JEE Main 2014 — Thermal Properties of Matter Question with Solution

A black coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with a 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 $T$ 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)