Chap. Measurments Tips and Tricks

→   The standard of Weight and Measures Act was passed in India in

1976. It recommended the use of SI in all fields of science, technology,

trade and industry.

→   The dimensions of many physical quantities, especially those in

heat, thermodynamics, electricity and magnetism in terms of mass,

length and time alone become irrational. Therefore, SI is adopted which

uses 7 basic units.

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→   The dimensions of a physical quantity are the powers to which

→   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.

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→   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.

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→   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.

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→   Any repetitive phenomenon, such as an oscillating pendulum,

spinning of earth about its axis, etc can be used to measure time.

→   The product of numerical value of the physical quantity (n) and its

unit (U) remains constant..

→   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.

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→   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 4

steradian.

A measurement of a physical quantity is said to be accurate if the

systematic error in its measurement is relatively very low. On the other

hand, the measurement of a physical quantity is said to be precise if the

random error is small.

→   A measurement is most accurate if its observed value is very close

to the true value.

→   Errors are always additive in nature.

→   For greater accuracy, the quantity with higher power should have

least error.

→   The absolute error in each measurement is equal to the least count

of the measuring instrument.

→   Percentage error = relative error × 100.

→   The unit and dimensions of the absolute error are same as that of

quantity itself.

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→   Absolute error is not dimensionless quantity.

→   Relative error is dimensionless quantity.

→   Smaller the least count, higher is the accuracy of measurement.

→   Larger the number of significant figures after the decimal in a

measurement, higher is the accuracy of measurement.

→   Significant figures do not change if we measure a physical quantity

in different units.

→   Significant figures retained after mathematical operation (like

addition, subtraction, multiplication and division) should be equal to the

minimum significant figures involved in any physical quantity in the

given operation.

→   Significant figures are the number of digits upto which we are sure

about their accuracy.

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→   If a number is without a decimal and ends in one or more zeros,

then all the zeros at the end of the number may not be significant.

→   1 inch = 2.54 cm

1 foot = 12 inches = 30.48 cm = 0.3048 m

1 mile = 5280 ft = 1.609 km

→   1 yard = 0.9144 m

1 slug = 14.59 kg

→   1 barn = 10–28 m2

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→   1 liter = 103 cm3 = 10–3 m3

→   1 g/cm3 = 1000 kg/m3

→   1 atm. = 76 cm of Hg = 1.013 × 105 N/m2

1 N/m2 = Pa (Pascal)

→   When we add or subtract two measured quantities, the absolute

error in the final result is equal to the sum of the absolute errors in the

measured quantities.

→   When we multiply or divide two measured quantities, the relative

error in the final result is equal to the sum of the relative errors in the

measured quantities

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