A metre stick moves along its length with a certain speed. The apparent length of the moving metre stick as measured by a stationary observer on the ground is found to be 98 cm. Then, the velocity $$v$$​ of the metre stick in terms of the speed of light in vacuum c will be:

Correct option is B

​$$\text{Given:} \\\bullet \quad \text{Proper length } L_0 = 1\, \text{m} = 100\, \text{cm} \\\bullet \quad \text{Observed length } L = 98\, \text{cm} = 0.98\, \text{m} \\\bullet \quad \text{Speed of light } c$$

$$\frac{L}{L_0} = \sqrt{1 - \frac{v^2}{c^2}} \implies \left(\frac{L}{L_0}\right)^2 = 1 - \frac{v^2}{c^2}$$

$$\implies \frac{v^2}{c^2} = 1 - \left(\frac{L}{L_0}\right)^2$$

$$\implies \frac{v}{c} = \sqrt{1 - \left(\frac{L}{L_0}\right)^2} = \sqrt{1 - (0.98)^2}$$

$$\quad (0.98)^2 = 0.9604\implies \frac{v}{c} = \sqrt{1 - 0.9604} = \sqrt{0.0396} = 0.199$$​​​​​​