question_answer

An Indian rubber cord 'L' metres long and area of cross section \[A({{m}^{2}})\]is suspended vertically. Density of rubber is \[\rho \,\,kg/{{m}^{3}}\]and young's modulus of rubber is\[Y\,N/{{m}^{2}}\]. If the rod extends \[\ell \] metres under its own weight, then extension \[\Delta \ell \] is:

A) \[\frac{{{L}^{2}}\rho g}{Y}\]              

B) \[\frac{{{L}^{2}}\rho g}{2Y}\]

C) \[\frac{{{L}^{2}}\rho g}{4Y}\]            

D) \[\frac{Y}{{{L}^{2}}\rho g}\]

Correct Answer: B

Solution :

[b] \[Y=\frac{FL}{A\,\Delta \ell }\] \[Y=\frac{mg}{2}\frac{L}{A\,\Delta \ell }m=V\ell \] \[Y=\frac{AL}{2A}\frac{\ell Lg}{\Delta \ell }m=AL\ell \] \[\Delta \ell =\frac{g{{L}^{2}}\ell }{zY}\]