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.

Question

Philoid · Accepted Answer

Let the energy be proportional to m and c with powers p and q respectively

E m^p c^q

Dimensions of E = [ML²T^-2]

Dimensions of m = [M]

Dimensions of c = [LT^-1]

Let us assume a dimensionless constant K such that

E=Km^p c^q

Dimensionally

[ML²T^-2] = [M]^p[LT^-1] ^q

=[M^pL^qT^-q]

On comparing, p=1 and q=2

So the relation between mass, speed and energy is

E=kmc²

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

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.