TRUE OR FALSE — INTRODUCTION TO PHYSICS AND MATTER
Physics & Mathematical Tools
1. Physics
Statement 1: Physics is a scientific discipline that studies matter, energy and the fundamental forces of nature.
ANSWER: True
Statement 2: The word "physics" originates from the Latin word "physica", meaning "natural thing".
ANSWER: True
Statement 3: Physics relies solely on mathematical modelling and never on observation or experimentation.
ANSWER: False — Physics relies on observation and experimentation as well as mathematical modelling.
2. Trigonometric Ratios
Statement 1: Sine, cosine and tangent are the three trigonometric ratios.
ANSWER: True
Statement 2: Trigonometric ratios relate the angles of a right triangle to the lengths of its sides.
ANSWER: True
Statement 3: Trigonometric ratios, in their basic form, apply only to triangles that are not right-angled.
ANSWER: False — In their basic form, trigonometric ratios apply to right triangles.
3. Pythagoras' Theorem
A right triangle has legs of $3.0\text{ cm}$ and $4.0\text{ cm}$.
Statement 1: Given the data above, the hypotenuse works out to 5.0 cm.
ANSWER: True — $c = \sqrt{3.0^2+4.0^2} = \sqrt{9.0+16} = \sqrt{25} = 5.0\text{ cm}$.
Statement 2: If the legs were instead $6.0\text{ cm}$ and $8.0\text{ cm}$, the hypotenuse would be 10 cm.
ANSWER: True — $c = \sqrt{6.0^2+8.0^2} = \sqrt{36+64} = \sqrt{100} = 10\text{ cm}$.
Statement 3: If the legs were instead $5.0\text{ cm}$ and $12\text{ cm}$, the hypotenuse would be 15 cm.
ANSWER: False — $c = \sqrt{5.0^2+12^2} = \sqrt{25+144} = \sqrt{169} = 13\text{ cm}$, not 15 cm.
4. Sine Rule
In a triangle, angle A = 30°, angle B = 90°, and the side opposite A, side a, is $5.0\text{ cm}$.
Statement 1: Given the data above, side b (opposite the 90° angle) works out to 10 cm.
ANSWER: True — $b = \dfrac{a \sin B}{\sin A} = \dfrac{5.0 \times 1.0}{0.50} = 10\text{ cm}$.
Statement 2: If side a were $8.0\text{ cm}$ instead, side b would be 16 cm.
ANSWER: True — $b = \dfrac{8.0 \times 1.0}{0.50} = 16\text{ cm}$.
Statement 3: If side a were $4.0\text{ cm}$ instead, side b would be 4.0 cm (the same as side a).
ANSWER: False — $b = \dfrac{4.0 \times 1.0}{0.50} = 8.0\text{ cm}$, not 4.0 cm.
5. Cosine Rule
In a triangle, sides a and b are both $5.0\text{ cm}$, and the included angle C = 60°.
Statement 1: Given the data above, side c works out to 5.0 cm.
ANSWER: True — $c^2 = a^2+b^2-2ab\cos C = 25+25-2(5.0)(5.0)(0.50) = 25$, so $c = 5.0\text{ cm}$.
Statement 2: If sides a and b were both $8.0\text{ cm}$ instead, with the same 60° angle, side c would be 8.0 cm.
ANSWER: True — $c^2 = 64+64-2(8.0)(8.0)(0.50) = 64$, so $c = 8.0\text{ cm}$.
Statement 3: If the included angle were 90° instead, with sides a and b still $5.0\text{ cm}$ each, side c would still be 5.0 cm.
ANSWER: False — $c^2 = 25+25-2(5.0)(5.0)(0) = 50$, so $c = 7.1\text{ cm}$, not 5.0 cm.
6. Indices (Laws of Indices)
Using the laws of indices, consider $2^3 \times 2^2$.
Statement 1: Given the data above, $2^3 \times 2^2$ works out to $2^5 = 32$.
ANSWER: True — adding the exponents of same-base powers gives $2^{3+2}=2^5=32$.
