AP Inter 1st Year Physics Notes Chapter 2 Units and Measurements

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AP Inter 1st Year Physics Notes 2nd Lesson Units and Measurements

→ The accuracy depends on the errors and also on the precision of measuring instrument.

→ There will be certain amount of uncertainty inherent in the measurement of physical quantities by any instrument. This uncertainty is called the error.

→ When the result of a series of measurements are in error by the same amount. Such an error is called constant error.

→ Systematic errors are those errors that tend to be always in one direction.

→ Systematic errors with a constant magnitude are called constant errors.

→ The different types of systematic errors are

1. Imperfection in experimental technique or procedure
2. Environmental errors,
3. Personal errors or Observational errors.

→ When the random errors could be eliminated we say the measurements are precise.

→ When all types of errors are eliminated then the measurements are accurate.

→ When two quantities are added or subtracted, the (maximum) absolute error in the result (in both cases) will be the sum of the absolute errors in the two quantities.

→ When two quantities are multiplied or divided, the (maximum) relative error in the result (in both cases) will be the sum of the relative errors in the two quantities.

→ The digits of a number that are definitely known plus one more digit that is estimated are called significant digits or significant figures.

→ The process of emitting the non-significant digits and retaining only the desired number of significant digits incorporating the required modifications to the last significant digit is called “rounding off the number”.

→ A physical quantity which is independent of any other physical quantity is called a fundamental quantity, e.g. : length, mass, time, temperature, strength of current, intensity of light and quantity of matter.

→ The units of fundamental quantities are called fundamental units.

→ The physical quantities which can be expressed in terms of the fundamental quantities are called derived physical quantities, e.g.: Volume, Velocity, Work etc.

→ The units of derived physical quantities are called the derived units.

→ S.I. System : It consists seven fundamental physical quantities. They are :

1. length
2. mass,
3. time,
4. thermodynamic temperature,
5. intensity of light,
6. strength of electric current,
7. quantity of matter.

→ The power to which the fundamental quantities are to be raised to obtain one unit of the physical quantity is called the “dimensions” of that physical quantity.

→ The derived quantity can be expressed as M^a L^b T^c which is called the dimensional formula. The powers a, b, c are called dimensions.

→ Uses of dimensional equations :
a) To change one system of units into another.
b) To derive a relation connecting different physical quantities.
c) To check the correctness of an equation for a physical quantity.

→ Limitations of dimensional method :

1. The proportionality constant in an equation cannot be obtained by dimensional method.
2. The equations involving trigonometrical or exponential functions cannot be derived.
3. The equations containing more than three physical quantities cannot be derived.
4. If the formula of a physical quantity is represented by the sum of some physical quantities dimensional method cannot be used to derive that formula.
5. Some proportionality quantities possess units. In such cases dimensional method cannot be used to analyse it.

→ The accuracy of a measurement of any physical quantity made by any measuring instrument is a measure of how close the measured value is to the true value of the quantity.

→ Large distances such a$ the distance of stars (or) of a planet from the earth can be measured using parallax method.

→ The smallest value that can be measured by the measuring instrument is called its least count.

→ A vernier callipers is used for lengths to an accuracy of 10^-4 m.

→ A screw gauge and a spherometer can be used to measure lengths as less as to 10^-5 m.

→ 1 Å = 10^-10 m = 10^-8 cm.

→ 1 light year = 9.46 × 1^-15 m
1 parsec = 3.08 × 10¹⁶ m.

→ 1 a.m.u — 1.66 × 10^-27 kg.

→ 1 Fermi = 10^-15 m.

Formulae

a_mean = true value = \(\frac{1}{n} \sum_{i=1}^n a_i\)

Relative error = \(\frac{\Delta \mathrm{a}_{\text {mean }}}{\mathrm{a}_{\text {mean }}}\)

Percentage error = δa = \(\left(\frac{\Delta \mathrm{a}_{\text {mean }}}{\mathrm{a}_{\text {mean }}} \times 100\right) \%\)

Relative error in multiplication \(\frac{\Delta x}{x}=\frac{\Delta a}{a}+\frac{\Delta b}{b}\)

Relative error in division \(\frac{\Delta x}{x}=\frac{\Delta a}{a}+\frac{\Delta b}{b}\)

Maximum relative error in (x – aⁿ) = \(\frac{\Delta x}{x}=n\left(\frac{\Delta a}{a}\right)\)