A metal rod of Young’s modulus $2\ imes 10^{10}\ Nm^{- 2}\ $undergoes an elastic strain of 0.06%. The energy per unit volume stored in J $m^{- 3}\ is$

Question

A metal rod of Young’s modulus $2\ 	imes 10^{10}\ Nm^{- 2}\ $undergoes an elastic strain of 0.06%. The energy per unit volume stored in J $m^{- 3}\ is$

Dr. Abubacker · Accepted Answer

(a) Energy / volume = $\frac{1}{2}\  	imes stress\  	imes strain\ $
= $\frac{1}{2}Y 	imes strain 	imes strain = \frac{1}{2}Y\  	imes strain^{2}$
= $\frac{1}{2} 	imes 2 	imes 10^{10} 	imes 0.06\  	imes 10^{- 2} 	imes 0.06\  	imes 10^{- 2}$
= $3600\ J\ m^{- 3}$

Q. A metal rod of Young’s modulus $2\ \times 10^{10}\ Nm^{- 2}\ $undergoes an elastic strain of 0.06%. The energy per unit volume stored in J $m^{- 3}\ is$

Explanation

Reviewed by Dr. Abubacker

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