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  • 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

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 \mathrm{ \theta} with the vertical. The strain produced in the wire will be.

Option: 1

\mathrm{\frac{m g \cos \theta}{A Y}}


Option: 2

\mathrm{\frac{m g}{A Y \cos \theta}}


Option: 3

\mathrm{\frac{m g \sin \theta}{A Y}}


Option: 4

\mathrm{\frac{m g}{A Y \sin \theta}}


Answers (1)

best_answer

For vertical equilibrium

\mathrm{ T \cos \theta=m g }
or        \mathrm{ T=\frac{m g}{\cos \theta} }

If L is the original length of the wire, the increase in length is

\mathrm{ \begin{aligned} l & =\frac{T L}{A Y} \\\\ \therefore \quad \text { Strain } & =\frac{l}{L}=\frac{T}{A Y}=\frac{m g}{A Y \cos \theta} \end{aligned} }

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Rishi

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