Modern Physics | JEE Main 2025 Solution

JEE MAIN 2025

24-01-2025 SHIFT-2

Question

The energy $E$ and momentum $p$ of a moving body of mass $m$ are related by some equation. Given that e represents the speed of light, identify the correct equation

Select the correct option:

$\mathrm{E}^{2}=\mathrm{pc}^{2}+\mathrm{m}^{2} \mathrm{c}^{2}$

$\mathrm{E}^{2}=\mathrm{p}^{2} \mathrm{c}^{2}+\mathrm{m}^{2} \mathrm{c}^{2}$

$\mathrm{E}^{2}=\mathrm{p}^{2} \mathrm{c}^{2}+\mathrm{m}^{2} \mathrm{c}^{4}$

$\mathrm{E}^{2}=\mathrm{pc}^{2}+\mathrm{m}^{2} \mathrm{c}^{4}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$[\mathrm{E}]=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$
$[\mathrm{Pc}]=\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1} \cdot \mathrm{~L}^{1} \mathrm{~T}^{-1}=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$
$\left[\mathrm{mc}^{2}\right]=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$
$\mathrm{E}^{2}=\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}$
$\mathrm{E}^{2}=\mathrm{P}^{2} \mathrm{c}^{2}+\mathrm{m}^{2} \mathrm{c}^{4}$

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JEE Main

Physics

Medium

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