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.

Answer 1

Let E energy, $E\alpha M^a{C}^b$, where

M = Mass,

C = speed of light

$\to E=K{M}^a{C}^b$

where, K = Proportionality constant

Dimension of left side

$E=\left[M{L}^2{T}^{-2}\right]$

Dimension of right side $M^a{C}^b$

$=M^a[L{T}^{-1}{]}^b$

$\therefore [M{L}^2{T}^{-2}=[Ma\left]\right[L{T}^{-1}]{]}^b$

$\Rightarrow a=1,b=2$

So, the relation is $E=KM{C}^2$