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 relation among the quantities using the method of dimensions.

Answer 1

According to the theory of relativity, E α m^ac^b
⇒ E = km^ac^b, where k = proportionality constant

Dimension of the left side, [E] = [ML²T⁻²]

Dimension of the right side, [m^ac^b]= [M]^a [LT⁻¹]^b

Equating the dimensions of both sides, we get:
 [ML²T⁻²] = [M]^a [LT⁻¹]^b
⇒ a = 1, b = 2
∴ E = kmc²