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Question
A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m0 of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special 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-v^2)^(1/2)`
Guess where to put the missing c.
Solution
From the given equation, `m_0/m = sqrt(1-v^2)`
Left hand side is dimensionless
Therefore, right hand side should also be dimensionless.
It is possible only when `sqrt(1-v^2) "should be" sqrt(1-v^2/c^2)`
Thus the correct formula is m = `m_0 (1 - v^2/c^2)^((-1)/2)`
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