1. Measurement in physics means
ⓐ. writing only the name of a quantity without a value
ⓑ. replacing all quantities by the same unit
ⓒ. guessing the size of an object from its appearance
ⓓ. comparison with a chosen standard unit
Correct Answer: comparison with a chosen standard unit
Explanation: Measurement is the process of finding how many times a chosen standard unit is contained in a physical quantity. For example, saying a table is \(2\,\text{m}\) long means its length has been compared with the standard unit \(1\,\text{m}\). A guess may be useful in daily life, but it is not a reliable measurement in physics. A measurement is also incomplete if it gives only a quantity name without a numerical value and unit. The standard unit makes the result understandable and repeatable for different observers.
2. The statement “a measured quantity is expressed as ______” is completed by
ⓐ. material and shape
ⓑ. value and unit
ⓒ. unit only
ⓓ. instrument name only
Correct Answer: value and unit
Explanation: A measured physical quantity needs both a numerical value and a unit. In symbolic form, it may be written as \(Q=n u\), where \(Q\) is the physical quantity, \(n\) is the numerical value, and \(u\) is the unit. For instance, in \(5\,\text{m}\), the number is \(5\) and the unit is \(\text{m}\). The number alone does not tell whether the measurement is in \(\text{m}\), \(\text{cm}\), or another unit. The unit gives the scale with which the quantity has been compared.
3. In the statement “the length of a table is \(1.2\,\text{m}\)”, the physical quantity being measured is
ⓐ. the word table
ⓑ. table length
ⓒ. \(\text{m}\)
ⓓ. \(1.2\)
Correct Answer: table length
Explanation: The physical quantity is the measurable property of the object, so here it is the length of the table. The number \(1.2\) is only the numerical value obtained after measurement. The symbol \(\text{m}\) is the unit used for comparing the length. The object itself is not the measured quantity; a property of the object is being measured. Keeping quantity, number, and unit separate prevents early confusion in measurement language.
4. A road distance is written once as \(2\,\text{km}\) and once as \(2000\,\text{m}\). The item that remains the same in both records is the
ⓐ. selected unit size
ⓑ. written unit symbol
ⓒ. same physical distance
ⓓ. changed numerical value
Correct Answer: same physical distance
Explanation: The same road distance is being described in both records. The numerical value changes from \(2\) to \(2000\) because \(\text{km}\) and \(\text{m}\) are different-sized units. The physical distance does not become larger just because the number becomes larger. A smaller unit gives a larger numerical value for the same quantity. This is why a measurement must always be read as number plus unit, not as number alone.
5. A measuring tape gives the width of a notebook as \(18\,\text{cm}\). In this record, the unit is
ⓐ. width
ⓑ. \(\text{cm}\)
ⓒ. \(18\)
ⓓ. \(\text{mm}\)
Correct Answer: \(\text{cm}\)
Explanation: In \(18\,\text{cm}\), the symbol \(\text{cm}\) is the unit used to express the measured width. The number \(18\) tells how many such units are counted. The word width names the physical quantity, not the unit. The notebook is the object whose property is being measured. A measurement record becomes meaningful only when the numerical value is attached to a definite unit.
6. Standard units are needed mainly because they
ⓐ. make every numerical value equal to \(1\)
ⓑ. allow measurements to be compared reliably
ⓒ. make all physical quantities dimensionless
ⓓ. remove the need for instruments
Correct Answer: allow measurements to be compared reliably
Explanation: A standard unit provides a common reference for measurement. If different people use different personal units, their results may not be comparable. For example, measuring a desk in handspans can give different numbers for different people. A standard such as \(\text{m}\) gives a fixed scale independent of the observer. Reliable comparison is one of the main reasons physics uses agreed units.
7. Two people measure the same stick using their own handspans and obtain different numbers. The best explanation is that
ⓐ. length cannot be measured directly
ⓑ. every measurement must have the same number
ⓒ. handspan is not a reproducible standard unit
ⓓ. the stick changed length during measurement
Correct Answer: handspan is not a reproducible standard unit
Explanation: A handspan varies from person to person, so it is not a fixed standard unit. The stick may have the same physical length, but the numerical value depends on the size of the unit used. A longer handspan gives a smaller number of handspans for the same stick. This does not show that length is impossible to measure. It shows why physics prefers well-defined standards instead of body-based units.
