Physics - SHM Question with Solution | TestHub

$t_0=2\pi \sqrt{\mathit{\text{l}}/\text{g}}$...............(i)


Due to upthrust of water on the top, its apparent weight decreases
upthrust = weight of liquid displaced

$\therefore$Effective weight =$\mathit{\text{m}}\text{g}-\left(\mathit{\text{V}}\sigma \text{g}\right)=\mathit{\text{V}}\rho \text{g}-\mathit{\text{V}}\sigma \text{g}$

$\mathit{\text{V}}\rho {\text{g}}^{\prime }=\mathit{\text{V}}\text{g}\left(\rho -\sigma \right)$, where$\sigma$is density of water


or${\text{g}}^{\prime }=\text{g}\left(\frac{\rho -\sigma }{\rho }\right)$

$\therefore$$t=2\pi \sqrt{\mathit{\text{l}}/{\text{g}}^{\prime }}=2\pi \sqrt{\frac{\mathit{\text{l}}\rho }{\text{g}\left(\rho -\sigma \right)}}$.............(ii)

$\therefore$$\frac{t}{t_0}=\sqrt{\frac{\mathit{\text{l}}\rho }{\text{g}\left(\rho -\sigma \right)}\times \frac{\text{g}}{\mathit{\text{l}}}}=\sqrt{\frac{\rho }{\rho -\sigma }}$

$\; \; \; =\sqrt{\frac{4\times 1000/3}{\left(\frac{4000}{3}-1000\right)}}=2$


or$t=t_0\times 2=2t_{0.}$