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JEE Main 202524 JanuaryEvening Shift

Exam: JEE Main
Year: 2025
Date: 24 January
Shift: Evening Shift
Subject: Physics
Chapter: Dual Nature of Matter

JEE Main 2025 · 24 January · Evening Shift · Physics · Dual Nature of Matter

The energy E and momentum p of a moving body of mass m are related...

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

Options

A $\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^2$
B $\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^2$
C $\mathrm{E}^2=\mathrm{pc}^2+\mathrm{m}^2 \mathrm{c}^4$
D $\mathrm{E}^2=\mathrm{p}^2 \mathrm{c}^2+\mathrm{m}^2 \mathrm{c}^4$

Correct answer

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

Step-by-step 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)

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