A wide vessel with a small hole at the bottom is filled with two liquids. The density and height of one liquid are `rho_1` and `h_1` and that of the other are `rho_2` and `h_2(rho_1 gt rho_2)`. The velocity of liquid coming out of the hole is:

Options

A. `v=sqrt(2g(h_(1)+h_(2)))`
B. `v=sqrt(2(h_(1)rho_(1)+h_(2)rho_(2))//(rho_(1)+rho_(2)))`
C. `v=sqrt(2g(h_(1)+(h_(2)rho_(2))/(rho_(1))))`
D. `v=sqrt(2g((h_(1)rho_(1))/(rho_(2))+h_(2)))`

Answer

C

Explanation

`P_(0)+h_(1)rho_(1)g+h_(2)rho_(2)g+0=P_(0)+1/2 rho_(1)v^(2)`
`v=sqrt(2g(h_(1)+(h_(2)rho_(2))/(rho_(1))))`