Explanation

(b) The relativistic mass $M\ is\ \ M = \gamma m$
Where, $m$ is rest mass and $\gamma = \frac{1}{\sqrt{1 - \frac{u^{2}}{c^{2}}}}$ is the Lorentz factor
having $u$ the relative velocity between the observer and object and $c$ is the speed of light.
$\therefore M = \ \frac{m}{\sqrt{1 - \frac{u^{2}}{c^{2}}}}$
Given, $M = 2m$
$\therefore 2m = \frac{m}{\sqrt{1 - \frac{u^{2}}{c^{2}}}}\ \Rightarrow \left( \sqrt{1 - \frac{u^{2}}{c^{2}}} \right)^{2} = \left( \frac{1}{2} \right)^{2}$
$\Rightarrow 1 - \frac{u^{2}}{c^{2}} = \frac{1}{4}\ \Rightarrow \frac{u^{2}}{c^{2}} = 1 - \frac{1}{4} = \frac{3}{4}$
$\Rightarrow \frac{u^{2}}{c^{2}} = \frac{3}{4} \Rightarrow \frac{u}{c} = \frac{\sqrt{3}}{2}$
$\Rightarrow u = \frac{\sqrt{3}}{2}c = \frac{\sqrt{3}}{2} \times 3 \times 10^{8} = 2.59 \times 10^{8}\ {ms}^{- 1}$