JEE Main 2025 · 24 January · evening · Single correct · +4 / −1
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
- (a) E²=pc²+m² c⁴
- (b) E²=pc²+m² c²
- (c) E²=p² c²+m² c⁴
- (d) E²=p² c²+m² c²
Answer and solution
Answer (c) E²=p² c²+m² c⁴
Solution
Physics sir · 3 steps
Every term must have units of energy squared, and at rest the formula must give back E = mc².
- Two energy pieces. pc has units of energy: kg m s⁻¹ × m s⁻¹ = kg m²s⁻², the joule. mc² is also an energy, the rest energy. So each term on the right must be one of these squared.
Term Written as Units of energy squared? pc² (pc) × c No, it is energy times speed p²c² (pc)² Yes m²c² (mc)² No, mc is a momentum m²c⁴ (mc²)² Yes - Check the limits. For a body at rest, p = 0 gives E = mc². For a photon, m = 0 gives E = pc. Both known results come out correctly from the formula below.
E² = p²c² + m²c⁴
- So. Only (c) has both terms in units of energy squared, so (c) is the correct relation.
The idea to keep. When you cannot recall a formula, check its units: quantities you add must have the same units. Then test the limits p = 0 (rest energy) and m = 0 (photon, E = pc).
Answer from the NTA final answer key. Solution by PrepWiser.