A current of 200 $$\mu$$A deflects the coil of a moving coil galvanometer through 60°. The current to cause deflection through $$\frac{\pi}{10}$$ radian is

Galvanometer relationship: $$I = k\theta \implies I \propto \theta$$

Given initial conditions:

$$I_1 = 200\ \mu\text{A}$$

$$\theta_1 = 60^\circ = 60 \times \frac{\pi}{180} = \frac{\pi}{3}\text{ rad}$$

Given final condition: $$\theta_2 = \frac{\pi}{10}\text{ rad}$$

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

$$\frac{I_2}{200} = \frac{\left(\frac{\pi}{10}\right)}{\left(\frac{\pi}{3}\right)} = \frac{3}{10} \implies I_2 = 200 \times \frac{3}{10} = 60\ \mu\text{A}$$