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A sphere , a cube and a thin circular pl...

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

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.

Text Solution

Verified by Experts

The correct Answer is:
C

As we know density `=("mass")/("volume")`. But for all three, mass and density are same hence, volume is also same.
As the thickness of plate is least, its area is maximum.
From Stefan-Boltzman law,
`:.HalphaA`
Now,
`H_("sphere"):H_("solid"):H_("plate")=A_("sphere"):A_("solid"):A_("plate")`
But area of plate is maximum hence, loss of heat is maximum and for sphere it is maximum Hence, plate will be cooled down quickly than sphere as its area is minimum.
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