First slide

Elastic Modulie

Question

A rubber cord L metre long and having A m² area of cross-section is suspended vertically. If the wire extends 1 m under its own weight, then change in length (I) is (Take, density of rubber = D kgm^-3 and Young's modulus of rubber = E Nm^-2).

Moderate

A

$\frac{L^{2} D g}{2 E}$
B

$\frac{L^{2} D g}{E}$
C

$\frac{L^{2} D g}{4 E}$
D

L

Solution

Volume of the rubber cord = AL
Weight of the rubber cord = ALDg
$∴ Stress = \frac{A L D g}{A} = L D g$
The weight of the rubber cord acts at the centre of gravity which is $\frac{L}{2}$ from the top.
$∴ Strain = \frac{l}{L / 2} = \frac{2 l}{L}$
So, Youngs modulus, $E = \frac{Stress}{Strain} = \frac{L D g}{2 l / L} = \frac{L^{2} D g}{2 l} or l = \frac{L^{2} D g}{2 E}$

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