Explain this statement clearly:
“To call a dimensionless quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison,” In view of this, which of the following statements are complete:
(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.
Answer
643.5k+ views
Hint: Physical quantities are described as large or small depending upon the standard or the unit of measurement. A dimensionless quantity is a quantity which has no physical dimensions, in other words it is independent of the fundamental units.
Complete answer:
The given statement is correct. Now, for an example we know that angle is a dimensionless quantity.
If we say that $\angle \theta = {70^ \circ }$ is greater than $\angle \theta = {20^ \circ }$, this statement is said to be meaningful because a standard is specified for comparison for the dimensionless quantity.
Now, from the given statements, statement (e) and statement (f) are correct because a standard is specified for the comparison. Even if the given physical quantity is dimensionless, we can find out whether it is small or large. While in the statements (a), (b), (c) and (d) a standard for comparison is needed to be specified to make it a meaningful statement.
Hence, in view of this, statements (e) and (f) are complete.
Additional Information:
Dimensional formula of a given physical quantity is defined as the expression which shows how and which of the fundamental quantities represent the dimensions of a physical quantity. The equation which is obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the given physical quantity.
Note:
Students tend to confuse between Dimensionless physical quantity and a Dimensional constant physical quantity. A dimensionless physical quantity is one which has dimensions. In other words, it would have no units associated with it. On the other hand, dimensional constants may or may not have units associated with it but its value is fixed and depends only on the chosen fundamental units being used to represent it, not the system itself.
Complete answer:
The given statement is correct. Now, for an example we know that angle is a dimensionless quantity.
If we say that $\angle \theta = {70^ \circ }$ is greater than $\angle \theta = {20^ \circ }$, this statement is said to be meaningful because a standard is specified for comparison for the dimensionless quantity.
Now, from the given statements, statement (e) and statement (f) are correct because a standard is specified for the comparison. Even if the given physical quantity is dimensionless, we can find out whether it is small or large. While in the statements (a), (b), (c) and (d) a standard for comparison is needed to be specified to make it a meaningful statement.
Hence, in view of this, statements (e) and (f) are complete.
Additional Information:
Dimensional formula of a given physical quantity is defined as the expression which shows how and which of the fundamental quantities represent the dimensions of a physical quantity. The equation which is obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the given physical quantity.
Note:
Students tend to confuse between Dimensionless physical quantity and a Dimensional constant physical quantity. A dimensionless physical quantity is one which has dimensions. In other words, it would have no units associated with it. On the other hand, dimensional constants may or may not have units associated with it but its value is fixed and depends only on the chosen fundamental units being used to represent it, not the system itself.
Watch videos on
Explain this statement clearly:
“To call a dimensionless quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison,” In view of this, which of the following statements are complete:
(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.
“To call a dimensionless quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison,” In view of this, which of the following statements are complete:
(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.

NCERT EXERCISE 1.4 | NCERT Solution for Class 11 Physics Chapter 1 | Units and Measurement NCERT
Subscribe
likes
13.7K Views
3 years ago
Recently Updated Pages
Write structures of the following compounds i 2 Chloro3methylpentane class 11 chemistry CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

A Paragraph on Pollution in about 100-150 Words

XIX+XXX A 49 B 51 C 55 D 44 class 5 maths CBSE

If x a + bt + ct2 where x is in meters and t is in class 11 physics CBSE

Trending doubts
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Find the value of the expression given below sin 30circ class 11 maths CBSE

What do you mean by retardation What is its SI uni class 11 physics CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

10 examples of friction in our daily life

Difference between physical and chemical change class 11 chemistry CBSE

