A bimetallic strip is formed out of two identical strips, one of copper and other of brass. coeffici

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10-1.Thermometry, Thermal Expansion and Calorimetry

hard

A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are ${\alpha _C}$ and ${\alpha _{B}}.$ On heating, the temperature of the strip goes up by $\Delta T$ and the strip bends to form an arc of radius of curvature $R.$ Then $R$ is

Proportional to $\Delta T$

Inversely proportional to $\Delta T$

Inversely proportional to $|{\alpha _B} - {\alpha _C}|$

Both $(B)$ and $(C)$

(IIT-1999)

Solution

(d) Let $L_0$ be the initial length of each strip before heating.

Length after heating will be

${L_B} = {L_0}(1 + {\alpha _B}\Delta T) = (R + d)\theta $

${L_C} = {L_0}(1 + {\alpha _C}\Delta T) = R\theta $

==> $\frac{{R + d}}{R} = \frac{{1 + {\alpha _B}\Delta T}}{{1 + {\alpha _C}\Delta T}}$

==> $1 + \frac{d}{R} = 1 + ({\alpha _B} – {\alpha _C})\Delta T$

==> $R = \frac{d}{{({\alpha _B} – {\alpha _C})\Delta T}}$ ==> $R \propto \frac{1}{{\Delta T}}$ and $R \propto \frac{1}{{({\alpha _B} – {\alpha _C})}}$

Standard 11

Physics

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(JEE MAIN-2017)

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hard

(JEE MAIN-2019)

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medium

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medium

Solution

Similar Questions

In an experiment to find the liquid expansion coefficient $(\gamma)$ a column. of experimental liquid at $T\,^oC$ is balanced against another column of experimental liquid at $0\, ^o C$ by taking them in $U-$ tube. The expansion coefficient $(\gamma)$ is ?

The coefficient of volume expansion of glycerin is $49 \times 10^{-5} \;K ^{-1} .$ What is the fractional change in its density for a $30\,^{\circ} C$ rise in temperature?

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