First slide

Elastic Modulie

Question

A wire of length L, area of cross-section A is hanging from a fixed support. The length of the wire changes
to L) when mass M is suspended from its free end. The expression for Young's modulus is [NEET 2020]

Easy

A

$\frac{Mg (I_{1} - L)}{A I}$
B

$\frac{M g L}{A L_{1}}$
C

$\frac{M g L}{A (L_{1} - L)}$
D

$\frac{M g L_{1}}{A L}$

Solution

Here, change in length, $Δ L = (L_{1} - L)$
Area =A
Force, F = Mg
Young's modulus,
$Y = \frac{Normal stress}{Longitudinal strain}$
$\Rightarrow Y = \frac{(F / A)}{(\frac{Δ L}{L})} = \frac{\frac{M g}{A}}{(\frac{L_{1} - L}{L})} = \frac{M g L}{A (L_{1} - L)}$

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