Gravitational Force

Question

Suppose the force of attraction between mass m1 and mass m2 is F when the distance between the masses is d. Answer each of the following in terms of F.

(a) What is the force between two objects of mass 4m1 and 3m2 when the distance between their centers is

1/4d?

(b) What is the force between two objects of mass 1/2m1 and 4m2 when the distance between their centers is 5d?

Answer 1

The attractive force between the two masses is given by F = Gm₁m₂/d²

a) For the new masses 4m₁ and 3m₂ with separation distance of 1/4d, the new attractive force is

F = G(4m₁)(3m₂)/(1/4d)² = 12Gm₁m₂/((1/16)d²) = 12(16)F

b) For new masses .5m₁ and 4m₁ with separation distant of 5d, the new force becomes

F = G(.5m₁)(4m₂)/(5d)² = 2Gm₁m₂/25d² = (2/25)F

NB: G is universal gravitational constant