Question

Mass M is divided into two parts m1and m2.fr a given separation the ratio of m1/M forwhich the gravitational attraction between the two parts becomes maximum is

1:1

1:2

1:3

1:4

Ans option 2 how?

Answer 1

Given mass M is divided into 2 - m1 & m2. ie(M=m1+m2)
The gravitational force of attraction is, F = Gm1 (M - m1)/d²

Differentiating w.r.t m1,

dF/dm1 = G/d2 (M - 2m1) ;
d²F/dm²< 0

When Force of attraction (F) is maximum between parts,

G/d² (M - 2m1) = 0

=> M = 2m1

=> m1 = M/2
ie , m1 /M = 1/2 or 1: 2