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Q.
A force $F=-k / x^{2}(x \neq 0)$ acts on a particle in $x$-direction. Find the work done by the force in displacing the particle from $x=-a$ to $x=2 a$.
Work, Energy and Power
Solution:
Work done by the force in displacing the particle from $x=-a$ to $x=2 a$ will be
$W=\int F d x=\int\limits_{x=-a}^{x=2 a}\left(-\frac{k}{x^{2}}\right) d x$
$=\left[\frac{k}{x}\right]_{-a}^{2 a}$
$=\frac{k}{2 a}-\frac{k}{(-a)}=\frac{3 k}{2 a}$