Question

If the force constant of a wire is $K$, the work done in increasing the length $l$ of the wire by $l$ is

• A. $3Kl$
• B. $2Kl$
• C. $\frac{K{l}^2}{2}$
• D. $\frac{K{l}^2}{3}$

Answer 1

The correct option is C $\frac{K{l}^2}{2}$

$Workdone={\int }_0^{l}Fdx$
$={\int }_0^{l}Kxdx(\because force(f)=Kx)$

where $x$ is elongation in the wire
$=\frac{1}{2}K{x}^2{|}_0^l$
$=\frac{1}{2}K{l}^2-\frac{1}{2}k(0{)}^2$
$=\frac{1}{2}K{l}^2$