Statement 2: $3^2 \times 3^1$ works out to $3^3 = 27$.
ANSWER: True — $3^{2+1}=3^3=27$.
Statement 3: $2^4 \div 2^1$ works out to $2^2 = 4$.
ANSWER: False — $2^4 \div 2^1 = 2^{4-1} = 2^3 = 8$, not $2^2=4$.
Quantities and Units
7. Physical Quantity
Statement 1: A physical quantity is a characteristic or property that can be measured or quantified.
ANSWER: True
Statement 2: Physical quantities are classified into fundamental and derived quantities.
ANSWER: True
Statement 3: Every physical quantity in physics is fundamental; none are derived.
ANSWER: False — Physical quantities are classified as either fundamental or derived, not fundamental alone.
8. Fundamental Quantity
Statement 1: A fundamental quantity cannot be defined in terms of other physical quantities.
ANSWER: True
Statement 2: Length, mass, time, temperature, electric current, amount of substance and luminous intensity are the seven fundamental quantities.
ANSWER: True
Statement 3: Force is an example of a fundamental quantity.
ANSWER: False — Force is a derived quantity, not a fundamental one.
9. Derived Quantity
Statement 1: A derived quantity is obtained by mathematically combining one or more fundamental quantities.
ANSWER: True
Statement 2: Volume, pressure, energy and velocity are examples of derived quantities.
ANSWER: True
Statement 3: Derived quantities are independent of fundamental quantities.
ANSWER: False — Derived quantities are built upon fundamental quantities, not independent of them.
10. Basic (Fundamental) Units
Statement 1: A basic unit is defined independently and cannot be derived from other units.
ANSWER: True
Statement 2: The metre, kilogram and second are examples of basic units.
ANSWER: True
Statement 3: The International System of Units recognises only three basic units.
ANSWER: False — SI recognises seven basic (fundamental) units.
11. Derived Units
Statement 1: A derived unit is formed by combining fundamental units according to specific mathematical relationships.
ANSWER: True
Statement 2: The newton and the pascal are examples of derived units.
ANSWER: True
Statement 3: Derived units measure only fundamental quantities, never derived ones.
ANSWER: False — Derived units measure quantities derived from the fundamental quantities.
Dimensions
12. Dimension (of a Physical Quantity)
Statement 1: A dimension relates a physical quantity to the fundamental quantities.
ANSWER: True
Statement 2: Dimensions are represented using square brackets, such as [L] for length.
ANSWER: True
Statement 3: The dimension of a quantity is expressed using its numerical value rather than square brackets.
ANSWER: False — Dimensions are expressed using square brackets, not numerical values.
13. Dimensional Analysis
Statement 1: Dimensional analysis is used to check the consistency of equations.
ANSWER: True
Statement 2: Dimensional analysis can be used to convert units and derive relationships between physical quantities.
ANSWER: True
Statement 3: Dimensional analysis accounts for numerical constants in an equation.
ANSWER: False — Dimensional analysis does not account for numerical constants.
Errors and Measuring Instruments
14. Least Count
Statement 1: The least count is the smallest value a measuring instrument can accurately measure.
ANSWER: True
Statement 2: Knowing the least count helps in selecting an appropriate instrument for a measurement.
ANSWER: True
Statement 3: The least count refers to the maximum value an instrument can measure, not the smallest.
ANSWER: False — It refers to the smallest measurable value, not the maximum.
15. Systematic Error
Statement 1: A systematic error consistently deviates from the true value in the same direction.
ANSWER: True
Statement 2: A systematic error can arise from a zero error in equipment.
ANSWER: True
Statement 3: A systematic error is unpredictable and varies randomly from one reading to the next.
ANSWER: False — That describes a random error, not a systematic error.
16. Random Error
Statement 1: A random error is unpredictable and can be caused by the observer or by experimental conditions.
ANSWER: True
Statement 2: Repeating a reading several times and averaging can reduce random error.