8. The pair that shows a physical quantity followed by a suitable unit is
ⓐ. mass — \(\text{kg m}^{-3}\)
ⓑ. length — \(\text{s}\)
ⓒ. time — \(\text{kg}\)
ⓓ. volume — \(\text{m}^3\)
Correct Answer: volume — \(\text{m}^3\)
Explanation: Volume measures the space occupied by a body, and \(\text{m}^3\) is a suitable unit for volume. The unit \(\text{m}\) is used for length, not mass. The unit \(\text{s}\) is used for time, not length. The unit \(\text{kg}\) is used for mass, not time. A quantity-unit pair must match the physical property being measured.
9. A floor area is reported as \(12\,\text{m}^2\). This record shows that
ⓐ. area and length are the same quantity
ⓑ. the unit \(\text{m}^2\) measures time
ⓒ. the number \(12\) alone is the complete measurement
ⓓ. area is expressed using a square unit
Correct Answer: area is expressed using a square unit
Explanation: Area measures the extent of a surface, so its unit is built from length multiplied by length. In SI-based notation, this gives a unit such as \(\text{m}^2\). Length itself is measured in \(\text{m}\), so area and length are related but not the same quantity. The number \(12\) becomes meaningful only with the unit \(\text{m}^2\). The power \(2\) in the unit signals that a surface, not a line length, is being measured.
10. A bottle label gives volume \(750\,\text{cm}^3\), a package gives mass \(0.50\,\text{kg}\), and a stopwatch gives time \(30\,\text{s}\). These records all show that measured quantities are written with
ⓐ. a shape and a material
ⓑ. only an instrument reading
ⓒ. only a unit name
ⓓ. a number and a unit
Correct Answer: a number and a unit
Explanation: Each record combines a numerical value with a unit. The volume has \(750\) with \(\text{cm}^3\), the mass has \(0.50\) with \(\text{kg}\), and the time has \(30\) with \(\text{s}\). The quantities are different, but the structure of the measurement record is the same. The unit tells the scale used in the comparison. Without the unit, the numerical value would not identify the size of the physical quantity clearly.
11. A physical quantity is best described as a property that can be
ⓐ. measured with value and unit
ⓑ. named without any comparison
ⓒ. memorised without measurement
ⓓ. changed into a unit symbol
Correct Answer: measured with value and unit
Explanation: A physical quantity is a measurable property such as length, mass, time, area, volume, or speed. Measurement gives a numerical value, and the unit tells the standard used for comparison. A property that cannot be measured or compared with a unit does not function as a physical quantity in this sense. Naming a property is not enough to make a measurement. The measurable nature of the property is what connects physical quantities to experiments and observations.
12. The group containing only fundamental physical quantities from the usual mechanics starting set is
ⓐ. speed, area, density
ⓑ. force, volume, energy
ⓒ. length, mass, time
ⓓ. acceleration, pressure, work
Correct Answer: length, mass, time
Explanation: Length, mass, and time are fundamental quantities in the usual beginning treatment of mechanics. They are not defined in terms of other mechanical quantities. Speed, area, density, force, volume, energy, acceleration, pressure, and work are derived quantities because their definitions use other quantities. For example, speed uses length and time. The distinction is about how a quantity is defined, not about whether it is useful.
13. Speed is treated as a derived quantity because it is obtained from
ⓐ. mass and temperature
ⓑ. luminous intensity and amount of substance
ⓒ. current and time
ⓓ. length and time
Correct Answer: length and time
Explanation: Speed describes how much distance or length is covered per unit time. Its basic relation is \(v=\frac{\text{distance}}{\text{time}}\). Since it depends on length and time, it is not a fundamental quantity in the mechanics starting set. A derived quantity is formed by combining fundamental quantities through a definition or formula. The unit \(\text{m s}^{-1}\) also shows that speed is built from \(\text{m}\) and \(\text{s}\).
