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The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed o…

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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

[JEE Main 2025, 24 Jan (Shift 2)]

a

\({E}^{2}=p{c}^{2}+{m}^{2}{c}^{4}\)

b

\({E}^{2}={p}^{2}{c}^{2}+{m}^{2}{c}^{4}\)

c

\({E}^{2}=p{c}^{2}+{m}^{2}{c}^{2}\)

d

\({E}^{2}={p}^{2}{c}^{2}+{m}^{2}{c}^{2}\)

✓ Correct answer: b)

\({E}^{2}={p}^{2}{c}^{2}+{m}^{2}{c}^{4}\)

Explanation

\([E]={M}^{1}{L}^{2}{T}^{-2}\\ [Pc]={M}^{1}{L}^{1}{T}^{-1}\cdot {L}^{1}\\ \left[m{c}^{2}\right]={M}^{1}{L}^{2}{T}^{-2}\\ \Rightarrow [E]=[pc]=\left[m{c}^{2}\right]\)

From principle of homogenity \({E}^{2}={p}^{2}{c}^{2}+{m}^{2}{c}^{4}\)

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