Question

A solid sphere and a hollow sphere of same material and size are heated to some temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surrounding is T, then:
A. The hollow sphere will cool at a faster rate for all values of T
B. The solid sphere will cool at a faster rate for all values of T
C. Both spheres will cool at the same rate for all values of T
D. Both spheres will cool at the same rate only for small values of T

Answer 1

Hint: Here there is a solid sphere and hollow sphere of the same material. Not only do they have the same material but they are also heated and allowed to cool in the same surroundings. We have to find which will cool faster. For attending this question too, you have to know all about factors affecting cooling.



Formula used:
Rate of change of heat, $\frac{dQ}{dt}=ms\frac{dT}{dt}$
Where Q is heat, m is mass, s is specific heat, T is temperature difference between each sphere and its surrounding.




Complete answer:
We know that rate of change is:
$\frac{dQ}{dt}=ms\frac{dT}{dt}$
It is given that both spheres are made up of the same material and have the same size. So obviously they have the same radius and surface area. Therefore, if they are heated to the same temperature and allowed to cool in the same temperature, then the rate of change of heat will be the same.
Therefore, we can write that the rate of cooling is inversely proportional to the mass of the sphere.
Mathematically, $\frac{dT}{dt}\propto \frac{1}{m}$
We know that the mass of a hollow sphere is less than a solid sphere. So, the hollow sphere cools faster than that of a solid sphere.
Therefore, the answer is option (C)



Note: There will be many simple questions like this. We just have to read the question carefully and choose wisely. But for that you should know the very basic concepts beautifully.