JEE MAIN - Physics (2025 - 24th January Evening Shift - No. 10)
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
$\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4$
$\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2$
$\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4$
$\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2$
Explanation
$$\begin{aligned}
& {[E]=M^1 L^2 T^{-2}} \\
& {[P c]=M^1 L^1 T^{-1} \cdot L^1 T^{-1}=M^1 L^2 T^{-2}} \\
& {\left[\mathrm{mc}^2\right]=\mathrm{M}^1 L^2 T^{-2}} \\
& E^2=\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2} \\
& E^2=\mathrm{P}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4
\end{aligned}$$
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