Statement-1: Work done by electrostatic force is zero if a charge is moving along an equipotential surface.

Statement-2: Equipotential surfaces are perpendicular to electric field.

The correct option is: Both statements are true.

Let us analyze both statements step-by-step to understand the underlying physical concepts:

1. Understanding Statement-1:
The work done $W$ by an electrostatic force in moving a charge $q$ from a point $A$ to a point $B$ is given by the relation:
$W=-q\Delta V=-q(V_B-V_A)$
where $V_A$ and $V_B$ are the electrostatic potentials at points $A$ and $B$, respectively. By definition, an equipotential surface is a surface where the electric potential is the same at every point. Therefore, for any two points $A$ and $B$ on this surface:
$V_A=V_B\Rightarrow V_B-V_A=0$
Substituting this into the work formula gives:
$W=-q\left(0\right)=0$
Thus, the work done by the electrostatic force when moving a charge along an equipotential surface is indeed zero. Statement-1 is true.

2. Understanding Statement-2:
The relation between the electric field $\mathbf{E}$ and the electric potential $V$ is given in differential form by:
$dV=-\mathbf{E}·d\mathbf{r}$
where $d\mathbf{r}$ represents a small displacement vector along the surface. For displacement along an equipotential surface, the potential does not change, meaning:
$dV=0$
Substituting this back into the relation:
$\mathbf{E}·d\mathbf{r}=0$
The dot product of two non-zero vectors is zero when the vectors are perpendicular to each other. Since $d\mathbf{r}$ lies along the equipotential surface, the electric field vector $\mathbf{E}$ must be perpendicular to the surface at every point. Thus, equipotential surfaces are always perpendicular to the electric field. Statement-2 is true.