Question

A cylindrical tank having cross-sectional area A = 0.5 $m^2$ is filled with two liquids of density ${\rho }_1$ = 900 kg $m^{-3}$ and ${\rho }_2$ = 600 kg $m^{-3}$, to a height h = 60 cm each as shown in figure. A small hole having area a = 5 $c{m}^2$ is made in right vertical wall at a height y = 20 cm from the bottom. A horizontal force F is applied on the tank to keep it in static equilibrium. The tank is lying on a horizontal surface. Neglect mass of cylindrical tank comparison to mass of liquids. Horizontal force F to keep the cylinder in static equilibrium, if it is placed on a smooth horizontal plane

• A. 7.2 N
• B. 10 N
• C. 15.5 N
• D. 20.4 N

Answer 1

The correct option is A

7.2 N

When cylinder is on smooth horizontal plane force F required to keep cylinder stationary equals horizontal thrust exerted by fluid jet.
But that is equal to mass flowing per second × change in velocity of this mass.

$\therefore$ F = ( avρ)( v - 0) = aρ$v^2$

or F = 7.2 N.