Question

A cylindrical tank stands on a frictionless surface.The seal over a circular hole of radius $0.5cm$ in the wall of the tank ruptures when the level of water above the hole is $1$ metre. The force that a person must apply on the cylinder to keep it from being set in motion is

• A. $1.54\times {10}^{-3}N$ forward
• B. $1.54\times {10}^{-3}N$ backward
• C. $1.54N$ forward
• D. $1.54N$ backward

Answer 1

The correct option is C $1.54N$ forward

From Touicellis Theorem,
Velocity of water=$V=\sqrt{2gH}=\sqrt{2\times 10\times 1}=\sqrt{20}m/s$
Area of orifice $=\pi \times {(0.5\times {10}^{-2})}^2=\pi 2.5\times {10}^{-5}{m}^2$
So,
=Force Applied by person to prevent the movement of tank$=fa{v}^2$
$=1000\times 2.5\times \pi \times {10}^{-5}\times 20N$
$=1.539N\approx 1.54N$