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Units and Measurement

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Physics Part I

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Class 10 Class 12
The unit of length convenient on the nuclear scale is a fermi : 1 f = 10–15 m. Nuclear sizes obey roughly the following empirical relation :
r = r0 A1/3 

 r is the radius of the nucleus, A its mass number, and
ro is a constant equal to about, 1.2 f.
Show that the rule implies that nuclear mass density is nearly constant for different nuclei.
Estimate the mass density of sodium nucleus. Compare it with the average mass density of a
sodium atom obtained in Exercise. 2.27.

Radius of nucleus r is given by the relation, 

                 r = r0 A1/3

r0 = 1.2 f = 1.2 × 10-15 m 

Volume of nucleus, V = (4 / 3) π r

                                = (4 / 3) π (rA1/3)3 

                                = (4 / 3) π rA       ... (i) 

Now, the mass of a nuclei M is equal to its mass number.

That is, 

M = A amu = A × 1.66 × 10–27 kg

Density of nucleus, ρ = Mass of nucleus / Volume of nucleus

                            = A X 1.66 × 10-27 / (4/3) π r03 A

                            = 3 X 1.66 × 10-27 / 4 π r03  Kg m-3

Density of sodium nucleus is given by,

ρSodium = 3 × 1.66 × 10-27 / 4 × 3.14 × (1.2 × 10-15)3

          = 4.98 × 1018 / 21.71

          = 2.29 × 1017 Kg m-3 


Define physical quantity.


A measurable quantity in terms of which laws of Physics can be expressed is called physical quantity.

The result of a measurement of a physical quantity is expressed by a number accompanied by a unit.


Give four examples of physical quantities.

Examples of Physical quantitie are force, mass, density and power.

Define unit.

The quantity used as a standard of measurement is called unit. 

Example: Unit of time is second. 


What is measurement?

Measurement is the process of attaching a numeric value to an aspect of a natural phenomenon. Measurement is making the quantitative knowledge of a physical quantity. 

What is the need of measurement?

To get the complete knowledge of any physical quantity, measurement is needed. Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. Knowledge without measurement is incomplete and unsatisfactory.