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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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Answer Text

Solution :
From the given equation, `m_(0)/m=sqrt(1-v^(2))` <br> Left hand side is dimensionless. <br> Therefore, right hand side should also be dimensionless. <br> It is possible only when `sqrt(1-v^(2))` should be `sqrt(1-v^(2)/c^(2))`. <br> Thus, the correct formula is `m=m_(0) (1-v^(2)/c^(2))^(-1//2)`

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