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Question

A force F acting on a particle depends on displacement as Fxn. Then, power delivered by the force depends on x as:

A
xn
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B
x(2n+1)
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C
x3n+12
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D
x5n+22
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Solution

The correct option is C x3n+12
Given that,
FxnF=kxn .....(1)

Here, the force is a variable force as it depends on the position of the particle.

Hence, the acceleration can be written as a=vdvdx
we can rewrite (1) as,

mvdvdx=kxn

Seperating the variables and integrating on both sides, we get

mvdv=kxndx

v22=kmxn+1(n+1)+C

vxn+12

We know from the definition of power, P=Fv

i.e Pxn×xn+12Px3n+12

Thus, option (c) is the correct answer.

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