A particle is moving along x-axis under the action of a force F, which varies with its position `(x)as fprop(1)/(sqrtx).`Find the variation of power due to this force with x.

Options

A. `x^(1/3)`
B. `x^(1/8)`
C. `x^(1/2)`
D. `x^(1/4)`

Answer

`(2)`

Explanation

`F infty x ^(-1/4) Rightarrow a infty x ^(-1/4)`
`a = kx^(-1/4)`
`(dv)/(dt) = v(dv)/(dx) = kx^(-1/4)`
`int v dv = k int x^(-1/4) dx`
`v^(2)/2 = k (x^(3/4))/(3/4)`
`v^(2) infty x^(3/4) Rightarrow v infty x^(3/8)`
`therefore P = Fv Rightarrow P infty (x^(3/8))/(x ^(1/4))`
`P infty x^(1/8)`