Equal mass of three liquids are kept in three identical cuylindrical vessels A, B and C. the densities are `rho_A, rho_B, rho_C` with `rho_Altrho_Bltrho_C`. The force on the base will be

Options

A. maximum in vessel `A`
B. maximum in vessel `B`
C. maximum in vessel `C`
D. same in all the three vessels

Answer

D

Explanation

Let `m` be mass of the liquid. Let `h_(A), h_(B)` and `h_(C)` be the heights of liquid level in three vessels. Then
`m=rho_(A)Axxh_(A)=rho_(B)Axxh_(B)=rho_(C)xxAxxh_(C)`
`rho_(A)h_(A)=rho_(B)h_(B)=rho_(C)h_(C)=m/A`
Pressure at the bottom is vessel `A`, `p_(A)=p_(0)+rho_(A)gh_(A)`
similarly at `B` and `C p_(B)=p_(0)+rho_(B)gh_(B)`
`p_(C)=p_(0)+rho_(C)gh_(C)`
i.e., `p_(A)=p_(B)=P_(C)`
so, the same force will be exerted by the liquid in all the three vessels.