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Question

A famous relation in physics relates moving mass m to the rest mass m0 of a particle in terms of its

speed v and the speed of light c. (This relation first arose as a consequence of special theory of relatively

given by Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant

c. He writes m=m0(1−v2)12. Guess where to put the missing c?


A

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B

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C

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D

None of these

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Solution

The correct option is C


Dimension of L.H.S. should be equal to R.H.S.

m=m0(1v2)12

L.H.S. = [M]

R.H.S. we already have m0 whose dimension will be [M]

So denominator should be dimensionless

Denominator is (1v2)

1 is dimensionless

But v has dimension [LT]

Also c has same dimension

v2c2 will be dimensionless

m=m0[1(VC)2]12


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