If velocity of light in air (3x10⁸m/s), acceleration due to gravity (9.8m/s²) and density of mercury (13600kg/m³) be chosen as fundamental units, then find the unit of mass, length and time.

Solution

Given that,
$V e l o c i t y space o f space l i g h t space equals space open square brackets L to the power of 1 T to the power of negative 1 end exponent close square brackets equals 3 cross times 10 to the power of 8 space m divided by s space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis A c c e l e r a t i o n space d u e space t o space g r a v i t y equals space open square brackets L to the power of 1 T to the power of negative 2 end exponent close square brackets space equals space 9.8 m divided by s squared space space space space space space space space space space space space space... left parenthesis 2 right parenthesis D e n s i t y space o f space m e r c u r y comma space open square brackets M to the power of 1 L to the power of negative 3 end exponent close square brackets equals 13600 space k g divided by m cubed space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 3 right parenthesis$
Now, dividing equation (1) by (2),
{T} = 3.061 x 10⁷s ....(4)
From(1) and (4)
L = 3 x 10⁸x T

= 9.183 x 10¹⁵m ....(5)
Therefore, from equation (3) and (5), we have
M = 13600 x L³
= 13600 x (9.183 X 10¹⁵)³
M = 1.053 x 10⁵²kg

Some More Questions From Units and Measurement Chapter

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Units And Measurement

If velocity of light in air (3x10⁸m/s), acceleration due to gravity (9.8m/s²) and density of mercury (13600kg/m³) be chosen as fundamental units, then find the unit of mass, length and time.

Some More Questions From Units and Measurement Chapter

Define unit.

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

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For Daily Free Study Material Join wiredfaculty

Units And Measurement

If velocity of light in air (3x108m/s), acceleration due to gravity (9.8m/s2) and density of mercury (13600kg/m3) be chosen as fundamental units, then find the unit of mass, length and time.

Some More Questions From Units and Measurement Chapter

Define unit.

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If velocity of light in air (3x10⁸m/s), acceleration due to gravity (9.8m/s²) and density of mercury (13600kg/m³) be chosen as fundamental units, then find the unit of mass, length and time.