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 solve the question of identifying the set of physical quantities that are dimensionally different, we need to analyze the dimensions of each option provided. Let's break down the solution step by step.

### Step 1: Identify the Physical Quantities in Each Option
We need to define the physical quantities in each option. Let's assume the options are as follows:

- Option A: Velocity (v)
- Option B: Energy (E), Work (W), and Heat (Q)
- Option C: Frequency (f), Angular frequency (ω), and Wave number (k)
- Option D: Dipole moment (p), Electric flux (Φ), and Electric field (E)

### Step 2: Determine the Dimensions of Each Quantity
Now we will find the dimensional formula for each quantity in the options.

1. **Option A: Velocity (v)**
- Dimension of velocity = [L][T]⁻¹

2. **Option B: Energy (E), Work (W), Heat (Q)**
- Dimension of energy = [M][L]²[T]⁻²
- Dimension of work = [M][L]²[T]⁻²
- Dimension of heat = [M][L]²[T]⁻²
- All three have the same dimension.

3. **Option C: Frequency (f), Angular frequency (ω), Wave number (k)**
- Dimension of frequency = [T]⁻¹
- Dimension of angular frequency = [T]⁻¹
- Dimension of wave number = [L]⁻¹
- Frequency and angular frequency have the same dimension, but wave number is different.

4. **Option D: Dipole moment (p), Electric flux (Φ), Electric field (E)**
- Dimension of dipole moment = [M][L]²[I]⁻¹[T]⁻²
- Dimension of electric flux = [M][L]³[I]⁻¹[T]⁻³
- Dimension of electric field = [M][L][I]⁻¹[T]⁻³
- All three have different dimensions.

### Step 3: Conclusion
From the analysis:
- Option A has the same dimension (velocity).
- Option B has the same dimension (energy, work, heat).
- Option C has two with the same dimension (frequency and angular frequency) and one different (wave number).
- Option D has all different dimensions.

Thus, the set of physical quantities that are dimensionally different is **Option D**.

### Final Answer
The set of physical quantities among the following which is dimensionally different is **Option D**.

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