Question

A string of length $L$ and force constant $K$ is stretched to obtain extension $l$. It is further stretched to obtain extension $l_1$.The work done in second stretching is

• A. $\frac{1}{2}k{l}_1(2l+l_1)$
• B. $\frac{1}{2}K{l}_1^2$
• C. $\frac{1}{2}K(l^2-l_1^2)$
• D. $\frac{1}{2}K\left({2l_1^2-l}^2\right)$

Answer 1

The correct option is C $\frac{1}{2}K(l^2-l_1^2)$

Work done= Final total energy-Initial Total energy

Let us assume difference in first and second extention is $l-l_1$

Workdone$=\frac{K{l}^2}{2}-\frac{K{l}_1^2}{2}$

$=\frac{1}{2}K(l^2-l_1^2)$