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Nitika Shan
Asked: 2022-11-11T00:00:32+05:30 In:

A famous relation in phyics relates the 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 the special theory of relativity due to Albert Einstein). A body 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 phyics relates the 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 the special theory of relativity due to Albert Einstein). A body 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`.
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  1. 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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