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The work done by external agent in stretching a spring of force constant k from length $l_{1} to l_{2} is$

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$k ({l_{2}}^{2} - {l_{1}}^{2})$

$\frac{1}{2} k ({l_{2}}^{2} - {l_{1}}^{2})$

$k (l_{2} - l_{1})$

$\frac{k}{2} (l_{2} + l_{1})$

answer is B.

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Detailed Solution

$U_{2} = \frac{1}{2} {kl}_{2}^{2}$

$U_{1} = \frac{1}{2} {kl}_{1}^{2}$

W = $U_{2} - U_{1}$

= $\frac{1}{2} {kl}_{2}^{2} - \frac{1}{2} {kl}_{1}^{2} = \frac{1}{2} k ({l_{2}}^{2} - {l_{1}}^{2})$

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