To determine which pair has the same dimensions, we analyze the dimensional formulae of the given quantities:
- Work (W): Defined as the product of force and displacement (W=F⋅d). Its dimensional formula is [ML2T−2] .
- Energy (E): Energy is the capacity to do work. Kinetic energy (K=21mv2) and potential energy have the same dimensions as work, which is [ML2T−2] .
- Power (P): Defined as the rate of doing work (P=W/t). Its dimensions are [ML2T−3] .
- Momentum (p): Defined as the product of mass and velocity (p=mv). Its dimensions are [MLT−1] .
- Force (F): Defined as mass times acceleration (F=ma). Its dimensions are [MLT−2] .
Conclusion: Comparing the dimensions, Work and Energy both possess the dimensional formula [ML2T−2].