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The gravitational field due to a mass di...

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.

A

`K//x`

B

`K//2x`

C

`K//x^(2)`

D

`K//2x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, `I = - dV//dr` or `dV = - I dr`
So, `V = underset(0) overset(x)int - I dr = underset(0) overset(x)int - K r^(-3) dr`
`= - K((r^(-3+ 1))/(-3 + 1))_(0)^(x) = (K)/(2x^(2))`
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