A sphere, a cube and a thin circular plate, all of same material and same mass are initially heated to same high temperture.

Options

A. Plate will cool fastest and cube the slowest
B. Sphere will cool fastest and cube the slowest
C. Plate will cool fastest and sphere the slowest
D. Cube will cool fastest and plate the slowest

Answer

C

Explanation

Consider the diagram where all the three objects are heated to same temperature T . We know that density
`rho = ("Mass")/("Volume")` as `rho` is same for all the three objects hence, volume will also be same .

As thickness of the plate is least hence, surface area of the plate is maximum. We know that, according to Stefan’s law of heat loss ` H prop AT^(4)`
Where, A is surface area of the object and T is temperature.
Hence, `H_("shere") : H_("cube") : H_("plate")`
` = A _("sphere") : A_("cube") : A_("plate")`
As `A_("plate")` is maximum.
Hence, the plate will cool fastest.
As, the sphere is having minimum surface area hence, the sphere cools slowest