Question

Three masses $m,\, 2\, m$ and $3\, m$ are arranged in two triangular configurations as shown in figure $1$ and figure $2$ . Work done by an external agent in changing, the configuration from figure $1$ to figure $2$ is

• A. $\frac{6Gm^{2}}{a}\left[2-\frac{6}{\sqrt{2}}\right]$
• B. 0
• C. $- \frac{Gm^{2}}{a}\left[ 6 + \frac{6}{\sqrt{2}}\right]$
• D. $- \frac{Gm^{2}}{a}\left[6-\frac{6}{\sqrt{2}}\right]$

Answer 1

Answer: (D)

$- \frac{Gm^{2}}{a}\left[6-\frac{6}{\sqrt{2}}\right]$

Answer 2

Work done to change configuration from 1 to 2 can be calculated by
$W_{12}=-\left(U_{f}-U_{i}\right)$
$=-\left[-\frac{G m^{2}}{a}\left(2+3+\frac{6}{\sqrt{2}}\right)-\left(-\frac{G m^{2}}{a}(2+3+6)\right)\right]$
$=-\frac{G m^{2}}{a}\left(6-\frac{6}{\sqrt{2}}\right)$