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A satellite is powered by a small nuclear generator that puts out 15W. How much mass is converted into energy in 10 years lifespan of the generator?
Question

A satellite is powered by a small nuclear generator that puts out 15W. How much mass is converted into energy in 10 years lifespan of the generator?

A.

15.6 g

B.

15.6 kg

C.

53 g

D.

53 μ g

Correct option is D

Given: Power output of generator P=15 W Lifespan t=10 years Speed of light c=3×108 m/s\begin{aligned}&\text{Given:} \\&\bullet \ \text{Power output of generator } P = 15 \, W \\&\bullet \ \text{Lifespan } t = 10 \, \text{years} \\&\bullet \ \text{Speed of light } c = 3 \times 10^{8} \, m/s\end{aligned}

Energy in 10 years will be:E=15 J/s=15×10×365×24×3600 J=4730.4×106 Jm=Ec2=4730.4×106(3×108)2=5.3×108 kg=53×109 kg=53×106 g=53 μg\begin{aligned}&\text{Energy in 10 years will be:} \\&E = 15 \, J/s = 15 \times 10 \times 365 \times 24 \times 3600 \, J \\[6pt]&= 4730.4 \times 10^6 \, J \\[10pt]&m = \frac{E}{c^2} = \frac{4730.4 \times 10^6}{(3 \times 10^8)^2} \\[6pt]&= 5.3 \times 10^{-8} \, kg \\[6pt]&= 53 \times 10^{-9} \, kg \\[6pt]&= 53 \times 10^{-6} \, g = 53 \, \mu g\end{aligned}​​​

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