Q134 / 160 · AP EAMCET 2024 (19 May Shift 2) · Physics

If the work done in stretching a wire by 1 mm is 2 J , the work necessary for stretching another wire of same material but with double radius of cross section and half the length by 1 mm is

Correct answer
A
16 J
B
8 J
C
4 J
D
$\frac{1}{4} \mathrm{~J}$

Solution

Work done in stretching a wire is $\begin{aligned} & \mathrm{w}=\frac{1}{2} \mathrm{kx}^2=\frac{1}{2}\left(\frac{\mathrm{YA}}{1}\right) \mathrm{x}^2 \Rightarrow \mathrm{w} \propto \frac{\mathrm{A}}{1} \\ & \therefore \frac{\mathrm{w}_2}{\mathrm{w}_1}=\left(\frac{\mathrm{r}_2}{\mathrm{r}_1}\right)^2\left(\frac{\mathrm{l}_1}{\mathrm{l}_2}\right)=(2)^2(2)=8 \\ & \therefore \quad \mathrm{w}_2=8 \mathrm{w}_1=8 \times 2=16 \mathrm{~J}\end{aligned}$

Hence, the correct answer is option: 'A'.

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