First slide

Elastic Modulie

Question

When a wire of uniform cross-sectional area, length l and density $ρ$ is suspended from one end, its elongation is found to be x. Then Young's modulus of its material is

Moderate

A

$ρ g l^{2} / x$
B

$\frac{2 ρ g l^{2}}{x}$
C

$ρ g l^{2} / 4 x$
D

$ρ g l^{2} / 2 x$

Solution

Mass of wire, $m = S l p$
Elongation, $x = \frac{m g . (\frac{l}{2})}{S . Y} = \frac{S l p . g . l}{2 S Y}$
$\Rightarrow Y = \frac{ρ g l^{2}}{2 x}$

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