Question

The ratio of the lengths of two rods is $4:3$ . The ratio of their coefficients of cubical expasion is $2:3$ . Then the ratio of their liner expansions when they are heated through same temperature difference is :

• A. $2:1$
• B. $1:2$
• C. $8:9$
• D. $9:8$

Answer 1

The correct option is C $8:9$

The relation between cubical expansion coefficient and linear expansion coefficient is,

$\gamma =3\alpha$

Thus,

$\frac{{\alpha }_1}{{\alpha }_2}=\frac{{\gamma }_1}{{\gamma }_2}=\frac{2}{3}$

The linear expansion is given as,

$\Delta l=\alpha l\Delta T$

Therefore,

$\frac{\Delta l_1}{\Delta l_2}=\left(\frac{{\alpha }_1}{{\alpha }_2}\right)\times \frac{l_1}{l_2}$

$=\frac{2}{3}\times \frac{4}{3}=\frac{8}{9}$