NTA Abhyas JEE Main2020PhysicsThermal Properties of MatterPractice
Two solid spheres A and B made of the same material have radii r A a n d r B respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of A and B is
Options
- Ar A r B
- Br B r A
- Cr A 2 r B 2
- Dr B 2 r A 2
Correct answer
B. r B r A
Step-by-step solution
4 π 3 r 3 ρ c - d T d t = σ 4 π r 2 ( T 4 - T 0 4 ) ∴ - d T d t = 3 σ ρ r c T 4 - T 0 4 = H (say) Ratio of rates of fall of temperature H A H B = r B r A