Question

In the famous ' Einstein theory of relativity,
m = m0/[1-(v/--)²] , one terms (symbol) is missing. Identify the missing terms ?​

Answer 1

${\color{#808099}{\boxed{\huge\mathfrak{Solution:-}}}}$

According to the principle of homogeneity of dimensions, powers of M, L, T on either side of the formula must be equal. For this, on RHS, the denominator $(1 - v {}^{2} ) {}^{ \frac{1}{2} }$ should be dimensionless. Therefore, instead of

$(1 - v {}^{2} ) {}^{ \frac{1}{2} }$ ,we should write $(1 - v {}^{2} \:/ \: {c}^{2} ) {}^{ \frac{1}{2} }$.

Hence, the correct formula would be,

${\color{#c85}{{\boxed{m = \frac{mo}{ \: (1 - v {}^{2} \:/ \: {c}^{2} ) {}^{ \frac{1}{2} }\: } }}}}$

Answer 2

Refer the above attachment ✍