Question

A water jet, whose cross sectional are is ${}^{\prime }{a}^{\prime }$ strikes a wall making an angle ${}^{\prime }\theta {}^{\prime }$ with the normal and rebounds elastically. The velocity of water of density ${}^{\prime }{d}^{\prime }$ is $V$.
Force exerted on wall is

• A. $2a{V}^{2}d\cos \theta$
• B. $2a{V}^{2}d\sin \theta$
• C. $2aVd\cos \theta$
• D. $aVdcos\theta$

Answer 1

The correct option is A $2a{V}^{2}d\cos \theta$

Change in momentum
$\Delta p=mV\cos \theta -(-mV\cos \theta )=2mV\cos \theta$
Force acting on the wall
$F=\frac{dp}{dt}=\left(2V\cos \theta \right)\frac{dm}{dt}$

The mass crossing an area in time $t$ for a small element would be
$m=V\times t\times a\times d.....\left(1\right)$

$\therefore \frac{dm}{dt}=Vad\therefore F=2a{V}^{2}d\cos \theta$