Question

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

Answer 1

Correct Answer - [`1//2`]
Let `rho` the density of liquid. Then
`F_(1)=(delta P)A=rho gh A`
In the second case, `F_(2)=`rate of change of momentum
`=` mass of water striking per sec x velocity
`=(A v xx rho)xx v= A rho v^(2) =A rho (sqrt(2 gh))^(2)`
`=A rho xx2 gh`
`:. (F_(1))/(F_(2))=(1)/(2)`