"Two point masses m and M are separated by a distance d. If the separation d remains fixed and the masses are increased to the values 3 m and 3 M respectively,
how does the gravitational force between them change?

The force of gravitational attraction increases by 9 as the two point masses increase by 3.

Explanation:

Gravitational force of attraction, F is the force that pulls two point masses, m and M which are separated by a distance, d.

Mathematically,

Fg = GMm/r^2

Initially,

M1 = M1

M2 = M2

The remaining parameters are unchanged.

Fg1 = G * M1 * m1/(d/2)^2

Then,

M1 = 3M1

M2 = 3M2

Fg2 = G * 3M1 * 3M2/(d/2)^2

Making the constants G/(d/2)^2 the subject of formula and then comparing both equations,

= Fg1 = (M1 * M2); Fg2 = (9 * M1 * M2)

= Fg2 = 9 * Fg1

The force of gravitational attraction increases by 9 as the two point masses increase by 3.

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