Question

A thick uniform rubber rope of density $1.5gc{m}^{-3}$ and Young's modulus $5\times {10}^6$ $N{m}^{-2}$ has a length of $8m$. When hung from the ceiling of a room, the increase in length of the rope due to its own weight will be

• A. $9.6\times {10}^{-2}$
• B. $19.2\times {10}^{-2}$
• C. $9.6\times {10}^{-3}$
• D. $9.6$

Answer 1

Answer: (B)

$19.2\times {10}^{-2}$

The youngs modulus $Y$ is defined as $Y=\frac{FL}{Ax}$ , where $F$ is force apllied , $L$ is original length $x$ is change in length and $\sigma =$density of the wire.

$\Rightarrow x=\frac{\sigma L^{2}g}{AY}(\therefore F=mg=\sigma \times A\times L\times g)$

$\Rightarrow x=\frac{\sigma L^{2}g}{Y}=\frac{1.5\times {10}^{-3}\times 64\times 10}{5\times {10}^6}=19.2\times {10}^{-2}$

Therefore option $B$ is correct