A cylindrical vessel contains a liquid of density `rho` up to a 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 (2 gh )`
B. ` sqrt (2 (gh + (mg ) /(rho A )) ) `
C. ` sqrt (2(gh + (mg )/(A))) `
D. ` sqrt ( 2 gh + (mg ) /(A)) `

Answer

B

Explanation

Pressure at bottom ` = (mg)/(A) + rho gh + P_ 0 `
Using Bernoulli’s theorem between points just inside and outside hole :
` rArr (mg )/(A) + rho gh + P_0 = (1)/(2) rhov ^2 + P _ 0 rArr v = sqrt((2)/(rho) ((mg)/(A) + rho gh)))`