A cylindrical vessel contains a liquid of density `rho` up to height `h`. The liquid is closed by a piston of mass `m` and area of cross section `A`. There is a small hole at the bottom of the vessel. The speed `v` with which the liquid comes out of the hole is

Options

A. `sqrt(2gh)`
B. `sqrt(2(gh+(mg)/(rhoA)))`
C. `sqrt(2(gh+(mg)/A))`
D. `sqrt(2(gh+(mg)/A))`

Answer

B

Explanation

Applying Bernoulli's theorem at point `1` and `2` difference in pressure energy between `1` and `2 =` difference in kinetic energy between `1` and `2`.
Here `rhohg=(mg)/A=1/2rhov^(2)`
or `v=sqrt((2gh_(2mg)/(rhoA))= sqrt(2(gh+(mg)/(rhoA)))`