NEET Sample Paper NEET Sample Test Paper-15

  • 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)  450

    C)  900               

    D)  1800

    Correct Answer: D

    Solution :

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

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