• # question_answer A spherical black body with a radius of 12 cm radiates 450 W power of 500 K. If the radius were half and temperature doubled, the power radiated in watt would be A)  225               B)  450C)  900               D)  1800

$P=\sigma {{T}^{4}}(4\pi {{r}^{2}})\propto {{T}^{4}}{{r}^{4}}$ $\therefore$$\frac{{{P}_{1}}}{{{P}_{2}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{r}}={{(2)}^{2}}\times {{\left( \frac{1}{2} \right)}^{2}}=4$ or ${{P}_{2}}=4{{P}_{1}}=4\times 50=1800\,\text{watt}$ Hence, the correction option is [d].