My question is how ratio can a physical quantity. In my understanding physical quantity must have magnitude (a number) and unit but sometimes ratio doesnt have any units.

Simliarly how just a scalar can be a physical quantity if theres no unit associated.

Guide me a good defination of physical quantity.

Answers (1)

Basic Definition - A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement

Neither the name of a physical quantity, nor the symbol used to denote it, implies a particular choice of unit, though SI units are usually preferred and assumed today due to their ease of use and all-round applicability. 

for instance, say someone tells you that the mass of the Earth is approximately 6 septillion (24 zeroes) kilograms. Surely this is a number with units, is it not. But… I could convey the exact same information by telling you that the ratio of the Earth’s mass and the mass of a particular reference weight is 6 septillion. So it would take 6 septillion such reference weights to build an object as massive as the Earth. This 6 septillion is just a number. It has no units. It expresses the ratio of two like things (two masses) and its value remains the same regardless of what units we choose to measure mass.

Or, if someone tells you that the Earth’s equator is 40 million meters long. But… instead of saying that, they tell you that the ratio of the Earth’s length to the length of their favorite meter stick is 40 million. Again, we have a ratio of two like things (two lengths), and this ratio is a number without units.

What about derived quantities? Say, speed, which is length divided by time. Well… same thing, really. We could choose a reference speed (the speed of light would be a good, natural choice) and just compare all other speeds to this reference speed.

Hope you understood the analogy, Good luck!