Three masses $m, 2 m$ and $3 m$ are arranged in two triangular configurations as shown in figure 1 and…

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
  1. $\frac{6 G m^2}{a}\left[2-\frac{6}{\sqrt{2}}\right]$
  2. 0
  3. $\frac{G m^2}{a}\left[6+\frac{6}{\sqrt{2}}\right]$
  4. $-\frac{G m^2}{a}\left[6-\frac{6}{\sqrt{2}}\right]$

Solution

Work done to change configuration from 1 to 2 can be calculated by $ W_{12}=-\left(U_f-U_i\right) $
$ \begin{aligned} & =-\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) \end{aligned} $

Asked in: AP EAMCET 2018 (22 Apr Shift 1)

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