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» <html><body><p>` ( M alpha ) /( <a href="https://interviewquestions.tuteehub.com/tag/16-276476" style="font-weight:bold;" target="_blank" title="Click to know more about 16">16</a> <a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</a> R^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>) <a href="https://interviewquestions.tuteehub.com/tag/sigma-1207107" style="font-weight:bold;" target="_blank" title="Click to know more about SIGMA">SIGMA</a>) "In" ((16)/(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>))`<br/>` ( M alpha)/( 4 pi R^(2) sigma) "In" ((3)/(2))`<br/>` ( M alpha)/( 16 pi R^(2) sigma) "In" ((3)/(2))`<br/>`( M alpha)/( 4pi R^(2) sigma) "In" ((16)/(3))`</p>Answer :A</body></html>