Final answer:
None of the physical quantities A) Speed, B) Acceleration, C) Force, or D) Power are dimensionless. Each contains dimensions of mass, length, or time, and the dimensional analysis shows they are not expressed solely as pure numbers without any unit or dimension.
Step-by-step explanation:
The question asks to verify whether the left-hand side of various physical quantity equations is dimensionless by using the MLT system of dimensions. Dimensional analysis involves making sure that the dimensions match on both sides of an equation and is a key concept in physics for ensuring equations are physically meaningful.
Here are the analyses for the given physical quantities:
- Speed (v) is dimensionally represented as LT-1, which is not dimensionless as it involves dimensions of Length (L) and Time (T).
- Acceleration (a) has dimensions LT-2 and is also not dimensionless.
- Force (F) equals mass times acceleration, or M(LT-2) which simplifies to MLT-2, and therefore is not dimensionless.
- Power (P) is the rate of doing work, which can be expressed as work (force times distance, ML2T-2) over time (T), resulting in the dimension ML2T-3, and is not dimensionless.
Therefore, none of the quantities A) Speed, B) Acceleration, C) Force, or D) Power are dimensionless, as they all contain the dimensions of mass (M), length (L), or time (T) in some combination.