Physics - SHM Question with Solution | TestHub

Ans. (B) For rigid body $\mathrm{T}=2\pi \sqrt{\frac{\mathrm{I}}{\mathrm{mgl}}}$ (Suppose $\ell$ is distance of point of pivoting from COM) $=2\pi \sqrt{\frac{\left(\frac{{\mathrm{mR}}^2}{2}+\mathrm{m}{\ell }^2\right)}{\mathrm{mg}\ell }}=2\pi \sqrt{\frac{{\mathrm{R}}^2+2{\ell }^2}{2\mathrm{g}\ell }}$ $L_{\text{eff }}=\frac{R^2+2{\ell }^2}{\ell }$ should be minimum for $T$ to be minimum $\frac{{\mathrm{dL}}_{\text{eff }}}{\mathrm{dl}}=\frac{\ell (+4\ell )-\left({\mathrm{R}}^2+2{\ell }^2\right)}{{\ell }^2}=0$

$4{\ell }^2-R^2-2{\ell }^2=0$

${\mathrm{R}}^2=2{\ell }^2$