First slide

Elastic Modulie

Question

The Young’s modulus of Brass and Steel are respectively $1 .0 \times 10^{10} N / m^{2} and 2 \times 10^{10} N / m^{2}$ . A Brass wire and a Steel wire of the same length are extended by 1mm under the same force, the radii of Brass and Steel wires are $R_{B} and R_{S}$ . The relation between radii is?

Moderate

A

$R_{S} = \sqrt{2} R_{B}$
B

$R_{S} = \frac{R_{B}}{\sqrt{2}}$
C

$R_{S} = 4 R_{B}$
D

$R_{S} = \frac{R_{B}}{4}$

Solution

$\begin{array}{l} Δ l = \frac{F l}{A Y} = \frac{F l}{π R^{2} Y} \\ Δ l, l a n d F a r e s a m e \\ H e n c e, R^{2} Y = c o n s \tan t \\ R \propto \frac{1}{\sqrt{Y}} \\ \frac{R_{S}}{R_{B}} = \sqrt{\frac{Y_{B}}{Y_{S}}} = \sqrt{\frac{1}{2}} \\ ∴ R_{S} = \frac{R_{B}}{\sqrt{2}} \end{array}$

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