Q. Density of substance at 0$℃$ is $10\ g/cc$ and at 100$℃$, its density is 9.7 g/cc. The coefficient of linear expansion of the substance is
A) 1.03 $\times 10^{- 4}$
B) 3 $\times 10^{- 4}$
C) 19.7 $\times 10^{- 3}$
D) $10^{- 3}$
Explanation
(a) Here, $\rho_{0} = 10g/cc$
$\rho_{100} = 9.7g/cc,\ \alpha = \ ?$
From $\rho_{0} = \ \rho_{100}(1 + \gamma \times 100)$
$\gamma = \ \frac{\rho_{0} - \ \rho_{100}}{\rho_{100} \times 100} = \ \frac{10 - 9.7}{9.7 \times 100} = 3.09 \times 10^{- 4}$
$\alpha = \frac{\gamma}{3} = \frac{3.09 \times 10^{- 4}}{3}$=1.03$\times 10^{- 4}℃^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.