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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.

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

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

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

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

answer is D.

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Detailed Solution

$\begin{aligned} [E] = M^{1} L^{2} T^{- 2} \\ [Pc] = M^{1} L^{1} T^{- 1} \cdot L^{1} T^{- 1} = M^{1} L^{2} T^{- 2} \\ [{mc}^{2}] = M^{1} L^{2} T^{- 2} \\ E^{2} = M^{1} L^{2} T^{- 2} \\ E^{2} = P^{2} c^{2} + m^{2} c^{4} \end{aligned}$

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