The ratio of Young's modulus of the material | vedclass

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Question

(A) The elastic potential energy per unit volume $(u)$ is given by the formula: $u = \frac{	ext{stress}^2}{2Y}$,where $Y$ is the Young's modulus.Give

Vedclass · Accepted Answer

$3:2$

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(A) The elastic potential energy per unit volume $(u)$ is given by the formula: $u = \frac{	ext{stress}^2}{2Y}$,where $Y$ is the Young's modulus.Given that the stress applied on both wires is the same,we have $u \propto \frac{1}{Y}$.Therefore,the ratio of elastic energy per unit volume for the two wires is:$\frac{u_1}{u_2} = \frac{Y_2}{Y_1}$.Given the ratio of Young's modulus is $\frac{Y_1}{Y_2} = \frac{2}{3}$,we substitute this into the equation:$\frac{u_1}{u_2} = \frac{3}{2}$.Thus,the ratio of elastic energy per unit volume is $3:2$.

The ratio of Young's modulus of the material of two wires is $2 : 3.$ If the same stress is applied on both,then the ratio of elastic energy per unit volume will be

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