b
For equilibrium, Buoyant force $=$ weight of the body
$\Rightarrow h_{A} \rho_{A} A g+h_{B} \rho_{B} A g=\left(h_{A}+h+h_{B}\right) A \rho_{C} g$
(where $\rho_{C}=$ density of cylinder)
$h=\left(\frac{h_{A} \rho_{A}+h_{B} \rho_{B}}{\rho_{C}}\right)-\left(h_{A}+h_{B}\right)=0.25 \mathrm{cm}$