question_answer

A stream of water of density \[\rho ,\] cross-sectional area A, and speed v strikes a wall that is perpendicular to the direction of the stream, as shown in the figure. The water then flows sideways across the wall. The force exerted by the stream on the wall is

A) \[\rho {{v}^{2}}A\]     

B)        \[\rho vA/w\]

C) \[\rho ghA\]       

D)        \[{{v}^{2}}A/\rho \]

Correct Answer: A

Solution :

[a] Using equation of continuity, \[Av=2A{{v}_{1}}\Rightarrow {{v}_{1}}=\frac{v}{2}\] Let a small volume having mass 'dm? then  \[{{P}_{i}}=dmv\,\,\,\,{{P}_{f}}=0\] \[dp=dmv\] \[F=\frac{dp}{dt}=\left( \frac{dm}{dt} \right)v=\rho A{{v}^{2}}\]