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Q.

Three identical particles each of mass ‘m’ are arranged on a straight line, such that the outer masses are at a distance ‘2r’ apart and the inner one is at the middle. The work to be done to move the middle particle to infinity is

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a

$- \frac{2 G m^{2}}{r}$

b

$\frac{G m^{2}}{2 r}$

c

$- \frac{G m^{2}}{2 r}$

d

$\frac{2 G m^{2}}{r}$

answer is C.

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Detailed Solution

$(m) - - - - (m) - - - - (m)$

$ω = P E_{f} - P E_{i}$

$ω = (\frac{- G m^{2}}{2 r}) - [- \frac{G m^{2}}{r} - \frac{G m^{2}}{r} - \frac{G m^{2}}{2 r}]$

$= \frac{- G m^{2}}{2 r} + \frac{5 G m^{2}}{2 r}$

$= \frac{2 G m^{2}}{r}$

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Three identical particles each of mass ‘m’ are arranged on a straight line, such that the outer masses are at a distance ‘2r’ apart and the inner one is at the middle. The work to be done to move the middle particle to infinity is