Question

Bob whose mass is 65 kg is standing near Sandra whose mass is 35 kg.  The force of gravitational attraction  between them is 5.42 x 10-8 N.  How far apart are Bob and Sandra? How far apart should they stand to have a quarter of that force.

Answer 1

a) From the law of universal gravitation, we have:

$$F=\dfrac{Gm_1m_2}{r^2},$$ $$r=\sqrt{\dfrac{Gm_1m_2}{F}},$$ $$r=\sqrt{\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot65\ kg\cdot35\ kg}{5.42\cdot10^{-8}\ N}}=1.67\ m.$$

b)

$$r=\sqrt{\dfrac{Gm_1m_2}{\dfrac{1}{4}F}}=2\sqrt{\dfrac{Gm_1m_2}{F}}=2r=2\cdot1.67\ m=3.34\ m.$$