Force constants of two wires A and B of the same material are k and 2k, respectively. If the two wires
are stretched equally, then the ratio of work done in stretching $\left(\frac{W_A}{W_B}\right)$ is 

Solution:

Work done in a stretched wire, $W=\frac{1}{2}k{x}^2$

Given,    $k_A=k\text{ and }{k}_B=2k$

$\Rightarrow W_A=\frac{1}{2}k{x}^2$

and   $W_B=\frac{1}{2}\left(2k\right)x^2=k{x}^2$

Hence, the ratio of work done in stretching the wires.

$\frac{W_A}{W_B}=\frac{(1/2)k{x}^2}{k{x}^2}\Rightarrow \frac{W_A}{W_B}=\frac{1}{2}$