First slide

Elastic Modulie

Question

A rubber rope of length 8 m is hung from the ceiling of a room. What is the increase in length of rope due to its own weight? (Young's modulus of elasticity of rubber = $5 \times 10^{6} {Nm}^{- 2} and density of rubber = 1.5 \times 10^{3} kg m^{- 3} . Take g = 10 {ms}^{- 2}$ )

Moderate

A

1.5 mm
B

6 mm
C

24 mm
D

96 mm

Solution

Y = $\frac{Mg}{A} \times \frac{\frac{L}{2}}{∆ L}$
( Length is taken as $\frac{L}{2} because weight acts at C . G .)$
Now, $M = ALρ$
[For the purpose of calculating mass, the whole of geometrical length L is to be considered]
$Y = \frac{ALρgL}{2 A ∆ L}$
or $∆ L = \frac{{ρgL}^{2}}{2 Y} = \frac{1.5 \times 10^{3} \times 10 \times 8 \times 8}{2 \times 5 \times 10^{6}} m$
= 9.6 $\times 10^{- 2} m = 9.6 \times 10^{- 2} \times 10^{3} mm$
= 96 mm

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