Q. 15 4.7( 32 Votes )

A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ mo 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:

Guess where to put the missing c.

Answer :

The dimension of the quantities involved are:

m = M1L0T0

m0 = M1L0T0

v = M0L1T-1

c = M0L1T-1

For a correct dimensional equation, the dimensions of LHS and RHS should be equal. We can see that dimensions of m and m0 are equal thus the remaining part of the equation should be constant.

should be unitless.

1 is dimensionless so should be dimensionless.

On subtraction, dimension of the 2 quantities should be same. So, dimension of 1 and v2 should be same. Therefore, v2 should be dimensionless and therefore v.

We can see that dimension of v and c are same. So, replacing v by v/c will make it dimensionless and the given equation dimensionally correct.

Hence, correct relation will be,

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.