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). The initial temperature of the sphere is 3T_(0). If the specific heat of the material of the sphere varies as alphaT^(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) (Hint : sigma(T^(4)-T_(0)^(4))xx4piR^(2)=Ms(dT)/dt&sigma=alphaT^(3))

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). The initial temperature of the sphere is 3T_(0). If the specific heat of the material of the sphere varies as alphaT^(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) (Hint : sigma(T^(4)-T_(0)^(4))xx4piR^(2)=Ms(dT)/dt&sigma=alphaT^(3))
Answer» `(Malpha)/(16piR^(2)SIGMA)LN(16/3)` `(Malpha)/(4piR^(2)sigma)ln(3/2)` `(Malpha)/(16piR^(2)sigma)ln(3/2)` `(Malpha)/(4piR^(2)sigma)ln(16/3)` ANSWER :A