Q. The coefficient of volumetric expansion of mercury is $18 \times 10^{- 5}/℃.$ A thermometer bulbs has a volume $10^{- 6}m^{3}$ and cross section of stem is $0.004\ cm^{2}.$ Assuming that bulb is filled with mercury at $0℃$ then the length of the mercury column at $100℃$ is
A) $18.8\ mm$
B) $9.2\ mm$
C) $7.4\ cm$
D) $4.5\ cm$
Explanation
(d) $V = V_{0}(1 + \gamma\mathrm{\Delta}\theta) \Rightarrow Change\ in\ volume$
$V - V_{0} = \mathrm{\Delta}V = A.\mathrm{\Delta}l = V_{0}\gamma\mathrm{\Delta}\theta$
$\Rightarrow \mathrm{\Delta}l = \frac{V_{0}.\gamma\mathrm{\Delta}\theta}{A} = \frac{10^{- 6} \times 18 \times 10^{- 5} \times (100 - 0)}{0.004 \times 10^{- 4}}$
$= 45 \times 10^{- 3}m = 4.5\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.