If length of oscillating simple pendulum is made $\frac{1}{3}$ times at a place keeping amplitude same, then its total energy (E) will be

Question

Aicharya · Accepted Answer

$T=2 \pi \sqrt{\frac{\ell}{g}}$ $\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{\ell}{g}}$ $\omega=\sqrt{\frac{\mathrm{g}}{\ell}} \quad 	herefore \omega \propto \frac{1}{\sqrt{\ell}}$ $	herefore \frac{\omega_{2}}{\omega_{1}}=\sqrt{\frac{\ell_{1}}{\ell_{2}}}=\sqrt{\frac{\ell_{1}}{\ell_{1} / 3}}=\sqrt{3}$ $	herefore \omega_{2}=\sqrt{3} \omega_{1}$ Now $E \propto \omega^{2}$ $	herefore \frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}=\frac{\omega_{2}^{2}}{\omega_{1}^{2}}=3$ $	herefore E_{2}=3 E_{1}$

If length of oscillating simple pendulum is made $\frac{1}{3}$ times at a place keeping amplitude same, then…

Solution