B

Step 1: Identify the angles involved. The angle of inclination of the plane is given as \( \theta = 30^{\circ} \). The angle \( a \) is the angle made by the plane of the hemisphere with the inclined plane.

Step 2: Since the hemispherical shell is in equilibrium and the surface is rough enough to prevent sliding, the angle \( a \) can be calculated as follows:
The force due to gravity acts vertically downward, splitting into two components: one parallel to the incline and another normal to it. Based on geometric considerations, we find that:

\( a + \theta = 90^{\circ} \)
Hence, \( a = 90^{\circ} - \theta = 90^{\circ} - 30^{\circ} = 60^{\circ} \).

Therefore, the angle \( a \) is \( 60^{\circ} \). Hence, option B is correct.