The pair of physical quantities not having same dimensions is :

Let's analyze the dimensions of each physical quantity in the given options.

(a) Torque and Energy

• Torque $\tau = \text{Force} \times \text{Distance}$ $$[\tau] = \left( MLT^{-2} \right) \times L = ML^2T^{-2}$$
• Energy $E = \text{Work} = \text{Force} \times \text{Displacement}$ $$[E] = \left( MLT^{-2} \right) \times L = ML^2T^{-2}$$

(b) Surface Tension and Impulse

• Surface Tension $S = \frac{\text{Force}}{\text{Length}}$ $$[S] = \frac{MLT^{-2}}{L} = MT^{-2}$$
• Impulse $J = \text{Force} \times \text{Time}$ $$[J] = (MLT^{-2}) \times T = MLT^{-1}$$

(c) Angular Momentum and Planck’s Constant

• Angular Momentum $L = \text{Moment of Inertia} \times \text{Angular Velocity}$ $$[L] = \left( ML^2 \right) \times \left( T^{-1} \right) = ML^2T^{-1}$$
• Planck’s Constant $h$ (from $E = h\nu$, where $\nu$ has $T^{-1}$) $$[h] = \frac{E}{\nu} = \frac{ML^2T^{-2}}{T^{-1}} = ML^2T^{-1}$$

(d) Pressure and Young’s Modulus

• Pressure $P = \frac{\text{Force}}{\text{Area}}$ $$[P] = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2}$$
• Young’s Modulus $Y = \frac{\text{Stress}}{\text{Strain}}$
  • Stress has the same dimensions as Pressure.
  • Strain is dimensionless.
  • [Y]=ML⁻¹T⁻²