Question

A load of $$4.0\ kg$$ is suspended from a ceiling through a steel wire of length $$20\ m$$ and radius $$2.0\ mm$$. It is found that the length of the wire increases by $$0.031\ mm$$ as equilibrium is achieved. If $$g=3.1\ x\ \pi\ ms^{-2}$$, the value of young's modulus in $$Nm^{-2}$$ is

A
2.0×1012
B
4.0×1011
C
2.0×1011
D
0.02×109

Solution

The correct option is A $$2.0 \times 10^{12}$$For  equilibriumWeight = Tension$$mg = T$$$$\therefore T = 4 \times 3.1 \pi$$$$= 12.4\pi N$$  (as can be inferred from the question)$$Y = \dfrac{T/A}{\triangle l/l}$$$$= \dfrac{12.4 \pi / \pi (\dfrac{2}{1000})^{2}}{\dfrac{0.031}{1000}/20}$$$$= \dfrac{12.4 \times 20 \times 1000 \times (1000)^{2}}{4 \times 0.031}$$$$=2 \times 10^{12} N/m^{2}$$Physics

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