A famous relation in physics relates 'moving mass' m to the 'rest mass' m_(0) 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.

A famous relation in physics relates 'moving mass' m to the 'rest mass

1.	A famous relation in physics relates 'moving mass' m to the 'rest mass' m_(0) 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.
Answer» Solution :For CORRECT equation, DIMENSIONAL formula of both sides must be same. Here, dimensions of m and `m_(0)` are same. Therefore, `(1-V^(2))^(1/2)` should be dimensionless. But is not. To make it dimensionless, `v^(2)` must be divided by `C^(2)`. Correct equation `m=(m_(0))/((1-(v^(2))/(c^(2)))^(1/2))`