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Longitudinal Stress

A stone of ma...

Question

A stone of mass m is attached to one end of a wire of cross-sectional area A and young's modulus Y. The stone is revolved in a horizontal circle at a speed such that the wire makes an angle $θ$ with the vertical. The strain produced in the wire will be,

A

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B

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C

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D

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Solution

The correct option is B

T cos $θ$ = mg

$\Rightarrow$ T = $\frac{m g}{c o s θ}$

Increase in the length of wire is, $Δ$ l = $\frac{T L}{A Y}$

Strain = $\frac{Δ l}{L}$ = $\frac{m g}{A Y c o s θ}$

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