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Question

When a belt moves horizontally at a constant speed of 1.5 ms1, gravels are falling on it at rate of 5 kg s1. Then, the extra power required to drive the belt is

A
11.25 W
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B
37.5 W
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C
7.5 W
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D
0.75 W
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Solution

The correct option is A 11.25 W
It is given that the velocity of the belt v=1.5 ms1

The rate at which the mass of the gravel falls is given by

dmdt=5 kg s1

By the newtons second law, we know that force is the rate of change of momentum (p=mv)

F=dpdt=dvdtm+dmdtv=5×1.5=7.5 N
(As the velocity v is constant, change in velocity dv=0)

P=F×v=7.5×1.5=11.25 W

Hence option A is the correct answer

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