question_answer

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) \[2a{{v}^{2}}\rho \,\cos \theta \]                             

B) \[a{{v}^{2}}\rho \,\cos \theta \]

C) \[2av\rho \,\cos \theta \]                            

D) \[av\,\cos \theta \]

Correct Answer: A

Solution :

The normal force acting on the wall = Rate of change of momentum of water jet \[=mv\,\cos \theta -(-mv\,cos\theta )\] \[-2\,mv\,\cos \,\theta \]                                                                         \[=2(volume\,\times density)vcos\theta \] \[=2(av\rho )v\,cos\,\theta =2a{{v}^{2}}\rho \cos \theta \]