The rate of cooling of an object depends on its surface area and volume. For objects of the same mass and made of the same material, the rate of cooling can be explained using Newton's law of cooling, which states that the rate of heat loss is proportional to the surface area exposed and the temperature difference.
Let’s analyze each object in terms of surface area (A) and volume (V):
Sphere:
The surface area of a sphere is given by: A_sphere = 4πr²
The volume of a sphere is given by: V_sphere = (4/3)πr³
Cube:
The surface area of a cube is given by: A_cube = 6a² (where "a" is the side length)
The volume of a cube is given by: V_cube = a³
Thin Circular Plate (Disk):
The surface area of a thin circular plate is given by: A_plate = πr²
The volume of a thin circular plate is very small compared to its surface area and can be approximated as A_plate * thickness (t).
Now, since the mass and material of all objects are the same, they have the same volume, which will determine their size (radius, side length, etc.). The rate of cooling is proportional to the surface area of each object because heat loss is primarily through the surface.
The sphere has the least surface area per unit volume compared to the cube and plate.
The thin circular plate has the maximum surface area for a given volume because the plate has a large surface but a relatively small volume.
Hence, the rate of cooling will be:
Maximum for the plate because it has the largest surface area for the same mass.
Minimum for the sphere because it has the smallest surface area for the same mass.
Thus, the correct answer is:
A. Minimum for the plate
