Question

Find the work done in bringing three particles each having a mass of 100 gm. From large distance to the vertices of an equilateral triangle of side 20 cm.

Answer 1

We note here that all three particles have the same mass. Hence, a product of mass in the expression of gravitational potential energy reduces to the square of mass. The gravitational potential energy of three particles at the vertices of the equilateral triangle is:
$U=-\frac{3G{m}^2}{a}$
where "a" is the side of the equilateral triangle.
Putting values.
$\Rightarrow U=-\frac{3\times 6.67\times {10}^{-11}\times 0.01}{0.2}$
Hence, work done by external force in bringing three particles from a large distance is:
$\Rightarrow W=U=-\frac{3\times 6.67\times {10}^{-11}\times 0.01}{0.2}$ = 10.005 $\times$ ${10}^{-12}$