Exam

JEE Main

Subject

Physics

Chapter

Mechanical Properties of Solids

JEE Main · Physics · Mechanical Properties of Solids

A rubber cord of density d, Young's modulus Y and length L is...

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

Step-by-step solution

$∵$ Young's modulus $Y = \dfrac{Stress}{Strain}$

$Y = \dfrac{\left(\dfrac{F}{A}\right)}{\left(\dfrac{∆ L}{L}\right)}$

$⇒ ∆ l = \dfrac{FL}{AY}$

extennsion in $dx$ at $‘x’$

$de = \dfrac{xdAg\left(dx\right)}{AY}$

total extension $e = \mathop{∫}_{0}^{L}\dfrac{xdAg\left(dx\right)}{AY}$

$= \dfrac{dg}{Y}\dfrac{L^{2}}{2}$

$0.5L = \dfrac{dgL^{2}}{Y 2} ⇒ L = \dfrac{Y}{dg}$