Four spheres A, B, C and D of different metals but all same radius are kept at same temperature. The ratio all their densities and specific heats are `2:3:5:1` and `3:6:2:4`. Which sphere will show the fastest rate all cooling (initially) (assume black body radiation for all of them)

Options

A. A
B. B
C. C
D. D

Answer

D

Explanation

Since, radius or volume of all the four spheres are equal, the ratio of their masses will be 2 : 3 : 5 : 1.
Heat capacity = (mass) (specific heat)
`therefore` Ratio of heat capacities will be 6 : 18 : 10 : 4. The sphere having the minimum heat capacity will show the fastest rate of cooling.
`therefore` correct option is (4)