Question

A long cylindrical tank of cross-section area 0.5$m^2$ is filled with water. It has an opening at a height 50 cm from the bottom, having area of cross-section $1\times {10}^{-4}{m}^2$ . A movable piston of cross-section area almost equal to 0.5 $m^2$ is fitted on the top of the tank such that it can slide in the tank freely. A load of 20 kg is applied on the top of the water by piston, as shown in the figure. Find the speed of the water jet with which it hits the surface when piston is 1m above the bottom (Ignore the mass of the piston).

• A. 3.56 m/s
• B. 3.3 m/s
• C. 5.56 m/s
• D. 4.56 m/s

Answer 1

The correct option is D

4.56 m/s

With respect to the opening the height of the piston is 0.5 m .
Pressure at the top is $P_1$ = $P_0+\frac{20\times 10N}{0.5m^2}$
Where $P_0$ is the atmospheric pressure.

Pressure at the opening is $P_2=P_0$.

From Bernoulli's equation, we have 1

$P_1+\rho gh+\frac{1}{2}\rho v_1^2=P_2+\frac{1}{2}\rho v_2^2$

Solving we get , $v_2$ = 3.3 m/s = $v_x$ , say

$v_y$ = $\sqrt{2gh}$

v = $\sqrt{v_x^2+v_y^2}$ = 4.56 m/s