Q.
An intense stream of water of cross-sectional area $A$ strikes a wall at an angle $\theta$ with the normal to the wall and returns back elastically. If the density of water is $\rho$ and its velocity is $v$, then the force exerted in the wall will be
A) $2Av\rho\cos\theta$
B) $2Av^{2}\rho\cos\theta$
C) $2Av^{2}\rho$
D) $2Av\rho$
Explanation
(b) Linear momentum of water striking per second to the wall $P_{1} = mv = Av\rho\ v = Av^{2}\ \rho$, similarly linear momentum of reflected water per second $P_{r} = Av^{2}\rho$
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Now making components of momentum along $x$- axes and $y$-axes. Change in momentum of water per second
$= P_{i}\cos\theta + P_{r}\cos\theta$
$= 2Av^{2}\ \rho\cos\theta$
By definition of force, force exerted on the Wall $= 2Av^{2}\ \rho\cos\theta$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.