A simple pendulum oscillating in air has a period of $\sqrt{3}$ s. If it is completely immersed in a non-viscous liquid, having density ${\left(\frac{1}{4}\right)}^{\mathrm{th}}$ of the material of the bob, the new period will be 

Time period of a simple pendulum,

$\mathrm{T}=2\pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

when it is immersed in a liquid, due to buoyant force, effective weight of the bob will be

$\mathrm{mg}(1-\frac{{\mathrm{d}}_1}{{\mathrm{d}}_{\mathrm{s}}})$

Hence, effective ‘g‘ value is $g(1-\frac{d_1}{d_s})$

so time period  $T^{\mathrm{\prime }}=2\pi \sqrt{\frac{1}{g(1-\frac{d_1}{d_s})}}$

here, it is given ${\mathrm{d}}_1={\mathrm{d}}_{\mathrm{s}}/4$

$T^{\mathrm{\prime }}=2\pi \sqrt{\frac{1}{g(1-\frac{1}{4})}}$

$=2\mathrm{\pi }\sqrt{\frac{1}{\mathrm{g}}}\sqrt{\frac{4}{3}}(\mathrm{T}=\sqrt{3}\mathrm{s})$

$=\sqrt{3}\cdot \frac{2}{\sqrt{3}}$

$=2\mathrm{s}$