Question:
The work done in stretching a wire by 1 mm is 2 J. The work necessary for stretching another wire of the same material but triple the radius and one third of length by 1 mm is:
The work done in stretching a wire by 1 mm is 2 J. The work necessary for stretching another wire of the same material but triple the radius and one third of length by 1 mm is:
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Work $\propto$ Radius squared / Length.
Updated On: Jun 6, 2026
- 8 J
- 27 J
- 54 J
- 18 J
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The Correct Option is C
Solution and Explanation
Step 1: Formula.
For a fixed extension, the stored work is $W = \dfrac{1}{2}\dfrac{YA}{L}(\Delta L)^2$, so with the same material and same $\Delta L$, $W \propto \dfrac{r^2}{L}$.
Step 2: Ratio.
$\dfrac{W_2}{W_1} = \left(\dfrac{r_2}{r_1}\right)^2\dfrac{L_1}{L_2} = 3^2 \times 3 = 27$.
Step 3: New work.
$W_2 = 27 \times 2 = 54$ J. \[ \boxed{54\ \text{J}} \]
For a fixed extension, the stored work is $W = \dfrac{1}{2}\dfrac{YA}{L}(\Delta L)^2$, so with the same material and same $\Delta L$, $W \propto \dfrac{r^2}{L}$.
Step 2: Ratio.
$\dfrac{W_2}{W_1} = \left(\dfrac{r_2}{r_1}\right)^2\dfrac{L_1}{L_2} = 3^2 \times 3 = 27$.
Step 3: New work.
$W_2 = 27 \times 2 = 54$ J. \[ \boxed{54\ \text{J}} \]
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