To determine the physical quantity corresponding to the unit Joule-second (J⋅s), we analyze the dimensions:
- Joule (J): SI unit of Work or Energy. Dimensional formula is [ML2T−2] .
- Second (s): SI unit of Time. Dimensional formula is [T].
- Joule-second (J⋅s): Multiply the dimensions: [ML2T−2]×[T]=[ML2T−1].
- Compare with Options:
- Work: [ML2T−2] (Unit: J). Mismatch.
- Momentum (Linear): [MLT−1] (Unit: kg⋅m⋅s−1 or N⋅s). Mismatch.
- Pressure: [ML−1T−2] (Unit: Pa or N⋅m−2). Mismatch.
- Angular Momentum: Formula is moment of momentum (r×p). Dimensions are [L]×[MLT−1]=[ML2T−1]. This matches the dimensions of J⋅s.
- Note: The unit J⋅s is also the unit of Planck's constant (h), which has the same dimensions as angular momentum .