Question

A sphere, a cube and a thin circular plate have the same mass and are made up of the same material. All of them are heated to the same temperature. The rate of cooling is
A.)The maximum for the sphere and minimum for the plate
B.)The maximum for the sphere and minimum for the cube
C.)Both (a) and (b)
D.)None of the above

Answer 1

Hint: Sphere, cube and circular plate have the same mass and are made up of the same material. Use the relation between rate of cooling and surface area. Compare the surface area of sphere, cube and circular plate and thus find the rate of cooling of all the three.

Complete answer:
Rate of cooling is directly proportional to surface area or exposed area. It means greater the surface area, less is the time required for it to cool.
It is mentioned that sphere, cube and circular plate have the same mass and all are made up of the same material hence their density is also the same. Thus, their volume is the same.
Surface area is maximum for circular plates and least for the sphere. Thus, the rate of cooling is maximum for the circular plate and minimum for the sphere. The cube takes less time to cool as compared to a sphere but takes more time as compared to a circular plate.
Hence, the correct answer is option D i.e. none of the above.

So, the correct answer is “Option D”.

Note:
As the rate of cooling is maximum for a circular plate, it drops to room temperature before the sphere and cube. Then, the temperature of the cube drops to room temperature. And then at last, the temperature of the sphere will drop to room temperature. Thus, the sphere takes the maximum time to drop to room temperature.