If a current of 200 μA deflects the coil of moving coil galvanometer through 60°, then the current required to cause deflection through π/10 radians is

The correct option is 60 μA.

For a moving coil galvanometer, the current passing through the coil is directly proportional to the angle of deflection of the coil. This relationship is represented by the formula:
$I\propto \theta$
Consequently, the ratio of the currents is equal to the ratio of their respective deflections:
$\frac{I_1}{I_2}=\frac{{\theta }_1}{{\theta }_2}$
where $I_1$ and $I_2$ represent the currents, and ${\theta }_1$ and ${\theta }_2$ represent the corresponding angles of deflection.

Given data:
Initial current, $I_1=200 \mathrm{\mu A}$
Initial deflection, ${\theta }_1=60°$
Final deflection, ${\theta }_2=\frac{\pi }{10} \mathrm{radians}$

To perform the calculation easily, we first convert the final deflection angle ${\theta }_2$ from radians into degrees. Since $\pi \mathrm{radians}=180°$:
${\theta }_2=\frac{180°}{10}=18°$

Now, substituting the values into the proportionality relation:
$\frac{200}{I_2}=\frac{60°}{18°}$
Rearranging the equation to solve for the final current $I_2$:
$I_2=200\times \frac{18}{60}$
$I_2=200\times 0.3$
$I_2=60 \mathrm{\mu A}$

Thus, the current required to cause a deflection of π/10 radians is 60 μA.