Two spheres of masses (m) and (M - m) are prepared from a sphere of mass M. They are kept at a distance x. For what ratio of `(m)/(M)` will the gravitational attraction between them be maximum ?

Options

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

Answer

C

Explanation

The gravitational force of attraction between the two sphere is
`F=(Gm(M-m))/(x^(2))=(GMm)/(x^(2))-(Gm^(2))/(x^(2))`
For this force to be maximum, `(dF)/(dm)=0`
`therefore (dF)/(dm)=(GM)/(x^(2))-(2Gm)/(x^(2))=0`
`therefore (GM)/(x^(2))=(2Gm)/(x^(2))" " therefore M = 2m` or `(m)/(M)=(1)/(2)`