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Q.

A sphere, a cube and a thin circular plate are made of same substance and all have same mass. These are heated to 200oC and then placed in a room. Then the 

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a

Temperature of cube drops to room temperature at last

b

Temperature of thin circular plate drop to room temperature at last

c

Temperature of sphere drops to room temperature at last

d

Temperatures of all the three drop to room temperature at the same time

answer is A.

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Detailed Solution

dTdt=eAσmcT4T04=eAσVρcT4T04

 Rate of cooling RA
(As masses are equal, volume of each body must be equal because material is same)
i.e., rate of cooling depends on the area of cross section and we know that for a given volume the area of cross section will be minimum for sphere. It means the rate of cooling will be minimum in case of sphere.
So the temperature of sphere drops to room temperature at last.

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