The work done in bringing three particles, each having a mass of 100 g, from large distances to the

Question

The work done in bringing three particles, each having a mass of 100 g, from large distances to the vertices of an equilateral triangle of side 20 cm.

Professor PC Thomas Classes · Answer

When the particles are infinitely separate $U=0$.
$\begin{aligned} U & =3 	imes\left[-\frac{G m_1 m_2}{r}ight] \ & =3 	imes\left[-\frac{6.67 	imes 10^{-11} \mathrm{~N}-\mathrm{m}^2 / \mathrm{kg}^2 	imes(0.1 \mathrm{~kg}) 	imes(0.1 \mathrm{~kg})}{0.20 \mathrm{~m}}ight] \ & =-1.0 	imes 10^{-11} \mathrm{~J}\end{aligned}$
The work done by the gravitational forces is $W=-U=1.0 	imes 10^{-11} \mathrm{~J}$. If the particles are brought by some external agency without changing the kinetic energy, the work done by the external agency is equal to the change in potential energy $=-1.0 	imes 10^{-11} \mathrm{~J}$.