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Question
A sphere, a cube and a thin circular plate, all of the same material and same mass are initially heated to same high temperature.
Options
Plate will cool fastest and cube the slowest
Sphere will cool fastest and cube the slowest
Plate will cool fastest and sphere the slowest
Cube will cool fastest and plate the slowest
Solution
Plate will cool fastest and sphere the slowest.
Explanation:
ρ = `"M"/"V"`
Given: Three things are made of the same materials, hence ρ is the same.
Also, M = same,
∴ All objects have the same volume, and a spherical has the smallest volume.
The plate's surface area is the highest among the offered items with constant volume.
Hence according to Stefan's law `"dQ"/"dt" ∝ "AT"^4`
As Aplate is maximum and Asphere is minimum The plate will cool fastest and the sphere cools slowest.
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