A force Facting on a body depends on its displacement Sas `F prop S^(-1//3)`. The power delivered by F will depend on displacement as 

Options

A. `S^(2//3)`
B. `S^(1//2)`
C. `S`
D. `S^@`

Answer

D

Explanation

As `F prop S^(-1//3)`
`:.` Acceleration, `a prop S^(-1//3)`
But `a = (dv)/(dt) = (dv)/(dS) (dS)/(dt) = (dv)/(dS) v :. V (dv)/(dS) prop S^(-1//3).`
Intergrating both sides, we find
`v^2 prop S^(2//3) or v prop S^(1//3)`
As `P = Fv`
`:. P prop (S^(-1//3))(S^(1//3)) = S^(0)`.
i.e., power is independent of S.