Question

A two point system consists of two masses, m and 2m, separated by a distance d. If mass m is replaced by a mass 3m and is kept at a distance d/2, what are the ratios of the gravitational potential energy of the two systems?

Answer 1

$F_1=\frac{k\cdot m\cdot 2m}{d^2}=\frac{2km^2}{d^2},$

$F_2=\frac{k\cdot 3m\cdot 2m}{(\frac d2)^2}=\frac{24m^2}{d^2},$

$\frac{F_2}{F_1}=12.$