q. There is a rod of length l and mass m It is hinged at one end to the ceiling. The period of small oscillations is

Oscillations

Solution:

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As $T=2 \pi \sqrt{\left(\frac{I}{m g h}\right)}$
Here, $I=\frac{m l^{2}}{3}$ and $h=\frac{l}{2}$
$\therefore T=2 \pi \sqrt{\left[\frac{\left(\frac{m l^{2}}{3}\right)}{m g \frac{l}{2}}\right]}=2 \pi \sqrt{\left(\frac{2 l}{3 g}\right)}$