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. `(1)/(3)`
B. `-(1)/(3)`
C. `(1)/(2)`
D. `-(1)/(2)`

Answer

B

Explanation

Here, acceleration `=v(dv)/(dx)=kx^(n)`, where `k` is a
constant. `:.v^(2)/(2)=k((x^(n+1))/(n+1))` or `vpropx^((n+1)/(2))`
Power `P=Fvprop(x^(n))(x^((n+1)/(2)))=x^(((3n+1)/(2)))`. For `P` to
be independent of `x`, `(3n+1)/(2)=0` or `n=-(1)/(3)`