Measurement and Units Important Points

 The dimensional formula is very helpful in writing the unit of a
physical quantity in terms of the basic units.

 The dimensions of a physical quantity do not depend on the system
of units.

 A physical quantity that does not have any unit must be
dimensionless.

 The pure numbers are dimensionless.

 Generally, the symbols of those basic units, whose dimension
(power) in the dimensional formula is zero, are omitted from the
dimensional formula.

 It is wrong to say that the dimensions of force are MLT–2. On the
other hand we should say that the dimensional formula for force is MLT–2
and that the dimensions of force are 1 in mass, 1 in length and –2 in
time.

 Physical quantities defined as the ratio of two similar quantities are
dimensionless.

 The physical relation involving logarithm, exponential,
trigonometric ratios, numerical factors etc. cannot be derived by the
method of dimensional analysis.

 Physical relations involving addition or subtraction sign cannot be
derived by the method of dimensional analysis.

 If units or dimensions of two physical quantities are same, these
need not represent the same physical characteristics. For example torque
and work have the same units and dimensions but their physical
characteristics are different.

 The standard units must not change with space and time. That is
why atomic standard of length and time have been defined. Attempts are
being made to define the atomic standard for mass as well.

 The unit of time, the second, was initially defined in terms of the
rotation of the earth around the sun as well as that about its own axis.
This time standard is subjected to variation with time. Therefore, the
atomic standard of time has been defined.

 The product of numerical value (n) and unit (U) of a physical
quantity is called magnitude of the physical quantity.
Thus : Magnitude = nU

 Poiseuille (unit of viscosity) = pascal (unit of pressure) × second.
That is : Pl : Pa- s.

 The unit of power of lens (dioptre) gives the ability of the lens to
converge or diverge the rays refracted through it.

 The order of magnitude of a quantity means its value (in suitable
power of 10) nearest to the actual value of the quantity.

 Angle is exceptional physical quantity, which though is a ratio of
two similar physical quantities (angle = arc / radius) but still requires a
unit (degrees or radians) to specify it along with its numerical value.

 Solid angle subtended at a point inside the closed surface is 4pi
steradian.