Question

(i) Explain this statement clearly
“To call a dimensional quantity ‘large’ or’ small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
(a) atoms are very small objects

(ii) Explain this statement clearly
“To call a dimensional quantity ‘large’ or’ small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
(b)a jet plane moves with great speed

(iii) Explain this statement clearly
“To call a dimensional quantity ‘large’ or’ small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
(c)the mass of Jupiter is very large

(iv) Explain this statement clearly
“To call a dimensional quantity ‘large’ or’ small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
(d)the air inside this room contains a large number of molecules

(v) Explain this statement clearly
“To call a dimensional quantity ‘large’ or’ small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
(e)a proton is much more massive than an electron

(vi) Explain this statement clearly
“To call a dimensional quantity ‘large’ or’ small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
(f) the speed of sound is much smaller than the speed of light

Answer 1

(i) The given statement is correct. Measurement is basically a comparison process. Without specifying a standard of comparison, it is not possible to get an exact idea about the magnitude of a dimensional quantity. For example, the statement that the mass of the earth is very large, is meaningless. To correct it, we can say that the mass of the earth is large in comparison to any object lying on its surface.
The size of an atom is much smaller than the sharp tip of a pin.

(ii) The given statement is correct. Measurement is basically a comparison process. Without specifying a standard of comparison, it is not possible to get an exact idea about the magnitude of a dimensional quantity. For example, the statement that the mass of the earth is very large, is meaningless. To correct it, we can say that the mass of the earth is large in comparison to any object lying on its surface.
A jet plane moves with a much larger speed than a superfast train.

(iii) The given statement is correct. Measurement is basically a comparison process. Without specifying a standard of comparison, it is not possible to get an exact idea about the magnitude of a dimensional quantity. For example, the statement that the mass of the earth is very large, is meaningless. To correct it, we can say that the mass of the earth is large in comparison to any object lying on its surface.
The mass of Jupiter is very large as compared to that earth.

(iv)The given statement is correct. Measurement is basically a comparison process. Without specifying a standard of comparison, it is not possible to get an exact idea about the magnitude of a dimensional quantity. For example, the statement that the mass of the earth is very large, is meaningless. To correct it, we can say that the mass of the earth is large in comparison to any object lying on its surface.
The air inside this room contains a very large number molecules as compared to that in a balloon.

(v) The given statement is correct. Measurement is basically a comparison process. Without specifying a standard of comparison, it is not possible to get an exact idea about the magnitude of a dimensional quantity. For example, the statement that the mass of the earth is very large, is meaningless. To correct it, we can say that the mass of the earth is large in comparison to any object lying on its surface.
The given statement “a proton is much more massive than an electron” is correct.

(vi) The given statement is correct. Measurement is basically a comparison process. Without specifying a standard of comparison, it is not possible to get an exact idea about the magnitude of a dimensional quantity. For example, the statement that the mass of the earth is very large, is meaningless. To correct it, we can say that the mass of the earth is large in comparison to any object lying on its surface.
The given statement “the speed of sound is much smaller than the speed of light.” is correct.