Question

The Young's modulus of a rubber string 8 cm long and density 1.5 $kg/m^3$ 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. 9.6 m

Answer 1

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

$y=5\times {10}^{8}N/m^2;a=g;l=8cm=8\times {10}^{-2}m;d=1.5kg/m^3$

$y=\frac{stress}{strain}=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}=\frac{\frac{F\times d}{A\times d}}{\frac{\Delta l}{l}}=\frac{\frac{F\times d}{v}}{\frac{\Delta l}{l}}=\frac{F\times d\times l}{v\times \Delta l}=dg\times \frac{A}{dl}$

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

$\Delta l=\frac{1.5\times 64\times {10}^{-4}\times 10}{2\times 5\times {10}^8}=\frac{0.3\times 64\times {10}^{-12}\times 10}{2}$

$\therefore \Delta l=9.6{10}^{-11}m$