Question

The velocity at which the mass of a particle become twice of its rest mass will be

Answer 1

As per Einstein's theory of relativity, the mass of a body increases relatively as compared to the rest mass.

Let the rest mass of the particle is m.

Let mass of the particle in motion is m'.

As per the question m' = 2m.

We are asked to calculate the speed of the particle.

As per Einstein's theory of relativity,

                             $m' =\frac{m}{\sqrt{1-\frac{v^2}{c^2}}}$

Here v is the velocity of the body and c is the velocity of light.

Squaring both sides we get-

                               $m'^2=\frac{m^2}{1-\frac{v^2}{c^2}}$

                               $[1-\frac{v^2}{c^2}]\ m'^2\ =\ m^2$

                               $1-\frac{v^2}{c^2} =\frac{m^2}{m'^2}$

                               $\frac{v^2}{c^2} =1-\frac{m^2}{m'^2}$

                                $=\ 1-\frac{m^2}{4m^2}$

                                $=1-\frac{1}{4}$

                                $=\frac{3}{4}$

                                 $v^2=c^2*\frac{3}{4}$

                                  $v=\sqrt{c^2*\frac{3}{4}$

                                   $v=\frac{\sqrt{3}c} {2}$     [ans]  

                           

Answer 2

Answer: 2.6×10^8 m/s

Explanation: