Two bodies of masses 1 kg and 2 kg respectively are placed at a separation of 1 m. Find the accelerations of the bodies assuming that only gravitational forces act.

The force of gravitation is

$\mathrm{F}=\frac{{\mathrm{Gm}}_1{\mathrm{m}}_2}{{\mathrm{r}}^2}$

$\mathrm{F}=\frac{\left(6.67\times {10}^{-11}\frac{{\mathrm{Nm}}^2}{{ \mathrm{kg}}^2}\right)\times (1 \mathrm{kg})\times (2 \mathrm{kg})}{(1 \mathrm{m}{)}^2}$

$\mathrm{F}=1.33\times {10}^{-10} \mathrm{N}$

Each body attracts the other with a force of this magnitude. The acceleration of the 1-kg body is

$\mathrm{a}=\frac{\mathrm{F}}{1 \mathrm{kg}}=\frac{1.33\times {10}^{-10} \mathrm{N}}{1 \mathrm{kg}}$

$\mathrm{a}=1.33\times {10}^{-10} \mathrm{m}/{\mathrm{s}}^2$

$\text{ The acceleration of the }2-\mathrm{kg}\text{ body is }$

$\mathrm{a}=\frac{\mathrm{F}}{2 \mathrm{kg}}=6.67\times {10}^{-11} \mathrm{m}/{\mathrm{s}}^2$