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 suspending on the ceiling in a room. The increase in the 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

The correct option is B. $9.6\times {10}^{-11}m$.

We know that,

$Y=\frac{F/A}{\frac{\Delta l}{l}}$ and $F=\frac{Mg}{2}$

$\Rightarrow \Delta l=\frac{FA}{AY}$ and $F=\frac{Al\rho g}{2}$

$\Rightarrow \Delta l=\frac{Al\rho gl}{2AY}=\frac{\rho l^{2}g}{2Y}$

$\Rightarrow \Delta l=\frac{1.5\times 64\times {10}^{-4}\times 10}{2\times 5\times {10}^8}$

$\Rightarrow \Delta l=9.6\times {10}^{-11}m$.