Question

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

• A. $\frac{1}{2}$
• B. $\frac{3}{2}$
• C. $\frac{1}{4}$
• D. $\frac{1}{3}$

Answer 1

Answer: (A)

$\frac{1}{2}$

Work done in stretching a wire by length $x$ is $\frac{1}{2}k{x}^2$.

Hence $W_A=\frac{1}{2}\left(K\right)x^2$

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

$⟹\frac{W_A}{W_B}=\frac{1}{2}$