First slide

Elastic Modulie

Question

A cord of mass m, length L, area of cross-section A and Young's modulus y is hanging from a ceiling with the help of a rigid support. The elongation developed in the wire due to its own weight is

Moderate

A

Zero
B

$\frac{mgL}{AY}$
C

$\frac{mgL}{2 AY}$
D

$\frac{2 mgL}{AY}$

Solution

Since the entire weight mg of the wire is concentrated at it at its centre of mass which lies at the geometrical centre of the wire. So the effective original length of the wire is $\frac{L}{2}$ . According to Hooke's Law
$Y = \frac{stress}{strain}$
Y = $\frac{\frac{mg}{A}}{\frac{∆ L}{\frac{L}{2}}} \Rightarrow ∆ L = \frac{mgL}{2 AY}$

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