KCET · Physics · Nuclear Physics
The energy equivalent to a substance of mass \( 1 \mathrm{~g} \) is
- A \( 18 \times 10^{(13)} \mathrm{J} \)
- B \( 9 \times 10^{(13)} \mathrm{J} \)
- C \( 18 \times 10^{6} \mathrm{~J} \)
- D \( 9 \times 10^{6} \mathrm{~J} \)
Answer & Solution
Correct Answer
(B) \( 9 \times 10^{(13)} \mathrm{J} \)
Step-by-step Solution
Detailed explanation
We know \(E=m c^{2}\)
Given \(m=1 \mathrm{~g}=1 \times 10^{-3} \mathrm{~kg}\)
We know \(c=3 \times 10^{8} \mathrm{~ms}^{-1}\)
\(\Rightarrow E=\left(1 \times 10^{-3}\right) \times\left(3 \times 10^{8}\right)^{2}=9 \times 10^{13}\)
Therefore, energy equivalent to a substance of mass \(1 \mathrm{~g}\) is \(9 \times 10^{13} \mathrm{~J}\)
Given \(m=1 \mathrm{~g}=1 \times 10^{-3} \mathrm{~kg}\)
We know \(c=3 \times 10^{8} \mathrm{~ms}^{-1}\)
\(\Rightarrow E=\left(1 \times 10^{-3}\right) \times\left(3 \times 10^{8}\right)^{2}=9 \times 10^{13}\)
Therefore, energy equivalent to a substance of mass \(1 \mathrm{~g}\) is \(9 \times 10^{13} \mathrm{~J}\)
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