Physics - Modern Physics Question with Solution | TestHub

Let the velocity of a particle be v where mass $\mathrm{m}$ is double the rest mass i.e., $\mathrm{m}=2{\mathrm{m}}_0$ then ${\mathrm{m}}_0=\mathrm{m}\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}\Rightarrow {\mathrm{m}}_0=2{\mathrm{m}}_0\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}$ $\frac{1}{2}=\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}\Rightarrow \frac{1}{4}=1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}$ $\Rightarrow \frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}=1-\frac{1}{4}=\frac{3}{4}$ $\Rightarrow \mathrm{v}=\sqrt{\frac{3}{4}}\mathrm{c}$