We compare dimensions of each pair.

Option A: torque and work

• Torque $= \text{force} \times \text{distance}$ $[\tau] = [F][L] = (MLT^{-2})(L) = ML^2T^{-2}$
• Work $= \text{force} \times \text{displacement}$ $[W] = [F][L] = ML^2T^{-2}$
• Same dimensions.

Option B: momentum and Planck's constant

• Momentum: $[p] = MLT^{-1}$
• Planck's constant $h$: $h = (\text{energy})\times(\text{time})$ $[h] = (ML^2T^{-2})(T) = ML^2T^{-1}$
• These are not same because momentum has $L^1$ while Planck's constant has $L^2$.
• So this pair has different dimensions.

Option C: stress and Young's modulus

• Stress $= \dfrac{\text{force}}{\text{area}}$ $[\text{stress}] = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2}$
• Young's modulus $= \dfrac{\text{stress}}{\text{strain}}$
• Strain is dimensionless, so $[Y] = [\text{stress}] = ML^{-1}T^{-2}$
• Same dimensions.

Option D: speed and $({\mu_0\varepsilon_0})^{-1/2}$

• From electromagnetic wave relation: $c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}$
• Since $c$ is speed, $({\mu_0\varepsilon_0})^{-1/2}$ has dimensions of speed: $LT^{-1}$
• Same dimensions.

Therefore, the only pair not having same dimensions is: $\boxed{\text{B}}$