Question

A vertical column 50 cm long at ${50}^{c}irc$ C balances another column of same liquid 60 cm long at ${100}^{c}irc$°C. The coefficient of absolute expansion of the liquid is

• A. 0.005/°C
• B. 0.0005/°C
• C. 0.002/°C
• D. 0.0002/°C

Answer 1

The correct option is A

0.005/°C

$\frac{h_1}{h_2}=\frac{{\rho }_1}{{\rho }_2}=\frac{(1+\gamma {\theta }_1)}{1+\gamma {\theta }_2}$ $[\because \rho =\frac{{\rho }_0}{(1+\gamma \theta )}]$

$\Rightarrow \frac{50}{60}=\frac{1+\gamma \times 50}{1+\gamma \times 100}\Rightarrow \gamma =0.005{/}^{\circ }C$