Q. An aluminium sphere of 20 cm diameter is heated from $0{^\circ}C$ to $100{^\circ}C$.Its volume changes by (given that coefficient of linear expansion for aluminium $(\alpha_{Al} = 23 \times 10^{- 6}/℃)$
A) 28.9 cc
B) 2.89 cc
C) 9.28 cc
D) 49.8 cc
Explanation
(a) Cubical expansion
$\ \ \ \ \ \ \mathrm{\Delta}V\ = \ \gamma V\mathrm{\Delta}T$
$\ \ \ \ \ \ \mathrm{\Delta}V\ = \ 3\alpha V\mathrm{\Delta}T$
= $3 \times 23 \times 10^{- 6} \times \ \left( \frac{4}{3}\pi \times 10^{3} \right) \times 100$
= 28.9cc
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.