Assertion : A solid sphere of copper of radius `R` and a hollow sphere of the same material of inner radius `r` and outer radius `R` are heated to the same temperature and allowed to cool in the same environment. The hollow sphere cools faster.
Reason : Rate of cooling is according to Stefan's law which is `E alpha T^(4)`

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If the assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

C

Explanation

As external radii of both the spheres are equal, the surface areas of the two are also equal. Therefore, when the two spheres are heated to same temperature, both will radiated hear at the same rate.
Now, rate of loss of heat from a sphere = `Mc(d theta)/(dt)` therefore, rate of cooling
`=(d theta)/(dt) = ("rate of loss of heat")/(Mc)`
or ` (d theta)/(dt) prop 1/M`
Since, mass of hollow sphere is lesser, its rate of cooling will be faster.