JEE Mains · Physics · STD 12 - 13. Nuclei
The energy \(E\) and momentum \(p\) of a moving body of mass \(m\) are related by some equation. Given that c represents the speed of light, identify the correct equation.
- A \(\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2\)
- B \(\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2\)
- C \(\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4\)
- D \(\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4\)
Answer & Solution
Correct Answer
(D) \(\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4\)
Step-by-step Solution
Detailed explanation
We need to check the dimensions only. With momentum the dimension \(E^2=p^2 C^2\) And with mass \(E^2=m^2 c^4\) So \(E^2=p^2 C^2+m^2 c^4\) (dimensionally)
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