A simple pendulum oscillating in air has period T . The bob of the...

Let the density of bob is $\sigma$ & density of liquid is $\dfrac{\sigma}{16}$ .
Now, Net downward force on bob = Weight - Buoyancy
$= \sigmaVg - \dfrac{\sigma}{16}Vg = \dfrac{15}{16}\sigmaVg$
Net effective gravitational acceleration $= \dfrac{\dfrac{15}{16}\sigmaVg}{\sigmaV} = \dfrac{15}{16}g$
Time period \left(T\right) = 2\pi\sqrt{\dfrac{l}{{g}_{eff}}} = 2\pi\sqrt{\dfrac{l}{\dfrac{15}{16}g}} = 2\pi\sqrt{\dfrac{16}{15}\dfrac{l}{g}} = \sqrt{\dfrac{16}{15}} ∙ \left(2\pi\sqrt{\dfrac{l}{g}}\right) = \dfrac{4}{\sqrt{15}}T$<br />$= 4T\sqrt{\dfrac{1}{15}}