Question

The centres of a 6kg lead ball and a 110g lead ball are separated by 15cm,

A) what gravitational force does each exert on the other?

B) what is the ratio of this gravitational force to the weight of the 110g ball?

Answer 1

(A) Here, m1 = 6.0 kg

m2 = 110 g = 110/1000 = 0.110 kg

Distance between them, r = 15 cm = 0.15 m

Expression of the gravitational force between two masses m1 and m2 is given by -

F = G*m1*m2 / r^2

Where G is the universal gravitational constant.

So, F = (6.674 x 10^-11 x 6.0 x 0.110) / 0.15^2 = 1.96 x 10^-9 N

(B) Weight of 110 g mass, W = m2*g = 0.110*9.8 = 1.078 N

Hence ratio of gravitational force to the weight of 110 g object = (1.96 x 10^-9) / 1.078 = 1.82 x 10^-9 (Answer)