1. Use the property of a moving coil galvanometer

   For a moving coil galvanometer, the deflection $\theta$ is directly proportional to the current $I$: $I \propto \theta$ Hence, $\frac{I_1}{I_2} = \frac{\theta_1}{\theta_2}$

2. Given data

   • Current $I_1 = 200\,\mu\text{A}$
   • Deflection $\theta_1 = 60^\circ$

   Required deflection: $\theta_2 = \frac{\pi}{10}\text{ rad}$

3. Convert units so both angles are in the same unit

   Since $180^\circ = \pi \text{ rad}$ therefore, $\frac{\pi}{10}\text{ rad} = \frac{180^\circ}{10} = 18^\circ$

4. Apply proportionality

   $\frac{I_1}{I_2} = \frac{\theta_1}{\theta_2}$

   $\frac{200}{I_2} = \frac{60}{18}$

   So, $I_2 = 200 \times \frac{18}{60}$

   $I_2 = 200 \times \frac{3}{10} = 60\,\mu\text{A}$

5. Match with options

   $60\,\mu\text{A}$ corresponds to Option D.

Final Answer: $60\,\mu\text{A}$