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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.
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Solution
According to the theory of relativity, E α macb
⇒ E = kmacb, where k = proportionality constant
Dimension of the left side, [E] = [ML2T−2]
Dimension of the right side, [macb]= [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
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