In the given circuit, the resistance of the galvanometer is $G = 100 Ω$. Resistance box R contributes 4900 Ω. When key K is closed. The needle of the galvanometer deflects to the 20th division. The figure of merit of the galvanometer is:

$2 × 10^{-5} A/div$

The correct answer is Option (1) → $2 × 10^{-5} A/div$

Given:

Galvanometer resistance, $G = 100\ \Omega$

Series resistance, $R = 4900\ \Omega$

Galvanometer deflection, $n = 20$ divisions

Total series resistance, $R_\text{total} = R + G = 4900 + 100 = 5000\ \Omega$

Let applied voltage be $V$.

Current through galvanometer, $I = \frac{V}{R_\text{total}}$

Figure of merit, $K = \frac{I}{n} = \frac{V}{R_\text{total} \cdot n}$

Substitute $V = 2\ \text{V}$:

$I = \frac{2}{5000} = 4 \times 10^{-4}\ \text{A}$

$K = \frac{4 \times 10^{-4}}{20} = 2 \times 10^{-5}\ \text{A/division}$

∴ The figure of merit of the galvanometer is $2 \times 10^{-5}\ \text{A/division}$