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

The correct option is A $\frac{1}{2}K{l}_1(2l+l_1)$

Stored potential energy $=\frac{1}{2}K{x}^2$, for an extension $x$.

Work done $=$ change in stored potential energy (by conservation of energy)

$\frac{1}{2}K(l+l_1{)}^2-\frac{1}{2}K{l}^2=\frac{1}{2}K(2l{l}_1+l_1^2)=\frac{1}{2}K{l}_1(2l+l_1)$