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(C) The work done in stretching a rod is equal to the elastic potential energy stored in it.The formula for the work done $(W)$ is given by:$W = \frac

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$y^2$

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(C) The work done in stretching a rod is equal to the elastic potential energy stored in it.The formula for the work done $(W)$ is given by:$W = \frac{1}{2} 	imes 	ext{Force} 	imes 	ext{Elongation}$From Hooke's Law,the force $(F)$ required to produce an elongation $(y)$ in a rod of length $L$ and area $A$ is:$F = \frac{Y A y}{L}$Substituting this into the work formula:$W = \frac{1}{2} 	imes \left( \frac{Y A y}{L} ight) 	imes y$$W = \frac{1}{2} \frac{Y A}{L} y^2$Since $Y$,$A$,and $L$ are constants for a given rod,we have:$W \propto y^2$Therefore,the work done is proportional to $y^2$.

$A$ metallic rod of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y$. If the rod is elongated by an amount $y$,then the work done is proportional to ......

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