• question_answer 29) A sphere and a cube of same material and same volume are heated upto the same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiations emitted will be- A) $1\,\,:\,\,1$                               B) $\frac{4\pi }{3}\,\,:\,\,1$C) ${{\left( \frac{\pi }{6} \right)}^{1/3}}\,:\,\,1\,$              D) $\frac{1}{2}{{\left( \frac{4\pi }{3} \right)}^{2/3}}\,:\,\,1\,$

${{V}_{1}}={{V}_{2}}$ $\frac{4}{3}\pi {{r}^{3}}\,\,=\,\,{{\ell }^{3}}$ $r={{\left( \frac{3}{4\pi } \right)}^{1/3}}\,\,\ell \Rightarrow {{r}^{2}}\,\,=\,\,{{\left( \frac{3}{4\pi } \right)}^{2/3}}{{\ell }^{2}}$ $\frac{dQ}{dt}\,\,\,\propto \,\,A$ $\Rightarrow \,\,\frac{{{R}_{{{h}_{1}}}}}{{{R}_{{{h}_{2}}}}}\,=\,\frac{4\pi {{r}^{2}}}{6{{t}^{2}}}$ $=\frac{4\pi }{6}\,{{\left( \frac{3}{4\pi } \right)}^{2/3}}\,\,=\,\,\frac{1}{2}\left( \frac{4\pi }{3} \right){{\,}^{1/3}}:1$