Question

Object A experiences a gravitational force due to object B of magnitude 2.5 x 10^-8 N. Determine the magnitude of the gravitational force if the separation distance is halved, mA increases seven times, and mB is reduced to one quarter of its original value.

Answer 1

The Newton's law of gravitation says

$$F=G\frac{m_Am_B}{r^2}$$

Hence,

$$F'=G\frac{7m_Am_B/4}{(r/2)^2}=7F.$$

$$F'=7\times 2.5\times 10^{-8}=1.75\times 10^{-7}\:\rm N.$$