Check if the following eqn is dimensionally consistent : E2= (mc2)2+ (pc)2where E, m and p are the energy, mass and momentum of a particle, respectively and c is the speed of light in vacuum.

hi ​Rushikesh Powar,

Please find below the solution to the asked query:

E2 = (MC2)2 +(PC)2Dimensional formula for E = [ML2T-2]So E2 = [ML2T-2]2 = [M2L4T-4]for (MC2)2Dimension of MC2 = [M] × [LT-1]2 = [ML2T-2]Dimension of (MC2)2 = [ML2T-2]2 = [M2L4T-4]For (PC)2Dimension of momentum = [MLT-1]Dimesion of PC =  [MLT-1]×[LT-1] =  [ML2T-2]Dimension of (PC)2 = [ML2T-2]2 = [M2L4T-4]hence all are same and the equation is dimensionally correct.

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