To determine which of the given sets have different dimensions, we will analyze the dimensions of each quantity in the options provided.
### Step 1: Analyze Option A - Pressure, Young's Modulus, and Stress
- **Pressure (P)**: Defined as force per unit area. Its dimensions are:
\[
[P] = \frac{[F]}{[A]} = \frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}]
\]
- **Young's Modulus (Y)**: Defined as stress (force per unit area) divided by strain (dimensionless). Its dimensions are:
\[
[Y] = \frac{[Stress]}{[Strain]} = \frac{[P]}{1} = [M][L^{-1}][T^{-2}]
\]
- **Stress (σ)**: Defined as force per unit area, similar to pressure. Its dimensions are:
\[
[σ] = [P] = [M][L^{-1}][T^{-2}]
\]
**Conclusion for Option A**: All three quantities have the same dimensions.
### Step 2: Analyze Option B - EMF, Potential Difference, and Electric Potential
- **EMF (Electromotive Force)**: Defined as work done per unit charge. Its dimensions are:
\[
[EMF] = \frac{[Work]}{[Charge]} = \frac{[M][L^2][T^{-2}]}{[I][T]} = [M][L^2][T^{-3}][I^{-1}]
\]
- **Potential Difference (V)**: Also defined as work done per unit charge, so its dimensions are the same as EMF:
\[
[V] = [EMF] = [M][L^2][T^{-3}][I^{-1}]
\]
- **Electric Potential (V)**: Defined similarly as work done per unit charge, thus:
\[
[Electric\ Potential] = [V] = [M][L^2][T^{-3}][I^{-1}]
\]
**Conclusion for Option B**: All three quantities have the same dimensions.
### Step 3: Analyze Option C - Heat, Work Done, and Energy
- **Heat (Q)**: A form of energy, so its dimensions are:
\[
[Q] = [Energy] = [M][L^2][T^{-2}]
\]
- **Work Done (W)**: Defined as force times distance, so its dimensions are:
\[
[W] = [F][d] = [M][L][T^{-2}][L] = [M][L^2][T^{-2}]
\]
- **Energy (E)**: Defined similarly to work done, thus:
\[
[E] = [W] = [M][L^2][T^{-2}]
\]
**Conclusion for Option C**: All three quantities have the same dimensions.
### Step 4: Analyze Option D - Dipole Moment, Electric Flux, and Electric Field
- **Dipole Moment (p)**: Defined as charge times distance, so its dimensions are:
\[
[p] = [Q][d] = [I][T][L] = [I][L][T]
\]
- **Electric Flux (Φ)**: Defined as electric field times area, so its dimensions are:
\[
[Φ] = [E][A] = [M][L][T^{-3}][I^{-1}][L^2] = [M][L^3][T^{-3}][I^{-1}]
\]
- **Electric Field (E)**: Defined as force per unit charge, so its dimensions are:
\[
[E] = \frac{[F]}{[Q]} = \frac{[M][L][T^{-2}]}{[I][T]} = [M][L][T^{-3}][I^{-1}]
\]
**Conclusion for Option D**: The dipole moment, electric flux, and electric field have different dimensions.
### Final Answer
The set that has different dimensions is **Option D**: Dipole Moment, Electric Flux, and Electric Field.
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