The energy E and momentum p of a moving body | vedclass

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(D) According to Einstein's theory of special relativity,the total energy $E$ of a particle with rest mass $m$ and momentum $p$ is given by the relati

Vedclass · Accepted Answer

$E^2 = p^2c^2 + m^2c^4$

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(D) According to Einstein's theory of special relativity,the total energy $E$ of a particle with rest mass $m$ and momentum $p$ is given by the relativistic energy-momentum relation.The total energy is the sum of the kinetic energy and the rest mass energy,expressed as:$E^2 = (pc)^2 + (mc^2)^2$Expanding this,we get:$E^2 = p^2c^2 + m^2c^4$Dimensional analysis confirms this:$[E] = [M^1 L^2 T^{-2}]$$[pc] = [M^1 L^1 T^{-1}] \cdot [L^1 T^{-1}] = [M^1 L^2 T^{-2}]$$[mc^2] = [M^1] \cdot [L^2 T^{-2}] = [M^1 L^2 T^{-2}]$Since all terms have the same dimensions,the equation $E^2 = p^2c^2 + m^2c^4$ is dimensionally consistent and physically correct.

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

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