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A famous relation in Physics relates moving mass m to the rest mass m_0 of a particle in terms of its speed upsilon and the sped of light c. (This relaiton first arose as a consequence of special theory of relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes m = (m_0)/((1 - upsilon^2)^(1//2)Guess where to put the missing c?

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Answer Text

Solution :
According to the principle of homogeneity of dimensions, powers of M, L, T on either side of the forumal <br> must be equal. For this on RHS, the denominator `(1 - upsilon^2)^(1//2)` should be dimensionless. Therefore instead <br> of `(1 -upsilon^2)^(1//2)`, we should write `(1 - upsilon^2//c^2)^(1//2)` <br> Hence, the correct formula would be `m = (m_0)/((1 -upsilon^2//c^2)^(1//2)`

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