The set of physical quantities among the following which is dimensionally different is

Options

A. Terminal velocity , drifty , drift velocity , critical velocity
B. Potential energy , work done, kinetic energy
C. Disintegration constant , frequency angular velocity
D. Dipole moment , electric flux , electric field

Answer

To determine which set of physical quantities is dimensionally different, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Analyze the First Option: Terminal Velocity, Drift Velocity, and Critical Velocity**
- All three quantities are types of velocity.
- The dimension of velocity is given by:
\[ [\text{Velocity}] = [L T^{-1}] \]
- Since all three quantities are velocities, they share the same dimension. Thus, this option is not dimensionally different.

2. **Analyze the Second Option: Potential Energy, Work Done, and Kinetic Energy**
- Potential Energy (U) is defined as:
\[ U = mgh \quad \text{(where } m \text{ is mass, } g \text{ is acceleration due to gravity, and } h \text{ is height)} \]
- The dimension of Potential Energy is:
\[ [U] = [M L^2 T^{-2}] \]
- Work Done (W) is defined as:
\[ W = \text{Force} \times \text{Displacement} \]
- The dimension of Work Done is also:
\[ [W] = [M L^2 T^{-2}] \]
- Kinetic Energy (KE) is defined as:
\[ KE = \frac{1}{2} mv^2 \]
- The dimension of Kinetic Energy is:
\[ [KE] = [M L^2 T^{-2}] \]
- All three quantities have the same dimension, so this option is also not dimensionally different.

3. **Analyze the Third Option: Disintegration Constant, Frequency, and Angular Velocity**
- Disintegration Constant (λ) has the dimension of:
\[ [\lambda] = [T^{-1}] \]
- Frequency (ν) is defined as:
\[ \nu = \frac{1}{T} \quad \Rightarrow \quad [\nu] = [T^{-1}] \]
- Angular Velocity (ω) is defined as:
\[ \omega = \frac{\theta}{T} \quad \Rightarrow \quad [\omega] = [T^{-1}] \]
- All three quantities have the same dimension, so this option is also not dimensionally different.

4. **Analyze the Fourth Option: Dipole Moment, Electric Flux, and Electric Field**
- Dipole Moment (p) is defined as:
\[ p = q \cdot d \quad \text{(where } q \text{ is charge and } d \text{ is distance)} \]
- The dimension of charge (q) is:
\[ [q] = [I T] \quad \text{(where I is current)} \]
- The dimension of distance (d) is:
\[ [d] = [L] \]
- Thus, the dimension of Dipole Moment is:
\[ [p] = [I T] \cdot [L] = [I L T] \]

- Electric Flux (Φ) is defined as:
\[ \Phi = E \cdot A \quad \text{(where E is electric field and A is area)} \]
- The dimension of Electric Field (E) is:
\[ [E] = [F/A] = \frac{[M L T^{-2}]}{[L^2]} = [M L^{-1} T^{-2}] \]
- The dimension of area (A) is:
\[ [A] = [L^2] \]
- Thus, the dimension of Electric Flux is:
\[ [\Phi] = [E] \cdot [A] = [M L^{-1} T^{-2}] \cdot [L^2] = [M L T^{-2}] \]

- Electric Field (E) has already been calculated as:
\[ [E] = [M L^{-1} T^{-2}] \]

- Therefore, we have:
- Dipole Moment: \([I L T]\)
- Electric Flux: \([M L T^{-2}]\)
- Electric Field: \([M L^{-1} T^{-2}]\)

- Since the dimensions of these three quantities are different, this option is dimensionally different.

### Conclusion:
The set of physical quantities that is dimensionally different is the **fourth option: Dipole Moment, Electric Flux, and Electric Field**.