Question

The Young's modulus 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 increases in length due to its own weigth 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

Given that,

Length of rubber band, $l=8cm$

Density, $d=1.5Kg/m^3$

Young’s modulus, $Y=5\times {10}^{8}N/m^2$

The relation for increase in length and young’s modulus is as follows:

$l=\frac{L^{2}dg}{2Y}$

$l=\frac{{(8\times {10}^{-2})}^{2}1.5\times 10}{2\times 5\times {10}^8}$

$l=\frac{64\times {10}^{-4}\times 1.5\times 10}{{10}^9}$

$l=96\times {10}^{-12}$

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