A rod of length l and radius r is held between two rigid walls so that it is not allowed to expand.

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10-1.Thermometry, Thermal Expansion and Calorimetry

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A rod of length $l$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to .........

A

$L$

B

$1 / L$

C

$r^2$

D

$r^{-2}$

Solution

(c)

$(\Delta L)$ Thermal expansion $=L \propto \Delta Q$

Where $L=$ Length original

$\propto=$ Coeffcient of linear expansion

$\Delta Q=$ Change in temperature

Or we can say

$\Delta L \propto L$

And force required to produce similar elongation can be calculated by $F=A Y \cdot \frac{\Delta L}{L} \quad[\because Y$ is constant $]$

So $F \propto r^2 \cdot \frac{\Delta L}{L}$

Also $\Delta L \propto L$

So $F$ only proportional to $r^2$

Standard 11

Physics

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