A work of $2 imes 10^{- 2}\ $J is done on a wire of length 50 cm and area of cross-section 0.5$mm^{2}$. If the Young’s modulus of the material of the wire is $2 imes 10^{10}{Nm}^{- 2}$ , then the wire must be

Question

A work of $2 	imes 10^{- 2}\ $J is done on a wire of length 50 cm and area of cross-section 0.5$mm^{2}$. If the Young’s modulus of the material of the wire is $2 	imes 10^{10}{Nm}^{- 2}$ , then the wire must be

Dr. Abubacker · Accepted Answer

(c) The work done by wire is stored as potential energy in the wire
$U = \frac{1}{2} 	imes {Young}^{'}s\ modulus\  	imes (strain)^{2}$
Given, $Y = 2 	imes 10^{10}{Nm}^{- 2}$
Strain$= \frac{l}{L} = \frac{l}{50 	imes 10^{- 2'}}U = 2 	imes 10^{- 2}J$
$	herefore$ $2 	imes 10^{- 2} = \frac{1}{2} 	imes 2 	imes 10^{10} 	imes \left( \frac{l}{50 	imes 10^{- 2}} ight)^{2}$
⟹ $l \approx 0.707\ mm$ (stretched)

Q. A work of $2 \times 10^{- 2}\ $J is done on a wire of length 50 cm and area of cross-section 0.5$mm^{2}$. If the Young’s modulus of the material of the wire is $2 \times 10^{10}{Nm}^{- 2}$ , then the wire must be

Explanation

Reviewed by Dr. Abubacker

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