Q. The volume of a metal sphere increases by 0.24% when its temperature is raised by 40$℃$ . The coefficient of linear expansion of the metal is …$/℃$.
A) $2 \times 10^{- 5}$
B) $6 \times 10^{- 5}$
C) $18 \times 10^{- 5}$
D) $1.2 \times 10^{- 5}$
Explanation
(a) Change in volume, $\mathrm{\Delta}V = V\gamma\ \mathrm{\Delta}t$
$\Rightarrow$ $0.24 = 100 \times \gamma \times 40$
$\gamma = \frac{0.24}{100 \times 40}$
$= 0.00006 = 6 \times 10^{- 5}$
$\alpha = \ \frac{\gamma}{3}$
$\Rightarrow$ $\alpha = 2 \times 10^{- 5}℃^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.