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Question

Theory of relativity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a realtion among the quantities using the method of dimensions.


Solution

Let E energy, EαMaCb, where

M = Mass,

C = speed of light

E=KMaCb

where, K = Proportionality constant

Dimension of left side

E=[ML2T2]

Dimension of right side MaCb

=Ma[LT1]b

 [ML2T2=[Ma][LT1]]b

a=1,   b=2

So, the relation is E=KMC2

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