If we use permitivity `epsilon`, resistance `R`, gravitational constant `G` and voltage `V` as fundamental physical quantities, then:

Options

A. [angular displacement]=`epsilon^(1)R^(0)G^(0)V^(0)`
B. [velocity]`=epsilon^(-1)R^(-1)G^(0)V^(0)`
C. [dipole moment] =`epsilon^(1)R^(0)G^(0)V^(-1)`
D. [force]=`epsilon^(2)R^(0)G^(0)V^(2)`

Explanation

To solve the problem, we need to analyze the dimensions of the given physical quantities: permittivity (ε), resistance (R), gravitational constant (G), and voltage (V). We will check which of the provided options (angular displacement, velocity, dipole moment, and force) can be represented correctly using these quantities.

### Step-by-Step Solution:

1. **Identify the Dimensions of Given Quantities:**
- **Permittivity (ε):**
\[ [\epsilon] = M^{-1} L^{-3} T^{4} A^{2} \]
- **Resistance (R):**
\[ [R] = M^{1} L^{2} T^{-3} A^{-2} \]
- **Gravitational Constant (G):**
\[ [G] = M^{-1} L^{3} T^{-2} \]
- **Voltage (V):**
\[ [V] = M^{1} L^{2} T^{-3} A^{1} \]

2. **Option A: Angular Displacement (θ)**
- Angular displacement is a dimensionless quantity, meaning it has no dimensions.
- The expression given is \( \epsilon^{1} \), which has dimensions.
- **Conclusion:** This option is incorrect.

3. **Option B: Velocity (v)**
- The dimension of velocity is:
\[ [v] = L T^{-1} \]
- The expression given is \( \epsilon^{-1} R^{-1} G^{0} V^{0} \).
- Substitute the dimensions:
\[ \epsilon^{-1} = M^{1} L^{3} T^{-4} A^{2} \]
\[ R^{-1} = M^{-1} L^{-2} T^{3} A^{2} \]
- Combining these:
\[ [v] = (M^{1} L^{3} T^{-4} A^{2})(M^{-1} L^{-2} T^{3} A^{-2}) = M^{0} L^{1} T^{-1} \]
- This matches the dimension of velocity.
- **Conclusion:** This option is correct.

4. **Option C: Dipole Moment (p)**
- The dimension of dipole moment is given by \( p = Q \cdot d \) where \( Q \) is charge and \( d \) is distance.
- Charge \( Q \) can be expressed as \( I \cdot T \) (current times time):
\[ [p] = [Q][d] = (A \cdot T)(L) = A \cdot T \cdot L \]
- The expression given is \( \epsilon^{1} R^{0} G^{0} V^{-1} \):
\[ [p] = [\epsilon] \cdot [V]^{-1} = (M^{-1} L^{-3} T^{4} A^{2})(M^{-1} L^{-2} T^{-3} A^{-1}) = M^{-2} L^{-5} T^{1} A^{1} \]
- This does not match the dimension of dipole moment.
- **Conclusion:** This option is incorrect.

5. **Option D: Force (F)**
- The dimension of force is:
\[ [F] = M^{1} L^{1} T^{-2} \]
- The expression given is \( \epsilon^{2} V^{2} R^{0} G^{0} \):
\[ [F] = [\epsilon]^{2} [V]^{2} = (M^{-1} L^{-3} T^{4} A^{2})^{2} (M^{1} L^{2} T^{-3} A^{1})^{2} \]
- Calculate:
\[ = M^{-2} L^{-6} T^{8} A^{4} \cdot M^{2} L^{4} T^{-6} A^{2} = M^{0} L^{-2} T^{2} A^{6} \]
- This does not match the dimension of force.
- **Conclusion:** This option is incorrect.

### Final Conclusion:
The only correct option is **Option B: Velocity**.