Class 11 NCERT PHYSICS • Chapter 1: Units and Measurement • Question 4

QUESTION 4

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

(b) A jet plane moves with great speed

(c) The mass of Jupiter is very large

(d) The air inside this room contains a large number of molecules

(e) a proton is much more massive than an electron

(f) the speed of sound is much smaller than the speed of light.

SOLUTION

We need to explain why dimensional quantities require standards and reframe the given statements using relative comparisons.

Concept: Dimensional quantity

The magnitude of a dimensional quantity is relative. To describe a quantity as "large" or "small," one must compare it to a standard of comparison of the same dimension. Mathematically, we evaluate the ratio:

R = \frac{Q_{\text{measured}}}{Q_{\text{standard}}}

If $R \gg 1$ , the quantity is "large"; if $R \ll 1$ , it is "small."

Given:

The following statements describing physical magnitudes:

(a) Atoms are very small objects.
(b) A jet plane moves with great speed.
(c) The mass of Jupiter is very large.
(d) The air inside this room contains a large number of molecules.
(e) A proton is much more massive than an electron.
(f) The speed of sound is much smaller than the speed of light.

Solving:

Explanation of the Statement

A dimensional quantity (like length, mass, or time) has no intrinsic "size" in isolation. For example, $1\,\text{meter}$ is large compared to $1\,\text{micrometer}$ but extremely small compared to the radius of the Earth. Without a reference, these adjectives are subjective and lack physical context.
Reframing the Statements
- (a) Atoms are very small compared to the size of a sharp pinhead.
- (b) A jet plane moves with great speed compared to a high-speed train.
- (c) The mass of Jupiter is very large compared to the mass of the Earth.
- (d) The air inside this room contains a large number of molecules compared to the number of people in a room.
- (e) This statement is already meaningful because it specifies a standard (the electron). It can be quantified: A proton is approximately $1836$ times more massive than an electron.
- (f) This statement is already meaningful because it specifies a standard (the speed of light). It can be quantified: The speed of sound in air is roughly $10^{-6}$ times the speed of light.

Units and Measurement