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(B) Given the relation,$m = \frac{m_{0}}{(1 - v^{2})^{1/2}}$.Dimension of $m = [M^{1} L^{0} T^{0}]$.Dimension of $m_{0} = [M^{1} L^{0} T^{0}]$.Dimensi

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$m = \frac{m_{0}}{(1 - v^{2}/c^{2})^{1/2}}$

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(B) Given the relation,$m = \frac{m_{0}}{(1 - v^{2})^{1/2}}$.Dimension of $m = [M^{1} L^{0} T^{0}]$.Dimension of $m_{0} = [M^{1} L^{0} T^{0}]$.Dimension of $v = [M^{0} L^{1} T^{-1}]$.Dimension of $v^{2} = [M^{0} L^{2} T^{-2}]$.Dimension of $c = [M^{0} L^{1} T^{-1}]$.The given formula will be dimensionally correct only when the dimension of the $L$.$H$.$S$. is the same as that of the $R$.$H$.$S$.This is only possible when the factor $(1 - v^{2})^{1/2}$ is dimensionless,i.e.,$(1 - v^{2})$ must be dimensionless.Since $1$ is dimensionless,$v^{2}$ must also be dimensionless. This is only possible if $v^{2}$ is divided by $c^{2}$,as the ratio $v^{2}/c^{2}$ is dimensionless.Hence,the correct relation is $m = \frac{m_{0}}{(1 - v^{2}/c^{2})^{1/2}}$.

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