A mass M is split into two parts, m and (M-m). They are then separated by a certain distance. The gravitational
force between these two parts will be maximum if the ratio `(m)/(M)` is equal to

Options

A. `(1)/(4)`
B. `(1)/(3)`
C. `(1)/(2)`
D. `(1)/(1)`

Answer

C

Explanation

`F=-G(m(M-m))/(R^(2)),` For maximum force, `("dF")/("dm")=0` or M-2m=0 `implies(m)/(M)=(1)/(2)`