The gravitational field due to a mass distribution is given by `E=K/x^3` in X-direction. Taking the gravitational potential to be zero at infinity, find its value at a distance x.

Options

A. `(K)/(x)`
B. `(K)/(2x)`
C. `(K)/(x^(2))`
D. `(K)/(2x^(2))`

Answer

D

Explanation

`intdV=--intI_(g).dx,int_(v)^(0)dV=-int_(r)^(infty)(k)/(x^(3))dx`
`0-V=[-(1)/(2x^(2))]_(r)^(infty)impliesV=+(k)/(2r^(2))impliesV=(k)/(2x^(2))`