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Question

A force F acting on a body depends on its displacement x as Fxn. The power delivered by F will be independent of x if n is:

A
13
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B
13
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C
12
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D
12
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Solution

The correct option is D 13

Here, acceleration =vdvdx=kxn, where k is a constant.

v22=k(xn+1n+1)

vxn+12

Power P=Fv(xn)xn+12=x3n+12

For P to be independent of x, 3n+12=0

or n=13


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