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

Explanation:

According to the theory of relativity, E

a macb

=

E = km@cb, where k = proportionality

constant

Dimension of the left side, [E] =

[ML2T-2]

Dimension of the right side, [macb]=

[M] [LT-13b

Equating the dimensions of both sides,

we get:

[ML2T-2] = [M]ª [LT-1]b

= a = 1, b = 2

:E = kmc2