Question

Two wire of same radius and length are subjected to the same load, One wire is of steel and the other is copper. If Young's modulus of steel is twice that of copper, then the ratio of elastic energy stored per unit volume of steel to that of copper wire is

• A. $2:1$
• B. $1:2$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is B $1:2$

$Y_S=2Y_C$, then the ratio of elastic energy stored per unit volume.

$E=\frac{1}{2}\frac{{YL}^2\alpha }{L}$

or, $\frac{E}{l^2\alpha }=\frac{1}{2}\frac{Y}{L}$

Since same length and same radius.

$\frac{E^1}{l^2\alpha }=\frac{1}{2}\frac{Y_C}{L}$

$\frac{E^{11}}{l^2\alpha }=\frac{1}{2}\times \frac{2Y_C}{L}$

$\frac{E^1}{E^{11}}=\frac{1}{2}$.