First slide

Stress and strain

Question

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

Moderate

A

9.6 cm
B

$19.2 \times 10^{- 5} m$
C

2.4 cm
D

5.6 cm

Solution

$Due to own weight, ΔI = \frac{mgL}{2 AY} = \frac{({LA}_{ρ}) gL}{2 AY}$
$\begin{array}{l} = \frac{L^{2} ρg}{2 Y} = \frac{(8)^{2} (1.5 \times 10^{3}) (10)}{2 \times 5 \times 10^{8}} \\ = 9.6 \times 10^{- 2} m = 9.6 cm \end{array}$

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