A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ mo 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). boy recalls the relation almost correctly but forgets where to put the constant c. He writes : m = mₒ / (1 - υ ²) ⅟² Guess where to put the missing c.

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Solution

The incorrect relation between the moving mass (m), rest mass (m0), speed of the moving mass (v) and the speed of light (c) is,

m= m 0 ( 1− v 2 ) 1/2

Rearrange the above equation further,

( 1− v 2 ) 1/2 = m 0 m 1− v 2 = m 0 m

Since the RHS term ( m 0 m ) is dimension less, so the relation to be dimensionally correct, the LHS term ( 1− v 2 ) must be dimensionless.

To make the LHS term dimensionless replace the term ( 1− v 2 ) by ( 1− v 2 c 2 ) .

Hence, the correct relation is given as,

m= m 0 ( 1− v 2 c 2 ) 1/2 = m 0 ( 1− v 2 / c 2 ) −1/2

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