
Specific gravity has ______ dimensions in mass, ___dimensions in length and ____ dimensions in time.
A. 0,0,0
B. 0,1,1
C. 1,0,0
D. 1,1,3
Answer
511.2k+ views
Hint: This question is based on the concept of specific gravity’s dimension For these types of questions you should know the basic rules to find out the dimensional formula of physical quantities of specific gravity.
Complete Step-by-Step solution:
According to the question we are asked about the dimensions of specific gravity. So, we should know what specific gravity is; Specific gravity can be defined as the ratio between the density of a substance and the density of a given reference substance. It is also known as relative density. The formula of specific density is = density of a substance/density of a given reference substance.
Therefore specific gravity = density of substance/density of water at ${4^ \circ }C$ .
So, we know that the formula of density which is = $\dfrac{{Mass}}{{Volume}}$
The dimensional formula of the volume is [${L^3}$] and that of mass is [M].
Therefore, the dimensional formula of density can be written as:$\dfrac{M}{{{L^3}}} = M{L^{ - 3}}$
Similarly the dimensional formula of the density of water is also $M{L^{ - 3}}$ .
Thus, the formula of specific gravity is = density of substance/ density of water ${4^ \circ }C$ .
So, the dimensional formula of specific gravity will be= $\dfrac{{M{L^{ - 3}}}}{{M{L^{ - 3}}}} = M^0L^0$ .
Therefore the units of density cancel out each other and the specific gravity becomes dimensionless.
Hence, M=0, L=0, T=0.
So, option A is the correct option.
Note: A dimensional formula can be explained as physical quantities in terms of fundamental quantities. Fundamental quantities are Mass, Length and Time knowing the Dimensional formula of specific gravity we can answer the given question.
Complete Step-by-Step solution:
According to the question we are asked about the dimensions of specific gravity. So, we should know what specific gravity is; Specific gravity can be defined as the ratio between the density of a substance and the density of a given reference substance. It is also known as relative density. The formula of specific density is = density of a substance/density of a given reference substance.
Therefore specific gravity = density of substance/density of water at ${4^ \circ }C$ .
So, we know that the formula of density which is = $\dfrac{{Mass}}{{Volume}}$
The dimensional formula of the volume is [${L^3}$] and that of mass is [M].
Therefore, the dimensional formula of density can be written as:$\dfrac{M}{{{L^3}}} = M{L^{ - 3}}$
Similarly the dimensional formula of the density of water is also $M{L^{ - 3}}$ .
Thus, the formula of specific gravity is = density of substance/ density of water ${4^ \circ }C$ .
So, the dimensional formula of specific gravity will be= $\dfrac{{M{L^{ - 3}}}}{{M{L^{ - 3}}}} = M^0L^0$ .
Therefore the units of density cancel out each other and the specific gravity becomes dimensionless.
Hence, M=0, L=0, T=0.
So, option A is the correct option.
Note: A dimensional formula can be explained as physical quantities in terms of fundamental quantities. Fundamental quantities are Mass, Length and Time knowing the Dimensional formula of specific gravity we can answer the given question.
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
A boat goes 24 km upstream and 28 km downstream in class 10 maths CBSE

The British separated Burma Myanmar from India in 1935 class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What are the public facilities provided by the government? Also explain each facility

Difference between mass and weight class 10 physics CBSE

SI unit of electrical energy is A Joule B Kilowatt class 10 physics CBSE
