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Question: How much mass has to be converted into energy to produce electric power of 500 MW for one hour?...

How much mass has to be converted into energy to produce electric power of 500 MW for one hour?

A

2×10−5kg2 \times 10^{- 5}kg

B

1×10−5kg1 \times 10^{- 5}kg

C

3×10−5kg3 \times 10^{- 5}kg

D

4×10−5kg4 \times 10^{- 5}kg

Answer

2×10−5kg2 \times 10^{- 5}kg

Explanation

Solution

: Here, P=500MW=5×108W,t=1h=3600sP = 500MW = 5 \times 10^{8}W,t = 1h = 3600s

Energy produced,

E=p×t=5×108×3600=18×1011JE = p \times t = 5 \times 10^{8} \times 3600 = 18 \times 10^{11}J

As E=mc2E = mc^{2}

∴m=Ec2=18×1011(3×108)2=18×10119×1016=2×10−5kg\therefore m = \frac{E}{c^{2}} = \frac{18 \times 10^{11}}{(3 \times 10^{8})^{2}} = \frac{18 \times 10^{11}}{9 \times 10^{16}} = 2 \times 10^{- 5}kg