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

Work done in stretching $=U_2-U_1$
U(Potential energy)$=\frac{1}{2}k{x}^2$
$\therefore$ x = extension from natural length
$U_2=\frac{1}{2}\times k{l}_1^2$
$U_1=\frac{1}{2}\times k{l}^2$
Work done $=\frac{k}{2}[l_1^2-l^2]$