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Work Done on & by the Object

A force F =- ...

Question

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.

A

\frac{k}{a}

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B

\frac{k}{a}

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C

- \frac{k}{2 a}

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D

\frac{k}{a}

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Solution

The correct option is C $- \frac{k}{2 a}$
By definition work done by force is
$W = \int F d x$
$= - k \int_{a}^{2 a} \frac{d x}{x^{2}}$
$= - k {[\frac{x^{- 2 + 1}}{- 2 + 1}]}_{a}^{2 a}$
$= k {[\frac{1}{x}]}_{a}^{2 a}$
$= k [\frac{1}{2 a} - \frac{1}{a}]$
$W = - \frac{k}{2 a}$

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