Question

A jet of water with a cross-sectional area a is striking against a wall at an angle $ \theta $ to the horizontal and rebounds elastically. If the velocity of water jet is v and the density is $ \rho , $ the normal force acting on the wall is

• A. $ 2av^{2}\rho \,\cos \theta $
• B. $ av^{2}\rho \,\cos \theta $
• C. $ 2av\rho \,\cos \theta $
• D. $ av\,\cos \theta $

Answer 1

Answer: (A)

The normal force acting on the wall $=$ Rate of - change of momentum of water jet
$=m v \cos \theta-(-m v \cos \theta)$
$=2 m v \cos \theta$

$=2$ (volume $\times$ density $) v \cos \theta$
$=2(a v \rho) v \cos \theta=2 a v^{2} \rho \cos \theta$