Q 11-13-104JEE MainJEE Main 2021 (31 Aug, Shift 2)Medium
A bob of mass $m$ suspended by a thread of length $\ell$ undergoes simple harmonic oscillations with time period $T$. If the bob is immersed in a liquid that has density $\dfrac14$ times that of the bob and the length of the thread is increased by $\dfrac13$rd of the original length, then the time period of the simple harmonic oscillations will be:
Answer: (B) $\dfrac43T$
Buoyancy reduces the effective gravity: $g_{\text{eff}} = g\left(1 - \dfrac{\sigma}{\rho}\right) = \dfrac34g$.
New length $\ell' = \dfrac43\ell$.
$$T' = 2\pi\sqrt{\frac{4\ell/3}{3g/4}} = 2\pi\sqrt{\frac{16\ell}{9g}} = \frac43T$$
Solution by Sreeraj P, M.Sc Physics