The opening near the bottom of the vessel shown in the figure has an area `A`. A disc is held against the opening keep the liquid from running out. Let `F_(1)` be the net forces on the disc applied by liquid and air in this case. Now the disc is moved away from the opening a short distance. The liquid comes out and strikes the disc in elastically. Let `F_(2)` be the force exerted by the liquid in this condition. The `F_(1)//F_(2)` is

Options

A. `1/2`
B. `1`
C. `2/1`
D. `1/4`

Answer

A

Explanation

Let `rho` be the density of the liquid. Then
`F_(1)=(/_\P)A=rhoghA`……..i
In the second case `F_(2) =` rate of change of momentum
`=rhoAu^(2)=rhoA(sqrtgh)^(2)=2rhoghA`……..ii
`:.(F_(1))/(F_(2))=1/2`