Write dimensions of each physical quantity

• Force: $F = ma$ Since $[m] = M, \quad [a] = LT^{-2}$ therefore, $[F] = MLT^{-2}$

• Work: $W = F \times s$ where displacement has dimension $[s] = L$. So, $[W] = [F][L] = (MLT^{-2})(L) = ML^2T^{-2}$

• Torque: $\tau = F \times r$ where perpendicular distance $r$ has dimension $L$. Hence, $[\tau] = [F][L] = (MLT^{-2})(L) = ML^2T^{-2}$

• Stress: $\text{Stress} = \frac{\text{Force}}{\text{Area}}$ Area has dimension $L^2$. Thus, $[\text{Stress}] = \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2}$

• Energy has same dimensions as work: $[E] = ML^2T^{-2}$

Check each option

• A: torque and work $[\tau] = ML^2T^{-2}, \quad [W] = ML^2T^{-2}$ These are equal. ✅

• B: stress and energy $[\text{Stress}] = ML^{-1}T^{-2}, \quad [E] = ML^2T^{-2}$ Not equal. ❌

• C: force and stress $[F] = MLT^{-2}, \quad [\text{Stress}] = ML^{-1}T^{-2}$ Not equal. ❌

• D: force and work $[F] = MLT^{-2}, \quad [W] = ML^2T^{-2}$ Not equal. ❌

Final answer

The pair having equal dimensions is: $\boxed{\text{Torque and Work}}$ So, Option A is correct.