Question

A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight. ( [Density of rubber is $1500\left(kg/m^3\right),Y=5\times {10}^{8}N/m^2)$

• A. 0.3 mm
• B. 0.15 mm
• C. 0.015 mm
• D. 0.03 mm

Answer 1

The correct option is B 0.15 mm

$\begin{array}{c}\text{According to the question,}\\ \text{length of cord}=10m\\ \text{Density of rubber}=1500kg/m^3\\ \text{young's Modulus}=5\times {10}^{8}N/m^2\end{array}$

$Stress=Weight/area=mg/A=\left(\rho Ag\right)/A=\rho g$ and
$strain=\delta L/L⟹$ change in length = $\rho gL/Y$
Also the length to be considered here is from the centre of gravity to the point of suspension, since the entire mass is assumed to be concentrated at the centre
Substituting the values, we get, extension = $(1500\times 10\times 5)/(5\times {10}^8)=0.15mm$
The correct option is (b)