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

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
  1. $\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2$
  2. $\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2$
  3. $\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4$
  4. $\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4$

Solution

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)

Asked in: JEE Main 2025 (24 Jan Shift 2)

Practice more Dual Nature of Matter questions on Aicharya