A force `F` acting on a body depends on its displacement `S` as `FpropS^(-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^(0)`

Answer

D

Explanation

As `F prop S^(-1//3) :.` acceleration, `a prop S^(-1//3)`
Now, `a=( dupsilon)/( dt)=(d upsilon)/( ds ) ( ds )/(dt)=(d upsilon)/( ds ) upsilon:. upsilon(dupsilon)/( ds) prop S^(-1//3)`
Integrating both sides, we find
`upsilon^(2) prop S^(2//3) ` or ` upsilon prop S^(1//3)`
As `P=Fupsilon :. P prop (S^(-1//3))(S^(1//3))=S^(0)`
`i.e.` power is independetn of `S`.