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MHT CET 2019 (2 May, Shift 1) · Elastic Potential Energy

Elastic Potential Energy question from MHT CET 2019 (2 May, Shift 1)

Q12MHT CET 2019 · 2 MAY · SHIFT 1Medium

Elastic Potential Energy

Work done in stretching a wire through 1 mm is 2 J. What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross section, by 1 mm?

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Answer: (d)

$W = \dfrac{YAx^2}{2L} = \dfrac{Y\pi r^2 x^2}{2L}$ , so for the same $x$ , $W \propto \dfrac{r^2}{L}$ .
$\dfrac{W_2}{W_1} = \dfrac{(2)^2}{1/2} = 8$
$W_2 = 8 \times 2 = 16\text{ J}$
So the answer is (d) 16 J.

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