Question

Two point objects of mass 2x and 3x are separated by a distance r. Keeping the distance fixed, how much
mass should be transferred from 3x to 2x, so that gravitational force between them becomes maximum?
(1) x/4
(2) x/3
(3) x/2
(4)2x/3​

Answer 1

• Mass that should be transferred from 3x to 2x so that gravitational force between them becomes maximum is x/2.

Given-

• Mass of first object (m₁) = 2x
• mass of second object (m₂) = 3x

• Let the fixed distance be r and mass transfer be m₀

Now,

m₁ = 2x + m₀

m₂ = 3x - m₀

So new force will be -

F = G (2x + m₀) (3x - m₀) / r²

F = G/r² (6x² +m₀x - m₀²)

For maximum force

dF/dm₀ = 0

So,

dG/dm₀ (6x² +m₀x - m₀²)/r² = 0 (m₀ is variable)

G/r² (0 + x -2m₀) = 0

m₀ = x/2

Regards