Question

A wire of length L and Density $\varphi$ and young's modulus Y is hanging from a support .Find the elongation in the length of the wire at which wire will break:

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

Answer 1

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

A wire of length $L$ and density $\varphi$ and young's modulus $Y$ is hanging from the support.

lets area $A=L^2$

The force is $F=mg$. . . . .(1)

Young's modulus, $Y=\frac{F/A}{\Delta L/L}$

$Y=\frac{mg/L^2}{\Delta L/L}$ (from equation 1)

$\Delta L=\frac{mg/L}{Y}$. . . .(2)

we know that, density $\varphi =\frac{m}{L^3}$

$m=\varphi L^3$ put in equation (2)

$\Delta L=\frac{\varphi L^{2}g}{Y}$ elongation in length.

The correct option is A.