First slide

Thermal expansion

Question

Two iron rods have their lengths in the ratio 5:3 and diameters in the ratio 2:1. When the rods are heated from $30^{0} C$ to $100^{0} C$ the ratio of their expansions is

Moderate

A

5:3
B

3:5
C

5:6
D

6:5

Solution

$g i v e n l e n g t h s r a t i o i s \frac{l_{1}}{l_{2}} = \frac{5}{3}; d i a m e t e r s r a t i o i s \frac{r_{1}}{r_{2}} = \frac{2}{1} \begin{array}{l} Δ t = s a m e \\ α = s a m e \end{array} α = \frac{∆ l}{l ∆ t} a s \begin{array}{l} Δ t = s a m e \\ α = s a m e \end{array} ∆ l α l s u b s t i t u t e t h e g i v e n r a t i o \frac{∆ l_{1}}{∆ l_{2}} = \frac{l_{1}}{l_{2}} = \frac{5}{3}$
Does not depend on radius in linear expansion

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