Which of the following set have different dimensions?

Step 1: Analyze Set (1) - Pressure, Young's modulus, Stress.

Pressure and stress are defined as force per unit area, and Young's modulus is stress divided by the dimensionless quantity strain.

$$[P] = [\sigma] = \frac{[F]}{[A]} = \frac{\text{M L T}^{-2}}{\text{L}^2} = \text{M L}^{-1}\text{T}^{-2}$$ $$[Y] = \frac{[\sigma]}{[\text{strain}]} = \text{M L}^{-1}\text{T}^{-2}$$

All three quantities share the same dimensional formula.

Step 2: Analyze Set (2) - EMF, Potential difference, Electric potential.

These quantities are defined as work done per unit charge.

$$[\varepsilon] = [V] = [\phi] = \frac{[W]}{[q]}$$ $$[\varepsilon] = \frac{\text{M L}^2\text{T}^{-2}}{\text{A T}} = \text{M L}^2\text{T}^{-3}\text{A}^{-1}$$

All three quantities share the same dimensional formula.

Step 3: Analyze Set (3) - Heat, Work done, Energy.

Heat and work are forms of energy, which is defined as force multiplied by displacement.

$$[Q] = [W] = [E] = [F][L]$$ $$[Q] = (\text{M L T}^{-2})(\text{L}) = \text{M L}^2\text{T}^{-2}$$

All three quantities share the same dimensional formula.

Step 4: Analyze Set (4) - Dipole moment, Electric flux, Electric field.

Calculate the dimensional formula for each quantity individually.

$$[p] = [q][L] = \text{M}^0\text{L T A}$$ $$[E_{\text{field}}] = \frac{[F]}{[q]} = \frac{\text{M L T}^{-2}}{\text{A T}} = \text{M L T}^{-3}\text{A}^{-1}$$ $$[\Phi] = [E_{\text{field}}][L^2] = \text{M L}^3\text{T}^{-3}\text{A}^{-1}$$

Since the dimensional formulas do not match, the quantities in this set have different dimensions.

Answer: (4) Dipole moment, Electric flux, Electric field