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

Rate of energy loss is same in all the cases, so `(dQ)/(dt)=k" so",ms(d theta)/(dt)=k`
So, `(d theta)/(dt)=(k)/(ms)=(k)/((rhos)v)=(k)/(rhos)"So",((d theta)/(dt))_(A):((d theta)/(dt))_(B):((d theta)/(dt))_(C):((d theta)/(dt))_(D)=(1)/(6):(1)/(18):(1)/(10):(1)/(4)`