A black coloured 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. Theinitial 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 T 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 is Stefan Boltzmann constant )

A black coloured solid sphere of radius R and mass M is inside a cavit

1.	A black coloured 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. Theinitial 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 T 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 is Stefan Boltzmann constant )
Answer» ` ( M alpha ) /( 16 PI R^(2) SIGMA) "In" ((16)/(3))` ` ( M alpha)/( 4 pi R^(2) sigma) "In" ((3)/(2))` ` ( M alpha)/( 16 pi R^(2) sigma) "In" ((3)/(2))` `( M alpha)/( 4pi R^(2) sigma) "In" ((16)/(3))` Answer :A