The pair having the same dimensions is:

To determine which pair has the same dimensions, we can analyze the dimensional formula for each quantity based on the sources:

1. Work ($W$): Defined as force multiplied by displacement ($W = F \cdot d$). Force has dimensions $[MLT^{-2}]$ and displacement is $[L]$, so work has dimensions $[ML^2T^{-2}]$ .
2. Torque ($\tau$): Defined as the product of force and the perpendicular distance from the axis of rotation ($\tau = r \times F$). Its dimensions are $[L] \times [MLT^{-2}] = [ML^2T^{-2}]$ .
3. Angular Momentum ($L$): Defined as the product of position vector and linear momentum ($L = r \times p$). Its dimensions are $[L] \times [MLT^{-1}] = [ML^2T^{-1}]$ .
4. Potential/Kinetic Energy: All forms of energy share the same dimensions as work, which is $[ML^2T^{-2}]$ .
5. Linear Momentum ($p$): Product of mass and velocity ($p = mv$), with dimensions $[MLT^{-1}]$ .
6. Velocity ($v$): Displacement per unit time, with dimensions $[LT^{-1}]$ .

Comparing the pairs, Work and Torque both share the dimensional formula $[ML^2T^{-2}]$, making Option B the correct choice.