Question

Two small bodies of masses 10 kg and 20 kg are kept a distance 1.0 m apart and released. Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to 0.5 m

Answer 1

$\begin{array}{c}\Delta U=U_{2G}-U_1{U}_1=\frac{GMm}{r}\\ =400G-200G{U}_1=\frac{G\times 10\times 20}{0.5}=200G\\ =200G{U}_2=\frac{G\times 10\times 20}{0.5}=400\end{array}$

By energy conservation $\frac{1}{2}m{v}^2=U$

$\begin{array}{c}\Rightarrow \frac{1}{2}\times \frac{20}{3}\times v^2=200G\\ v^2=60G\\ v=\sqrt{60G}\\ v=6.32\times {10}^{-5}m/s\end{array}$