Question

A rubber cord of density $d,$ Young’s modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5\, L$ under its own weight, then $L$ is

• A. $\frac{Y}{2dg}$
• B. $\frac{Y}{dg}$
• C. $\frac{2Y}{dg}$
• D. $\frac{dg}{2Y}$
• E. $\frac{dg}{Y}$

Answer 1

Answer: (B)

$\because$ Young's modulus, $Y=\frac{\text { Stress }}{\text { Strain }}$
$Y=\frac{\left(\frac{F}{A}\right)}{\left(\frac{\Delta L}{L}\right)}\,...(i)$
$\because$ Force exerted due to its own weight $=\frac{m g}{2}$
$\therefore Y=\frac{\left(\frac{m g}{2}\right)}{A\left(\frac{0.5}{L}\right)}=\left(\frac{m g}{A L}\right)$
So $L=\frac{Y}{\left(\frac{m g}{A L}\right)}=\frac{Y}{d g}\left(\because \frac{m}{A L}=d\right)$