Given information:
- Two concentric conducting spheres of radii R and 3R
- The potential at the inner sphere (radius R) is 2V₀
- The potential at the outer sphere (radius 3R) is V₀

To find:
- The potential at r = (3R)/2

Explanation:
Step 1: Understand the problem
- We have two concentric conducting spheres with different radii.
- The potential at the inner sphere is 2V₀ and at the outer sphere is V₀.
- We need to find the potential at a specific point between the two spheres, at r = (3R)/2.

Step 2: Determine the potential at the specific point
- To find the potential at r = (3R)/2, we need to use the concept of equipotential surfaces.
- Equipotential surfaces are imaginary surfaces where the potential remains constant.
- In this case, the equipotential surfaces are spheres centered at the origin.

Step 3: Analyze the potential distribution
- The potential at any point inside a conductor is constant.
- Therefore, the potential at any point within the inner sphere (radius R) is 2V₀.
- Similarly, the potential at any point within the outer sphere (radius 3R) is V₀.

Step 4: Determine the potential at the specific point
- The potential at any point between the two spheres can be determined by linearly interpolating the potentials at the inner and outer spheres.
- Since the radius of the specific point is between the radii of the inner and outer spheres, the potential at the specific point will lie between 2V₀ and V₀.

Step 5: Apply the linear interpolation formula
- The potential at the specific point, r = (3R)/2, can be calculated using the linear interpolation formula:
Potential at r = (3R)/2 = [(V₀ - 2V₀) / (3R - R)] * [(3R)/2 - R] + 2V₀

Step 6: Simplify the equation
- Potential at r = (3R)/2 = [-V₀ / (2R)] * [R/2] + 2V₀
- Potential at r = (3R)/2 = -V₀/4 + 2V₀
- Potential at r = (3R)/2 = (7V₀)/4

Conclusion:
- Therefore, the potential at r = (3R)/2 is (7V₀)/4.
- The correct option is (d) V₀.