First slide

Elastic Modulie

Question

A thick rope of rubber of length 8 m and density 1.5 X 10³kgm^-3 has Young's modulus 5 x 10⁶ 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 x 10^-5 m
C

2.4 cm
D

9.6 mm

Solution

Due to own weight, $Δ l = \frac{m g L}{2 A Y} = \frac{(L A ρ) g L}{2 A Y}$
$= \frac{L^{2} ρ g}{2 Y} = \frac{(8)^{2} (1.5 \times 10^{3}) (10)}{2 \times 5 \times 10^{6}}$
$= 9.6 \times 10^{- 2} m = 9.6 cm$

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