ANSWER: True
Statement 3: Random error always deviates from the true value in the same direction.
ANSWER: False — That describes systematic error, not random error.
17. Parallax Error
Statement 1: Parallax error is caused by incorrect eye position relative to a measuring scale.
ANSWER: True
Statement 2: The meniscus of a measuring cylinder is a common place where parallax error appears.
ANSWER: True
Statement 3: Parallax error is caused by a fault within the measuring instrument itself.
ANSWER: False — It is caused by incorrect eye position, not a fault in the instrument.
18. Precision
Statement 1: Precision describes how consistent or reproducible a set of measurements is.
ANSWER: True
Statement 2: A greater number of decimal places in a recorded measurement usually reflects greater precision.
ANSWER: True
Statement 3: Precision describes the closeness of a measurement to the true value.
ANSWER: False — That describes accuracy, not precision.
19. Accuracy
Statement 1: Accuracy describes the closeness of measured values to the true value.
ANSWER: True
Statement 2: Accuracy is influenced by the precision of the measuring tool, environmental conditions, human error and calibration.
ANSWER: True
Statement 3: A reading cannot be precise without also being accurate.
ANSWER: False — A reading can be precise (consistent) without being accurate (close to the true value).
20. Vernier Calliper
Statement 1: A vernier calliper can measure internal and external dimensions as well as depths.
ANSWER: True
Statement 2: The least count of a vernier calliper is typically 0.02 mm.
ANSWER: True
Statement 3: A vernier calliper's scale cannot be misread by failing to align the zero mark.
ANSWER: False — Misreading due to zero-mark misalignment is a common error made when using it.
21. Micrometer Screw Gauge
Statement 1: A micrometer screw gauge is known for very fine precision.
ANSWER: True
Statement 2: Excessive force on a micrometer's ratchet can compress the object being measured, causing an error.
ANSWER: True
Statement 3: A micrometer screw gauge should be tightened as forcefully as possible for the most accurate reading.
ANSWER: False — It should be used gently, not tightened forcefully, to avoid compressing the object.
22. Voltmeter
Statement 1: A voltmeter must be connected in parallel with the component being measured.
ANSWER: True
Statement 2: Connecting a voltmeter incorrectly can alter the circuit and provide incorrect readings.
ANSWER: True
Statement 3: A voltmeter must be connected in series with a circuit, never in parallel.
ANSWER: False — A voltmeter is connected in parallel, not in series.
23. Ammeter
Statement 1: An ammeter must be connected in series with a circuit.
ANSWER: True
Statement 2: Connecting an ammeter incorrectly can damage the meter or the circuit.
ANSWER: True
Statement 3: An ammeter must be connected in parallel with a circuit, never in series.
ANSWER: False — An ammeter is connected in series, not in parallel.
Scientific Notation
24. Scientific Notation
A measurement of $0.00045\text{ m}$ is to be expressed in scientific notation.
Statement 1: Given the data above, the measurement in scientific notation is $4.5\times10^{-4}\text{ m}$.
ANSWER: True
Statement 2: A measurement of $4500\text{ m}$ would be written as $4.5\times10^{3}\text{ m}$.
ANSWER: True
Statement 3: A measurement of $0.045\text{ m}$ would be written as $4.5\times10^{-3}\text{ m}$.
ANSWER: False — $0.045 = 4.5\times10^{-2}\text{ m}$, not $10^{-3}$.
25. Unit Prefix
A distance is measured as $2.0\text{ km}$.
Statement 1: Given the data above, this distance equals $2.0\times10^{3}\text{ m}$.
ANSWER: True — the prefix kilo means $\times10^3$.
Statement 2: A distance of $5.0\text{ mm}$ equals $5.0\times10^{-3}\text{ m}$.
ANSWER: True — the prefix milli means $\times10^{-3}$.
Statement 3: A distance of $3.0\text{ cm}$ equals $3.0\times10^{-3}\text{ m}$.
ANSWER: False — the prefix centi means $\times10^{-2}$, so $3.0\text{ cm} = 3.0\times10^{-2}\text{ m}$, not $10^{-3}$.
