LAWS OF MOTION (ADDITIONAL)
372248
An atom bomb weighing \(1 \mathrm{~kg}\) explodes releasing \(9 \times 10^{13} \mathrm{~J}\) of energy. 'What percentage of mass is converted into energy?
1 \(0.1 \%\)
2 \(1 \%\)
3 \(2 \%\)
4 \(10 \%\)
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Explanation:
A Given, \(\mathrm{E}=9 \times 10^{13} \mathrm{~J}\) \(\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-2}\) We know that, \(\mathrm{E}=\mathrm{mc}^{2}\) \(9 \times 10^{13}=\mathrm{m}\left(3 \times 10^{8}\right)^{2}\) \(\mathrm{~m}=\frac{9 \times 10^{13}}{\left(3 \times 10^{8}\right)^{2}}=\frac{9 \times 10^{13}}{9 \times 10^{16}}\) \(\mathrm{~m}=1 \times 10^{-3} \mathrm{~kg}\) \(\frac{\Delta \mathrm{m}}{\mathrm{m}} \times 100=10^{-3} \times 100=0.1 \%\)