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A famous relation in physics relates 'mo...

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.

Text Solution

Verified by Experts

According to the principle of homogenity of dimesnions power of M, L, T on either side of the formula must be equal. For this, on RHS, the denominator `(1-v^(2))^(1//2)` should be dimensionless. Therefore, instead of `(1-v^(2))^(1//2)`, we should write `((1-v^(2))/c^(2))^(1//2)`
Hence the correct formula would be
`" "m=m_(0)/((1-v^(2))/c^(2))^(1//2)`
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