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Question

How much force is required to produce an increase of $$0.2\%$$ in the length of a brass wire of diameter $$0.6\ mm$$? (Young's modulus for brass $$= 0.9 \times 10^{11} N / m^2$$) 


A
Nearly 17 N
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B
Nearly 34 N
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C
Nearly 51 N
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D
Nearly 68 N
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Solution

The correct option is B Nearly $$51\ N$$
From Young's modulus relation,
$$Y=\dfrac{F/A}{\Delta L/L}$$
$$\implies F=YA(\dfrac{\Delta L}{L})$$
$$=0.9\times 10^{11}\times \pi (0.0003)^2\times 0.002=50.8\ N\approx 51\ N$$

Physics

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