**Solution**.

The formula for calculating the acceleration due to gravity is :

$$ g=G \times \frac{M}{R^{2}} $$

Here, Gravitational constant :

$G=6.7 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$

Mass of the moon, $M=7.4 \times 10^{22} \mathrm{~kg}$

Radius of the moon, $R=1740 \mathrm{~km}$

$$

\begin{array}{l}

=1740 \times 1000 \mathrm{~m} \\

=1.74 \times 10^{6} \mathrm{~m}

\end{array} $$

Now, putting these values of $G, M$ and $R$ in the above formula, we get:

$$ g=\frac{6.7 \times 10^{-11} \times 7.4 \times 10^{22}}{\left(1.74 \times 10^{6}\right)^{2}} $$

$$

\text { or } \quad g=1.63 \mathrm{~m} / \mathrm{s}^{2}

$$

Thus, the acceleration due to gravity, $g$, on the surface of the moon is $1.63 \mathrm{~m} / \mathrm{s}$