Two wires A and B of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is $\frac{3}{2}$ times of that of wire B. The ratio of the forces produced in two wires will be

\frac{2}{3}

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\frac{9}{4}

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\frac{4}{9}

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\frac{3}{2}

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Solution

The correct option is D $\frac{3}{2}$
$F = Y A α Δ θ$
If y, A and $Δ θ$ are constant then $\frac{F_{A}}{F_{B}} = \frac{α_{A}}{α_{B}} = \frac{3}{2}$

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Two wires A and B of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is 32 times of that of wire B. The ratio of the forces produced in two wires will be

The correct option is D 32F=YAαΔθ If y, A and Δθ are constant then FAFB=αAαB=32

Two wires A and B of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is $\frac{3}{2}$ times of that of wire B. The ratio of the forces produced in two wires will be

The correct option is D $\frac{3}{2}$
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If y, A and $Δ θ$ are constant then $\frac{F_{A}}{F_{B}} = \frac{α_{A}}{α_{B}} = \frac{3}{2}$