Which physical quantities have the same dimensions?

To identify the pair with identical dimensions, we examine their dimensional formulae based on the sources:

1. Couple of Force (Torque) and Work: A couple of force (or torque) is defined as the rotational analogue of force, and its magnitude is the product of force and the perpendicular distance . Its dimensions are $[MLT^{-2}] \times [L] = [ML^2T^{-2}]$ . Work is defined as force multiplied by displacement ($W = F \cdot d$), resulting in the same dimensions: $[MLT^{-2}] \times [L] = [ML^2T^{-2}]$ .
2. Force and Power: Force has dimensions $[MLT^{-2}]$ . Power is work done per unit time ($P = W/t$), giving it dimensions of $[ML^2T^{-3}]$ .
3. Latent Heat and Specific Heat: Latent heat is heat energy per unit mass ($L = Q/m$), with dimensions $[L^2T^{-2}]$ . Specific heat is heat energy per unit mass per unit temperature change ($s = Q/m\Delta T$), with dimensions $[L^2T^{-2}K^{-1}]$ .

Therefore, only the first pair, Couple of force and work, shares the same dimensional formula.