Chemistry, asked by 41094aasika, 1 month ago

Mass is called fundamental quantity but velocity is called derived quantity? Give reason.

Answers

Answered by rishabhkumar91281
3

Answer:

Mass is called a fundamental quantity because it doesn't depends upon others physical quantity and made up of only one unit whereas velocity depends upon other fundamental quantity and made up of two or more than two units

Answered by 1234567890123565562
0

Answer:

Explanation:

In metrology physical quantities (and units) are called fundamental due to ignorance. “Fundamental” belongs in the realm of metaphysics. The intended terminology is “base [physical] quantity”, which is not the same thing as fundamental quantity, so quit using the wrong term. In SI mass is a base physical quantity, as is the case in the British imperial and US customary systems. In engineering unit systems excluding SI, it is common to declare force to be a base quantity rather than mass.

Physical quantities being base versus derived is a purely abstract mathematical construct originating in the realm of vector spaces, where the term is “basis vector”, and the choice of which physical quantities is mostly arbitrary. The only restriction is that base quantities must be linearly independent from one another, where linear independence refers to the tuplet of exponents applied to the base quantities to achieve any particular physical quantity.

Why is velocity is called a derived physical quantity?

Once the base quantities have been selected, all other physical quantities are defined by expressing a derivation in terms of the base quantities. Four common quantities are length (distance as scalar or displacement as vector), time duration, velocity (as vector) or speed (as scalar), and acceleration. You may use any two of these as base quantities and the other two will then be derivable in terms of the first two. One can certainly define speed or velocity to be a base quantity, but if you do so, you will have to give up one of length or time duration as a base quantity. Let’s try having time duration and speed as base quantities: then length is derived as the product of time duration and speed, and acceleration is derived as speed divided by time duration. Energy would then be derived as the product of mass and the square of speed. If you made speed and acceleration to be base quantities, then time duration would be derived as speed divided by acceleration and length would be derived as speed squared divided by acceleration. These can be seen mathematically in terms of the vectors mentioned above:

Time: (1, 0, 0, 0, 0, 0, 0)—call it T as above;

Length: (0, 1, 0, 0, 0, 0, 0)—call it L as above;

Speed: (−1, 1, 0, 0, 0, 0, 0)—call it S for this discussion;

Acceleration: (−2, 1, 0, 0, 0, 0, 0)—call it A for this discussion.

[NOTE: There is nothing in the definitions of vector spaces that require basis vectors to be of the form of nd all other components 0, nor even that the basis vectors be orthogonal or normalized.]

If T and L are the basis vectors for the first two dimensions, then:

S = L − T and A = L − 2T.

If T and S are the basis vectors for the first two dimensions, then:

L = S + T and A = S − T.

If S and A are the basis vectors for the first two dimensions, then:

L = 2S − A and T = S − A.

Similar relationships hold when L and S, or L and A, or T and A are chosen as the basis vectors for the first two dimensions. From a mathematical standpoint it is totally arbitrary which two you pick as the basis vectors. Regardless of which two are defined as base quantities, the other two can be derived from the first two and defined via that derivation. If you try to define three of these as base quantities, that requires tying each of the three independently to the outside world, and inevitably that leads at some point to a contradiction, so which two are the most important to retain and which one do we allow to be broken and ignored? If one is ignored, it just as well not exist, which means it just as well not have been made a base unit in the first place. This is not just a theoretical concern—it has actually happened in real life and caused some grief. The original metric system defined the meter, liter, and kilogram in a very tightly coupled manner. Within a few years, a metal bar definition replaced the Earth definition of the meter and a hunk of metal based definition of the kilogram replaced the liter of water definition.

Similar questions