Unit 1: Physical Quantities and Measurements — Short Questions

Non-physical quantities, such as emotions, intelligence, or satisfaction, cannot be directly measured using traditional instruments. However, they can be assessed indirectly through metrics, scales, or standardized tests. For example:

i. Intelligence is measured using IQ tests.

ii. Customer satisfaction can be quantified through surveys or rating scales.

These methods convert abstract concepts into numerical values that allow for comparison and analysis.

A measurement is a process of comparison of an unknown quantity with a widely accepted standard quantity. A measurement consists of two parts, a number and a unit. A measurement without unit is meaningless.

A standard unit ensures consistent and accurate measurements. It allows everyone to understand and compare results, which is important for science, trade, and construction.

Base Quantities Fundamental physical quantities from which other quantities are derived:

i. Length: Measured in meters (m).

ii. Mass: Measured in kilograms (kg).

iii. Time: Measured in seconds (s).

Derived Quantities Formed by combining base quantities:

i. Speed: Defined as distance/time (m/s).

ii. Area: Defined as length × width (m²).

iii. Density: Defined as mass/volume (kg/m³).

The height of a desk is typically expressed in centimeters (cm) or meters (m) for accurate and consistent measurement.

There are seven SI base units:

i. Length: Meter (m)

ii. Mass: Kilogram (kg)

iii. Time: Second (s)

iv. Electric current: Ampere (A)

v. Temperature: Kelvin (K)

vi. Amount of substance: Mole (mol)

vii. Intensity of light: Candela (cd)

Prefixes simplify the expression of very large or very small numbers by scaling the base unit. They make communication more efficient and measurements easier to read.

Sub-multiples

i. Milli (m): 10^-3 (e.g., 1 mm = 10^-3 m)

ii. Micro (μ): 10^-6 (e.g., 1 μm = 10^-6 m)

iii. Nano (n): 10^-9 (e.g., 1 ns = 10^-9 s)

Multiples

i. Kilo (k): 10³ (e.g., 1 km = 10³ m)

ii. Mega (M): 10⁶ (e.g., 1 MJ = 10⁶ J)

iii. Giga (G): 10⁹ (e.g., 1 GHz = 10⁹ Hz)

(a) 5 pm = 5×10^-12 m

(b) 15 ns = 15×10^-9 s

(c) 6 μm = 6×10^-6 m

(d) 5 fs = 5×10^-15 m

(a) A Vernier Caliper is an instrument used to measure small lengths with high precision, down to 1/10th of a millimeter. It is commonly used to measure the thickness, diameter, width, or depth of an object.

(b) The Vernier Caliper has two parts:

i. Main Scale: This scale has markings of 1 mm each.

ii. Vernier (sliding) Scale: The Vernier scale is 9 mm long and divided into 10 equal parts.

(c) The least count of a Vernier Caliper is the difference between the value of one main scale division (M.S) and one Vernier scale division (V.S).

Least count = 1 M.S div - 1 V.S div

Least count = 1 mm - 0.9 mm = 0.1 mm

Alternatively, the least count can also be determined by dividing the length of one small division on the main scale by the total number of divisions on the Vernier scale:

Least count = 1 mm / 10 = 0.1 mm.

(d) Zero error will exist if zero of vernier scale is not coinciding with zero of the main scale. There are two types of errors:

i. Positive zero error

Zero error will be positive if zero of vernier scale is on the right side of the zero of the main scale.

ii. Negative zero error

Zero error will be negative if zero of vernier scale is on the left side of the zero of the main scale.

Least Count

The least count of a vernier calipers is the value of the smallest measurement that can be taken using the vernier calipers.

To calculate the least count, we use the formula:

Least count = One small division on main scale / No.of division on vernier scale

Least count = 1 mm / 10 = 0.1 mm or 0.01 cm

Length

In the given figure

The main scale reading is 2.6 cm.

The Vernier scale division is 5th division.

Therefore, the total length is:

Length = Main scale reading + Vernier scale reading × L.C

Length = 2.6 cm + 5 × 0.01 cm = 2.65 cm

Thus, the length measured is 2.65 cm.

The correct reading is B because figure shows that the eye is exactly above the reading point.

No, a non-physical quantity does not have dimensions because it is not related to fundamental physical units and is not measurable in physical terms.

The unit of charge in terms of base units is ampere-second (A·s), derived from the relationship Q=I.t

The unit of pressure, pascal (Pa), can be expressed as 1 Pa = 1 N/m²

The kilogram is the only base unit that has prefix.

