Verified Solution • 2025–26 Session moderate

QJEEM25Phd596: JEE Main 2025 Physics - Class 12 JEEM25Phd596 Solution: The energy E and momentum p of a moving body of mass m are…

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

Multiple Choice Options

  • A E2=pc2+m2c4\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4
  • B E2=pc2+m2c2\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2
  • C E2=p2c2+m2c4\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4
  • D E2=p2c2+m2c2\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2

Step-by-Step Verified Solution

amp;[E]=M1L2T−2amp;[Pc]=M1L1T−1⋅L1T−1=M1L2T−2amp;[mc2]=M1L2T−2amp;E2=M1 L2 T−2amp;E2=P2c2+m2c4\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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