Question

A stream of water flowing horizontally with a speed of $15 m \,s^{-1}$ gushes out of a tube of cross-sectional area $10^{-2}$ $m^{2}$, and hits a vertical wall normally. Assuming that it does not rebound from the wall, the force exerted on the wall by the impact of water is

• A. $1.25 \times$ $10^{3} \, N$
• B. $2.25 \times$ $10^{3} \, N$
• C. $3.25 \times$ $10^{3} \, N$
• D. $4.25 \times$ $10^{3} \, N$

Answer 1

Answer: (B)

$2.25 \times$ $10^{3} \, N$

Answer 2

Here, $v=15\, m \,s^{-1}$ Area of cross section, $A=10^{-2}$ $m^{2}$ Density of water, $\rho=10^{3} \, kg$ $m^{-3}$ Mass of water hitting the wall per second $=\rho\times$ $A\times v$ = $10^{3}\, kg$ $m^{-3}$ $\times10^{-2}$ $m^{2}$ $\times15 \,m \,s^{-1}$ $= 150 \, kg \,s^{-1}$ Force exerted on the wall = Momentum loss of water per second $=150\, kg$ $s^{-1}$ $\times15 \,m\, s^{-1}$ $= 2250\, N$ $=2.25\times$ $10^{3 }\,N$