In a certain region of space gravitational field is given by `I = - (k//r)`. Taking the reference point to be at `r = r_(0)`, with gravitational potential `V = V_(0)`, find the gravitational potential at distance `r`.

Options

A. K log `(r)/(r_(0)) + V_(0)`
B. K log `(r_(0))/(r) + V_(0)`
C. K log `(r)/(r_(0)) - V_(0)`
D. log `(r_(0))/(r) - V_(0)r`

Answer

A

Explanation

We know that intensity is negative gradient of potential, i.e., I = - (dV/dr) and as here I = - (K/r), so
`(dV)/(dr) = (K)/(r) , i.e., int ` dV = K
or V - `V_(0) = K " log" (r)/(r_(0))`
so V = K"" log `(r)/(r_(0)) + v_(0)`