Two objects are attracting each other with a certain gravitational force. (a) If the distance between the objects is reduced to half, the new gravitational force will increase by what factor? if the original force btween the two objects is 0.90 N, and the distance is tripled, what is the new gravitational force between the objects?

a) The gravitational force increases 4 times.

b) The gravitational force becomes, F = 0.1 N

Explanation:

Given data,

a) Let the masses of the objects be, M = m kg

The distance between them is, R = r m

The gravitational force between them is,

F = G mm / r²

If the distance between them is reduced by half, d = r / 2 m

The force between them becomes,

F = G mm / (r/2) ²

= 4 Gmm / r²

The gravitational force increases 4 times.

b) Given

The gravitational force between the objects, F = 0.90 N

If the distance between them is tripled, the equation becomes

0.90 N = G mm/r²

If the distance is tripled,

F = Gmm / (3r) ²

= Gmm / 9 r²

= (1/9) Gmm / r²

Substituting the value from the above equation,

F = (1/9) 0.90 N

= 0.1 N

Hence, the gravitational force becomes, F = 0.1 N