Question

A wire of length $L$ and density $\rho$ and Young’s modulus $Y$ is hanging from a support. Find the elongation in the length of wire at which wire will break:

• A. $\frac{L^2\rho g}{Y}$
• B. $\frac{L^2\rho g}{4Y}$
• C. $\frac{L^2\rho g}{2Y}$
• D. $\frac{2L^2\rho g}{Y}$

Answer 1

The correct option is A $\frac{L^2\rho g}{Y}$

Calculate breaking stress of wire.
Formula used: $\sigma =\frac{F}{A}$
Given, length of wire =$L$
Density of the wire = $\rho$
and Young’s modulus =$Y$
Let the breaking stress of wire be 𝜎
Therefore,
$\sigma =\frac{F}{A}=\frac{\rho ALg}{A}$
$\sigma =\rho Lg$
Calculate elongation length of wire.
Formula used: $Y=\frac{\text{stress}}{\text{strain}}$
Let the elongation in the wire be $l$.
As we know, the young modulus will be
$Y=\frac{\text{stress}}{\text{strain}}$
$Y=\frac{\rho L^{2}g}{l}$
$l=\frac{\rho L^{2}g}{Y}$