JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Modern Physics

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.

Answer: (D)

Solution

The relativistic relation connecting the total energy

E

and momentum

p

of a body of mass

m

E^{2} = p^{2} c^{2} + m^{2} c^{4} .

This reduces to the familiar rest-energy formula

E = m c^{2}

when

p = 0

, and to

E = p c

for a massless particle such as a photon.

A dimensional check confirms the form: with

[E] = M L^{2} T^{- 2}

[p] = M L T^{- 1}

[c] = L T^{- 1}

[E^{2}] = M^{2} L^{4} T^{- 4}, [p^{2} c^{2}] = M^{2} L^{4} T^{- 4}, [m^{2} c^{4}] = M^{2} L^{4} T^{- 4},

all three terms match, confirming

E^{2} = p^{2} c^{2} + m^{2} c^{4}

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Single correct option