The relativistic mass of a particle moving with a speed of 2.0 × $$10^8$$​ m/s in an accelerator is found to be 2.4 × $$10^{-26}$$​ kg. The rest mass of the particle is: ($$c$$​ = 3.0 × $$10^8$$​ m/s)

Correct option is A

​$$\begin{aligned}&\text{Given:} \\&\bullet \ \text{Relativistic mass } m = 2.4 \times 10^{-26} \, \text{kg} \\&\bullet \ \text{Speed } v = 2.0 \times 10^8 \, \text{m/s} \\&\bullet \ \text{Speed of light } c = 3.0 \times 10^8 \, \text{m/s} \\[10pt]&\text{The relativistic mass is related to the rest mass as:} \\&m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} \Rightarrow m_0 = m \sqrt{1 - \frac{v^2}{c^2}}\end{aligned}$$

$$\begin{aligned}m_0 &= 2.4 \times 10^{-26} \sqrt{1 - \left( \frac{2 \times 10^8}{3 \times 10^8} \right)^2} = 2.4 \times 10^{-26} \sqrt{1 - \left( \frac{4}{9} \right)} = 2.4 \times 10^{-26} \sqrt{\frac{5}{9}} \\[8pt]m_0 &= 2.4 \times 10^{-26} \times \frac{\sqrt{5}}{3} \approx 2.4 \times 10^{-26} \times 0.745 = 1.79 \times 10^{-26} \, \text{kg}\end{aligned}$$​​​