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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

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))`
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