A solid sphere of copper of radius R and a hollow sphere of the same materail of inner radius r and outer radius A are heated to the same temperature and allowed to cool in the same environment. Which of tehm starts cooling faster?

Explanation

The surface area, emissivity and temperature and ambient temperature are same for both the sphere. The net rate of heat radiation by both the spheres is equal to
`(dQ)/(dt) = sigma e A (T^4 - T_0^4) ` ...(i)
Rate of heat radiation is equal to rate of heat loss due to decrease in temperature
So , ` (dQ)/(dt) = mc (-dT//dt)` ....(ii)
` therefore ` Rate of cooling from (i) and (ii) is given by
` - (dT)/(dt) = (sigma e A (T^4 - T_0^4))/(mc)`
mass of hollow sphere < mass of solid sphere
` therefore ( (-dT)/(dt) )_("hallow") gt ((-dT)/(dt) )_("solid")`