Question

A famous relation in physics relates '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 special relativity by Albert Einstein). A student recalls the relation almost correctly but forgets where to put the constant $c .$ He should write $: m=$

• A. $\frac{m_{0} c}{\left(1-v^{2}\right)^{\frac{1}{2}}}$
• B. $\frac{m_{0} c^{2}}{\left(1-v^{2}\right)^{\frac{1}{2}}}$
• C. $\frac{m_{0}}{\left(1-\frac{v^{2}}{c}\right)^{\frac{1}{2}}}$
• D. $\frac{m_{0}}{\left(1-\frac{v^{2}}{c^{2}}\right)^{\frac{1}{2}}}$

Answer 1

Answer: (D)

As $ \left[\frac{v^{2}}{c^{2}}\right]=$ dimensionless.
So $\left[\frac{m_{0}}{\left(1-\frac{v^{2}}{c^{2}}\right)^{\frac{1}{2}}}\right]=[m]$
All others, do not have the dimensions of mass.