Q 11-10-008JEE MainAIEEE 2011Easy
An aluminium sphere of $20$ cm diameter is heated from $0°$C to $100°$C. Its volume changes by (coefficient of linear expansion of aluminium $= 23 \times 10^{-6}\ °\text{C}^{-1}$)
Answer: (C) $28.9$ cc
Concept. For an isotropic solid the volume coefficient is three times the linear one: $\gamma=3\alpha$, so $\Delta V=V\cdot3\alpha\Delta T$.
Step 1. Volume of the sphere (radius $10$ cm): $V=\tfrac43\pi(10)^3=4189$ cm$^3$.
Step 2. Change. $\Delta V=4189\times3\times23\times10^{-6}\times100=28.9$ cm$^3$.
Answer. Option C.
Solution by Sreeraj P, M.Sc Physics
