K is force constant of a spring. work done in increasing its extension from {l₁} to {l₂} will be

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8.Mechanical Properties of Solids

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$K$ is the force constant of a spring. The work done in increasing its extension from ${l_1}$ to ${l_2}$ will be

A

$K({l_2} - {l_1})$

B

$\frac{K}{2}({l_2} + {l_1})$

C

$K(l_2^2 - l_1^2)$

D

$\frac{K}{2}(l_2^2 - l_1^2)$

Solution

(d) At extension ${l_1}$, the stored energy $ = \frac{1}{2}Kl_1^2$

At extension ${l_2}$, the stored energy$ = \frac{1}{2}Kl_2^2$

Work done in increasing its extension from ${l_1}$ to ${l_2}$

$ = \frac{1}{2}K(l_2^2 – l_1^2)$

Standard 11

Physics

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