Question

V(r) = 2gm r , where g is the universal gravitational constant. Find the inverse of v(r) as a function of v.

Answer 1

Given function V(r) = 2gm r is the function V or r.

Where, g is the universal gravitational constant.

In order to find it's inverse we need to solve it for r first.

We have 2gm is being multiplied with r on right side.

Reverse operation of multiplication is division. So we need to divide both sides by 2gm.

$\frac{V(r)}{2gm}=\frac{2gm\ r}{2gm}$

2gm crossed out on right side, we get

$\frac{V(r)}{2gm}=r.$

Switching V(r) and r, we get

$\frac{r}{2gm}=V(r).$

Therefore, required inverse function is

$V'(r)=\frac{r}{2gm}$.