(a) 0.00534 m

5.34×10^-3 m

(b) 2574.32 kg

2.57432×10³ kg

(c) 0.45 m

4.5×10^-1 m

(d) 0.004 kg

4.0×10^-3 kg

(e) 186000 s

1.86×10⁵ s

(i) Symbols, Not Abbreviations

Each unit is represented by a symbol, not an abbreviation (e.g., s, not sec).

(ii) No Plural Form

Symbols do not take a plural form (e.g., 10 mN, not 10 mNs).

(iii) Capitalization of Unit Names

Full unit names are written in lowercase, except Celsius. (e.g., metre, second, newton)

(iv) Uppercase for Certain Symbols

Symbols appear in lowercase, except L for liter and symbols named after scientists (e.g., N for newton).

(v) Prefix Placement

Prefixes are written directly before the unit (e.g., ms, not m, s).

(vi) Spacing Between Units

Units are written with one space apart (e.g., N m, not Nm).

(vii) No Compound Prefixes

Compound prefixes are not allowed (e.g., 7 ps, not 7 μμs).

Numbers must have the same exponent for addition or subtraction because the operation can only be performed on like terms. If the exponents are different, adjust the decimal point to make the exponents equal before performing the operation.

(i) Handle all apparatus and chemicals carefully and correctly.

(ii) Always check the label on the container before using the substance it contains.

(iii) Do not taste any chemical unless otherwise instructed by the teacher.

(iv) Do not eat, drink, or play in the laboratory.

(v) Do not tamper with the electrical mains and other fittings in the laboratory.

(vi) Never work with electricity near water.

(vii) Don't place flammable substances near naked flames.

(viii) Wash your hands after all laboratory work.

The standard measurement of any quantity if called its units.

There are two types of units:

(i) Base units

(ii) Derived units

Least count is the smallest measurement that can be taken accurately with an instrument.

Instrument | Range | Least count

Measuring tape | 1 cm to several metres | 1 mm

Metre rule | 1 mm to 1 m | 1 mm

Vernier Calipers | 0.1 mm to 15 cm | 0.1 mm

Micrometer Screw Gauge | 0.01 mm to 2.5 cm | 0.01 mm

Zero error of an instrument: A systematic error that occurs when the instrument reads a value other than zero when the true value is zero.

(a) Least count of screw gauge is calculated by formula:

Least count = Pitch of screw guage / No.of division on circular scale

(b) Least count of Vernier Calipers:

Usually, the least count is found by dividing the length of one small division of main scale by the total number of divisions on the Vernier scale which is again 1 mm / 10 = 0.1 mm.

Alternatively, the least count can also be determined by dividing the length of one small division on the main scale by the total number of divisions on the Vernier scale:

Least count = 1 mm / 10 = 0.1 mm.

When the thimble makes one complete turn, the spindle moves 0.5 mm (1 scale division) on the main scale. This movement is called the pitch of the screw gauge.

Area is a derived quantity because it is calculated by multiplying two base quantities, length and width. It is expressed in terms of square units, such as m².

(i) Base Units

Definition Fundamental units that cannot be expressed in terms of other units.

Examples Meter (m), kilogram (kg), second (s), Kelvin (K), etc.

(ii) Derived Units

Definition Units that can be expressed in terms of base units.

Examples Speed (m/s), force (N = kg m/s²), energy (J = kg m²/s²), etc.

(i) The rotation of the Earth on its axis.

(ii) The revolution of the Earth around the Sun.

(iii) The vibration of a cesium-133 atom.

(iv) The oscillation of a pendulum.

(i) Your eye level may move a bit while reading the meniscus.

Personal Error

(ii) Air current may cause the balance to fluctuate.

Random Error

(iii) The balance may not be properly calibrated.

Systematic Error

(iv) Some of the liquid may have evaporated while it is being measured.

Random Error

(i) 1.25×10²

3 significant figures

(ii) 12.5 cm

3 significant figures

(iii) 0.125 m

3 significant figures

(iv) 0.000125 km

3 significant figures

Difference between systematic and random errors:

Systematic Errors

Systematic errors refer to errors that influence all measurements of a particular type in the same way, resulting in consistent differences in readings. These errors may arise from factors such as zero error, poor calibration of instruments, or incorrect markings on the scale.

Random error

Random errors occur when repeated measurements of the same quantity produce different results under the same conditions. These errors are caused by unpredictable factors, and the experimenter has little or no control over them. They may arise due to fluctuations in environmental conditions, such as changes in temperature, pressure, humidity, or voltage.

Minimizing Systematic Errors

Comparing the instrument with another one known to be more accurate or applying a correction factor to adjust the measurements.

Minimizing Random Errors

Taking multiple readings and calculating the average or mean value. For example, when measuring the time of oscillations of a pendulum, the time for several oscillations (e.g., 30 oscillations) is measured, and the average time for one oscillation is then calculated.