Force constants of two wires A and B of the same material are k and 2k, respectively. If the two wiresare stretched equally, then the ratio of work done in stretching WAWB is

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

1. A

$\frac{1}{3}$

2. B

$\frac{1}{2}$

3. C

$\frac{3}{2}$

4. D

$\frac{1}{4}$

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### Solution:

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

Given,

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

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

$\frac{{W}_{A}}{{W}_{B}}=\frac{\left(1/2\right)k{x}^{2}}{k{x}^{2}}⇒\frac{{W}_{A}}{{W}_{B}}=\frac{1}{2}$

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