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

 $given lengths ratio is \frac{l_1}{l_2 }=\frac{5}{3} ;diameters ratio is \frac{r_1}{r_2}=\frac{2}{1}$

$$\begin{gathered} \alpha =\frac{∆l}{l∆t} as \begin{array}{l}\Delta t=same\\ \alpha =same\end{array} \\ ∆l \alpha l \\ substitute the given ratio \\ \frac{∆l_1}{∆l_2}=\frac{l_1}{l_2 }=\frac{5}{3} \end{gathered}$$

Does not depend on radius in linear expansion