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

Answer 1

Answer: (D)

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

Work done in stretching a string to obtain an extension $l$ is

$W_1=\frac{1}{2}K{l}^2$

Similarly, work done in stretching a string to obtain extension $l_1$ is

$W_2=\frac{1}{2}K{l}_1^2$

$\therefore$ Work done in second case $=W_2-W_1=\frac{1}{2}K(l_1^2-l^2)$