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  • Nearly   of the power of a <img alt="110 \mathrm{~W}" src="https://entrancecorner.oncodecogs.com/gif.latex?110%

Nearly 10 %  of the power of a 110 \mathrm{~W} light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 \mathrm{~m} from the bulb to a distance of 5 \mathrm{~m} is a \times 10^{-2} \mathrm{~W} / \mathrm{m}^{2}. The value of \mathrm{' a '} will be___________.

Option: 1

84


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{P_{delivered}=\eta \: P_{soura}}

                 \mathrm{=\frac{1}{10}\times 110=11W}

\mathrm{Intensity=\frac{P_{delivered}}{4\pi r^{2}}}

\mathrm{At\: \: r=1m,I_{1}=\frac{11}{4\pi \left ( 1 \right )^{2}}}

\mathrm{I_1 =\frac{11}{4 \times \frac{22}{7}}=\frac{7}{8} \mathrm{~W} / \mathrm{m}^2 }

\mathrm{\text { At } r =5 \mathrm{~m}, }

\mathrm{I_2 =\frac{11}{4 \pi(5)^2}=\frac{11}{4 \times \frac{22}{7} \times 25} }

\mathrm{I_2 =\frac{7}{2} \times 10^{-2} \mathrm{~W} / \mathrm{m}^2 }

\mathrm{I_1-I_2 =\frac{7}{8}-\frac{7}{2} \times 10^{-2} }

               \mathrm{=\left(\frac{700}{8}-\frac{28}{8}\right) \times 10^{-2} }

                \mathrm{=\frac{672}{8} \times 10^{-2} }

\mathrm{I_1-I_2 =84 \times 10^{-2} \mathrm{~W} / \mathrm{m}^2}

The value of a is 84










 

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chirag

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