The Young’s modulus of brass and steel are $10\ imes 10^{10}\ Nm^{- 2}\ and\ 2 imes 10^{11}\ Nm^{- 2}$ respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are $R_{B}\ and\ R_{S}\ $respectively. Then

Question

The Young’s modulus of brass and steel are $10\ 	imes 10^{10}\ Nm^{- 2}\ and\ 2 	imes 10^{11}\ Nm^{- 2}$ respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are $R_{B}\ and\ R_{S}\ $respectively. Then

Dr. Abubacker · Accepted Answer

(b) $Y = \frac{F}{\pi R^{2}}\  	imes \frac{l}{\mathrm{\Delta}l}$
$F,\ l\ and\ \mathrm{\Delta}l$ are constants.
$	herefore\ \ R^{2}\  \propto \frac{1}{Y}$
$\frac{R_{S}^{2}}{R_{B}^{2}}\  = \frac{Y_{B}}{Y_{S}} = \ \frac{10^{11}}{2\  	imes 10^{11}} = \frac{1}{2}$
Or $\frac{R_{S}}{R_{B}} = \frac{1}{\sqrt{2\ }}\ \ or\ \ R_{S} = \frac{R_{B}}{\sqrt{2}}\ $

Q. The Young’s modulus of brass and steel are $10\ \times 10^{10}\ Nm^{- 2}\ and\ 2 \times 10^{11}\ Nm^{- 2}$ respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are $R_{B}\ and\ R_{S}\ $respectively. Then

Explanation

Reviewed by Dr. Abubacker

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