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Question

A stream of a liquid of density ρ flowing horizontally with speed v rushes out of a tube of radius r and hits a vertical wall nearly normally. Assuming that the liquid does not rebound from the wall, the force exerted on the wall by the impact of the liquid is given by.

A
πrρv
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B
πrρv2
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C
πr2ρv
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D
πr2ρv2
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Solution

The correct option is B πr2ρv2
Cross-sectional area A=πr2,
Volume of liquid flowing per second=AV=πr2v
Mass of the liquid flowing out per second =πr2vρ
Initial momentum of liquid per second
= mass of liquid flowing × Speed of liquid
=πr2vρ×v=πr2v2ρ
Since the liquid does not rebound after impact, the momentum after impact is zero.
Rate of change of momentum =πr2v2ρ
According to Newton's second law, the force exerted on wall= rate of change of momentum =πr2ρv2.

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