Q. A vertical column 50 cm long at 50$℃\ $ balances another column of liquid 60 cm long at 100$℃$. The coefficient of absolute expansion of the liquid is
A) 0.005$℃^{- 1}$
B) 0.0005$℃^{- 1}$
C) 0.002$℃^{- 1}$
D) 0.0002$℃^{- 1}$
Explanation
(a) Here, $h_{1} = 50\ cm,\ t_{1} = 50℃$
$h_{2} = 60\ cm,\ t_{2} = 100℃$
Now, $\frac{h_{1}}{h_{2}}\ \ = \frac{d_{2}}{d_{1}} = \ \frac{d_{0}}{1 + \gamma t_{2}} \times \ \frac{1 + \gamma t_{1}}{d_{0}}$
$\frac{50}{60}\ = \ \frac{1 + \gamma \times 50}{1 + \gamma \times 100}$
$\therefore\ \gamma = \frac{1}{200} = 0.005℃^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.