**Question:**

**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 $\mathrm{T}_{0}$. The initial temperature of the sphere is $3 \mathrm{~T}_{0}$. If the specific heat of the material of the sphere varies as $\alpha \mathrm{T}^{3}$ per unit mass with the temperature $\mathrm{T}$ of the sphere, where $\alpha$ is a constant, then the time taken for the sphere to cool down to temperature $2 \mathrm{~T}_{0}$ will be $(\sigma$ is Stefan Boltzmann constant)**

$\frac{\mathrm{M} \alpha}{4 \pi \mathrm{R}^{2} \sigma} \operatorname{In}\left(\frac{3}{2}\right)$

$\frac{\mathrm{M} \alpha}{4 \pi \mathrm{R}^{2} \sigma} \operatorname{In}\left(\frac{16}{3}\right)$

$\frac{\mathrm{M} \alpha}{16 \pi \mathrm{R}^{2} \sigma} \operatorname{In}\left(\frac{16}{3}\right)$

$\frac{\mathrm{M} \alpha}{16 \pi \mathrm{R}^{2} \sigma} \operatorname{In}\left(\frac{3}{2}\right)$

Question of from chapter.

JEE Main Previous Year Online April 19, 2014

Correct Option: 3

**Solution:**

### Related Questions

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