Scalars and Vectors
26. Scalar Quantity
Statement 1: A scalar quantity is described solely by magnitude, with no direction.
ANSWER: True
Statement 2: Distance, speed, time and temperature are examples of scalar quantities.
ANSWER: True
Statement 3: A scalar quantity has both magnitude and direction.
ANSWER: False — That describes a vector quantity, not a scalar quantity.
27. Vector Quantity
Two perpendicular forces of $3.0\text{ N}$ and $4.0\text{ N}$ act on an object.
Statement 1: Given the data above, the resultant force works out to 5.0 N.
ANSWER: True — $F = \sqrt{3.0^2+4.0^2} = \sqrt{25} = 5.0\text{ N}$.
Statement 2: If the forces were instead $6.0\text{ N}$ and $8.0\text{ N}$, the resultant would be 10 N.
ANSWER: True — $F = \sqrt{6.0^2+8.0^2} = \sqrt{100} = 10\text{ N}$.
Statement 3: If the forces were instead $5.0\text{ N}$ and $12\text{ N}$, the resultant would be 15 N.
ANSWER: False — $F = \sqrt{5.0^2+12^2} = \sqrt{169} = 13\text{ N}$, not 15 N.
States of Matter
28. Matter
Statement 1: Matter is anything that has mass and occupies space.
ANSWER: True
Statement 2: Matter exists in states including solid, liquid, gas and plasma.
ANSWER: True
Statement 3: Matter is defined as anything with mass but no volume.
ANSWER: False — Matter has both mass and occupies space (has volume).
29. Solid (Solid State)
Statement 1: A solid has closely packed molecules arranged in a regular pattern.
ANSWER: True
Statement 2: A solid maintains a fixed shape, mass and volume.
ANSWER: True
Statement 3: A solid's particles move freely past one another due to weak intermolecular forces.
ANSWER: False — Strong intermolecular forces in a solid prevent particles from easily moving past one another.
30. Liquid (Liquid State)
Statement 1: A liquid has a fixed volume but takes the shape of its container.
ANSWER: True
Statement 2: A liquid is less compressible than a gas because of its intermolecular forces.
ANSWER: True
Statement 3: A liquid's molecules are packed as tightly as those in a solid.
ANSWER: False — Liquid molecules are close together but not as tightly packed as in a solid.
31. Gas (Gaseous State)
Statement 1: A gas has neither a fixed shape nor a fixed volume.
ANSWER: True
Statement 2: A gas's weak intermolecular forces allow it to be easily compressed.
ANSWER: True
Statement 3: A gas's molecules are spaced closely together and move in a fixed pattern.
ANSWER: False — Gas molecules are spaced far apart and move freely in all directions.
32. Plasma
Statement 1: Plasma is a mixture of positively charged ions and negatively charged electrons.
ANSWER: True
Statement 2: Plasma is formed when a gas becomes so hot that electrons are stripped away from their atoms.
ANSWER: True
Statement 3: Plasma is not considered a distinct state of matter.
ANSWER: False — Plasma is considered the fourth state of matter.
Density
33. Density
An object has a mass of $20\text{ g}$ and a volume of $4.0\text{ cm}^3$.
Statement 1: Given the data above, the density works out to 5.0 g/cm³.
ANSWER: True — $\rho = \dfrac{m}{V} = \dfrac{20}{4.0} = 5.0\text{ g/cm}^3$.
Statement 2: If the mass were $40\text{ g}$ instead, with the same volume, the density would be 10 g/cm³.
ANSWER: True — $\rho = \dfrac{40}{4.0} = 10\text{ g/cm}^3$.
Statement 3: If the volume were $8.0\text{ cm}^3$ instead, with the original mass of $20\text{ g}$, the density would be 5.0 g/cm³ still.
ANSWER: False — $\rho = \dfrac{20}{8.0} = 2.5\text{ g/cm}^3$, not 5.0 g/cm³.