A mass M is split into two parts, m and (M-m) . They are then separated by a certain distace. The gravitational force between these two parts will be maximum is 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 - 2 m = 0 rArr (m)/(M) = (1)/(2)`