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black colored solid sphere of radius "R"...

black colored solid sphere of radius "R" and mass "M" is inside a cavity with vacuum inside.The walls of the cavity are maintained at temperature `T_(0)` .The initial temperature of the sphere is `3T_(0)` .If the specific heat of the material of the sphere varies as `alpha T^(3)` per unit mass with the temperature of the sphere,where `alpha` is a constant,then the time taken for the sphere to cool down to temperature `2T_(0)` will be ( `sigma` Stefan Boltzmann constant)

A

` ( M alpha ) /( 16 pi R^(2) sigma) "In" ((16)/(3))`

B

` ( M alpha)/( 4 pi R^(2) sigma) "In" ((3)/(2))`

C

` ( M alpha)/( 16 pi R^(2) sigma) "In" ((3)/(2))`

D

`( M alpha)/( 4pi R^(2) sigma) "In" ((16)/(3))`

Text Solution

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The correct Answer is:
A
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