The fundamental unit which has the same power in the dimensional formula of surface tension and coefficient of viscosity is mass.

Surface Tension:
Surface tension is the force acting on the surface of a liquid that causes it to behave like a stretched elastic sheet. It is defined as the force per unit length acting perpendicular to the surface. The dimensional formula for surface tension can be derived using the following equation:

Surface tension = Force / Length

In the above equation, the force is the force acting on the liquid surface and is measured in Newtons (N), while length is the length along which the force is acting and is measured in meters (m). Therefore, the dimensional formula for surface tension is:

[M^1 L^0 T^-2]

Coefficient of Viscosity:
The coefficient of viscosity is a measure of a fluid's resistance to flow. It is defined as the ratio of the shear stress to the velocity gradient in a fluid. The dimensional formula for the coefficient of viscosity can be derived using the following equation:

Viscosity = Shear stress / (Velocity gradient x Area)

In the above equation, shear stress is the force acting parallel to the surface of the fluid and is measured in Newtons (N), velocity gradient is the change in velocity per unit length and is measured in meters per second per meter (m/s/m), and area is the cross-sectional area of the fluid and is measured in square meters (m^2). Therefore, the dimensional formula for the coefficient of viscosity is:

[M^1 L^-1 T^-1]

Comparison of Dimensions:
To determine the fundamental unit that has the same power in the dimensional formula of surface tension and coefficient of viscosity, we can compare the exponents of the fundamental units.

Surface tension: [M^1 L^0 T^-2]
Coefficient of viscosity: [M^1 L^-1 T^-1]

From the comparison, it is clear that the fundamental unit "mass" (M) has the same power of 1 in both surface tension and coefficient of viscosity. Therefore, the correct answer is option A) Mass.