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A force $F = - \frac{k}{x^{2}} (x \neq 0)$ acts on a particle in $x$ -direction. Find the work done by this force in displacing the particle from. $x = + a$ to $x = + 2 a$ . Here, k is a positive constant.

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$\frac{- k}{2 a}$

$\frac{k}{2 a}$

$\frac{2 k}{a}$

$\frac{3 k}{2 a}$

answer is A.

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Detailed Solution

$w = \int_{+ a}^{+ 2 a} (\frac{- k}{x^{2}}) = {[\frac{k}{x}]}_{+ a}^{+ 2 a} = - \frac{k}{2 a}$

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