Students can go through AP Inter 1st Year Physics Notes 2nd Lesson Units and Measurements will help students in revising the entire concepts quickly.

## 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

- Imperfection in experimental technique or procedure
- Environmental errors,
- 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 :

- length
- mass,
- time,
- thermodynamic temperature,
- intensity of light,
- strength of electric current,
- 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 :

- The proportionality constant in an equation cannot be obtained by dimensional method.
- The equations involving trigonometrical or exponential functions cannot be derived.
- The equations containing more than three physical quantities cannot be derived.
- 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.
- 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 × 10^{16} 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 – a^{n}) = \(\frac{\Delta x}{x}=n\left(\frac{\Delta a}{a}\right)\)