Question

The Young's modulus of a rubber string $8cm$ long and density $1.5kg/m^3$ is $5\times {10}^{8}N/m^2$, is suspended on the ceiling in a room. The increase in length due to its own weight will be ?

• A. $9.6\times {10}^{-5}m$
• B. $9.6\times {10}^{-11}m$
• C. $9.6\times {10}^{-3}m$
• D. $9.6m$

Answer 1

Answer: (B)

$9.6\times {10}^{-11}m$

$\begin{array}{cc}\text{mass of string}& =\rho \times V\\ & =\rho \times A\times l\\ \frac{F}{A}& =Y\frac{\Delta l}{l}\end{array}$

$\Rightarrow \Delta l=\frac{Fl}{AY}=\frac{\left(\rho Al\right)g\left(l/2\right)}{AY}$

$\begin{array}{c}=\frac{\rho g{l}^2}{2Y}\\ =\frac{1\cdot 5\times 9.8\times {(8\times {10}^{-2})}^2}{2\times 5\times {10}^8}\\ =\frac{960\times {10}^{-4}}{{10}^9}\\ =960\times {10}^{-13}\\ =9.6\times {10}^{-11}m.\end{array}$