First slide

Elastic Modulie

Question

If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is

Moderate

A

$\frac{2 a^{2} c}{b}$
B

$\frac{3 a}{2 b^{2} c}$
C

$\frac{2 ac}{b^{2}}$
D

$\frac{3 c}{2 {ab}^{2}}$

Solution

$T_{S} = 3 mg$
$\frac{3 mg}{A_{s}} = y_{S} \times \frac{∆ l_{S}}{l_{S}}$
$\frac{2 mg}{A_{b}} = y_{b} \times \frac{∆ l_{b}}{l_{b}}$
$\frac{∆ l_{s}}{∆ l_{b}} = \frac{3}{2} \times \frac{l_{s}}{l_{b}} \times \frac{A_{b}}{A_{S}} \times \frac{y_{b}}{y_{S}} = \frac{3}{2} \times \frac{a}{b^{2} c}$

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