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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
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B
4.0×1011
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C
2.0×1011
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D
0.02×109
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Solution

The correct option is A $$2.0 \times 10^{12}$$
For  equilibrium
Weight = 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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