Question

Three particles of mass $M$ each are placed at corners of an equilateral triangle of side ${}^{\prime }{d}^{\prime }$ if the sides are increased to ${}^{\prime }2d^{\prime }$ then :

• A. the P.E. $=\frac{-3G{M}^2}{2d}$
• B. work done $=\frac{3G{M}^2}{2d}$
• C. work done $=\frac{G{M}^2}{2d}$
• D. P.E. $=\frac{-3GM}{2d}$

Answer 1

The correct option is B work done $=\frac{3G{M}^2}{2d}$

Potential energy of system with three particles at distance $d=\frac{G{M}^2}{d}+\frac{G{M}^2}{d}+\frac{G{M}^2}{d}$

$=\frac{3G{M}^2}{d}$

Potential energy of system with three particles at distance $2d=\frac{3G{M}^2}{2d}$

Thus work done=Change in potential energy=$\frac{3G{M}^2}{2d}$