Question

A jet of water with 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 $\theta$, the normal force acting on the wall is:

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

Answer 1

Answer: (A), (D)

The correct options are
A

$2a{v}^2\rho cos\theta$

D

$avcos\theta$

Newton’s second law of motion
$F_{ext}=\frac{dp}{dt}{F}_{ext}=p_2-p_2{p}_2=mvcos\theta ,\rho =\frac{mass}{volume}=\frac{m}{av}{p}_2=\left(\rho av\right)vcos\theta =\rho a{v}^{2}cos\theta p_i=-\rho a{v}^{2}cos\theta$
Volume flow rate =velocity \times area
$F_{ext}=p_2-p_i=\rho a{v}^{2}cos\theta -(-\rho a{v}^{2}cos\theta )F_{ext}=2\rho a{v}^{2}cos\theta$