First slide

Elastic Modulie

Question

The Young's modulus of brass and steel are respectively 10 x 10¹⁰N ,/ m² and z x 10¹⁰ N / m^2. A brass wire and a steel wire of the same length are extended by 1 mm under the same force, the radii of brass and steel wires are R_B and R_srespectively. Then

Moderate

A

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

$R_{s} = R_{B} / \sqrt{2}$
C

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

$R_{s} = R_{B} / 4$

Solution

We know that, $Y = FL / {πr}^{2} l$
$∴ r^{2} = FL / (Yπl)$
or $R_{B}^{2} = FL / (Y_{B} πl)$
and $R_{S}^{2} = FL / (Y_{S} πl)$
$\begin{aligned} \frac{R_{B}^{2}}{R_{S}^{2}} = \frac{Y_{S}}{Y_{B}} = \frac{2 \times 10^{10}}{10^{10}} = 2 \\ R_{B}^{2} = 2 R_{S}^{2} or R_{B} = \sqrt{2} R_{S} \end{aligned}$
or $R_{S} = R_{B} / \sqrt{2}$

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