Question

A vessel contains a liquid filled upto $\frac{1}{10}$th of its volume. Another vessel contains same liquid upto $\frac{1}{8}$th of its volume. In both cases volume of empty space remains constant at all temperatures. Then the ratio of the coefficients of the cubical expansion of the two vessels is

• A. $2:5$
• B. $5:2$
• C. $4:5$
• D. $5:4$

Answer 1

Answer: (C)

$4:5$

Increase in volume of vessel = Increase in volume ofliquid

${\gamma }_1\times V_1={\gamma }_2\times V_2$

$\therefore \frac{{\gamma }_1}{{\gamma }_2}=\frac{V_2}{V_1}=\frac{\frac{1}{10}}{\frac{1}{8}}=\frac{8}{10}=\frac{4}{5}$