Question

Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are ρ_A, ρ_B, ρ_C with ρ_A < ρ_B < ρ_C. The force on the base will be
(a) maximum in vessel A
(b) maximum in vessel B
(c) maximum in vessel C
(d) equal in all the vessels

Answer 1

(d) equal in all the vessels

The force on the base is given by
$$\begin{gathered} F=h\rho g\times A \\ \Rightarrow F=\left(hA\rho \right)g \\ \Rightarrow \mathrm{F}=(\mathrm{Volume}\times \mathrm{Density})\times \mathrm{g} \\ \Rightarrow F=\mathrm{mg} \end{gathered}$$
In the question, the masses are equal. So, the force on the base is the same in all cases.