Sum

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.

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#### Solution

According to the theory of relativity, E α m^{a}c^{b}

⇒ E = km^{a}c^{b}, where k = proportionality constant

Dimension of the left side, [E] = [ML^{2}T^{−2}]

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

Equating the dimensions of both sides, we get:

[ML^{2}T^{−2}] = [M]^{a} [LT^{−1}]^{b}

⇒ a = 1, b = 2

∴ E = kmc^{2}

Concept: Concept of Physics

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