Effective weight of bob inside water,
\(W' = mg - {\rm{thrust}} = V\rho g - V\rho 'g\)
\( \Rightarrow V\,\,\rho {g_{eff}} = V(\rho - \rho ')g,\) where, \(\rho \) = Density of bob
\( \Rightarrow {g_{eff}} = \left( {1 - \frac{{\rho '}}{\rho }} \right)\,g\) and \(\rho '\) = Density of water
\(\therefore t = 2\,\pi \sqrt {\frac{l}{{{g_{eff}}}}} = 2\,\pi \sqrt {\frac{l}{{(1 - \rho '/\rho )g}}} \)    \(  (\because \rho ' = {10^3}kg/{m^3}  \,\,\rho  = \frac{4}{3} \times {10^3}kg/{m^3}) \)

\(\therefore \frac{t}{{{t_0}}} = \sqrt {\frac{1}{{1 - \rho '/\rho }}} = \sqrt {\frac{1}{{1 - \frac{3}{4}}}} \)

\( \Rightarrow t = 2\,{t_0}\).