14. Match the introductory symbols with the quantities they usually represent.
| Symbol | Quantity |
|---|
| P. \(l\) | 1. Time |
| Q. \(m\) | 2. Speed |
| R. \(t\) | 3. Length |
| S. \(v\) | 4. Mass |
The matching that fits the usual notation is
ⓐ. P-4, Q-3, R-1, S-2
ⓑ. P-3, Q-4, R-1, S-2
ⓒ. P-2, Q-4, R-1, S-3
ⓓ. P-3, Q-1, R-4, S-2
Correct Answer: P-3, Q-4, R-1, S-2
Explanation: The symbol \(l\) commonly represents length in elementary measurement contexts. The symbol \(m\) is commonly used for mass, while \(t\) represents time. The symbol \(v\) is often used for speed or velocity depending on context. These symbols are not units; they stand for physical quantities. Confusing a quantity symbol with a unit symbol can lead to wrong interpretation of formulas and measurement records.
15. Consider the following statements.
I. Length, mass, and time can be used as fundamental quantities in mechanics.
II. Density is derived because it uses mass and volume.
III. Time is derived from speed and length in the basic classification of quantities.
The valid statements are
ⓐ. I only
ⓑ. I, II and III
ⓒ. II only
ⓓ. I and II only
Correct Answer: I and II only
Explanation: Statement I is valid because length, mass, and time are taken as fundamental quantities in the usual mechanics foundation. Statement II is also valid because density is defined using mass and volume, as in \(\rho=\frac{m}{V}\). A quantity formed from other quantities by definition is called a derived quantity. Statement III reverses the classification: time is not treated as derived from speed and length in the basic system. Speed is the derived quantity because it uses length and time.
16. A record gives density using the relation \(\rho=\frac{m}{V}\). This relation shows that density is
ⓐ. a derived quantity formed from mass and volume
ⓑ. a unit without a physical quantity
ⓒ. a fundamental quantity independent of other quantities
ⓓ. only a numerical value with no unit
Correct Answer: a derived quantity formed from mass and volume
Explanation: The relation \(\rho=\frac{m}{V}\) defines density as mass per unit volume. Since density is obtained by combining mass and volume, it is a derived quantity. Mass is a basic quantity in the usual mechanics set, while volume is itself related to length cubed. Density is not merely a number because it must be reported with a unit such as \(\text{kg m}^{-3}\). The formula shows both the meaning of the quantity and the reason for its classification.
17. A unit is best understood as
ⓐ. the name of the instrument used in measurement
ⓑ. the numerical value written before a quantity
ⓒ. any word written after a number
ⓓ. a standard used for measuring
Correct Answer: a standard used for measuring
Explanation: A unit is a fixed standard chosen for comparison with a physical quantity. When a length is measured in \(\text{m}\), the metre is the standard unit used to express that length. The numerical value tells how many units are contained in the quantity, but it is not itself the unit. An instrument may help in measurement, but the instrument name is not the measurement unit. A unit must have a defined size so that measurements made at different places can be compared reliably.
18. Complete the statement: A physical quantity \(Q\) expressed as \(Q=n u\) has \(n\) as the ______ and \(u\) as the ______.
ⓐ. error, reading
ⓑ. instrument, standard
ⓒ. numerical value, unit
ⓓ. unit, numerical value
Correct Answer: numerical value, unit
Explanation: In the expression \(Q=n u\), \(Q\) represents the physical quantity being measured. The symbol \(n\) gives the numerical value, meaning how many times the chosen unit is contained in the quantity. The symbol \(u\) represents the unit or standard used for comparison. For example, in \(Q=5\,\text{m}\), the number \(5\) is \(n\) and \(\text{m}\) is \(u\). This form also shows why changing the unit changes the number even when the actual physical quantity remains unchanged.
19. A length is first written as \(3\,\text{m}\) and then as \(300\,\text{cm}\). The change from \(3\) to \(300\) happens because
ⓐ. the measurement lost its unit
ⓑ. \(\text{m}\) is a smaller unit than \(\text{cm}\)
ⓒ. \(\text{cm}\) is a smaller unit than \(\text{m}\)
ⓓ. the length has physically increased
Correct Answer: \(\text{cm}\) is a smaller unit than \(\text{m}\)
Explanation: The physical length is the same in both records. Since \(1\,\text{m}=100\,\text{cm}\), the unit \(\text{cm}\) is smaller than the unit \(\text{m}\). A smaller unit must be counted more times to cover the same length, so the numerical value becomes larger. The number therefore changes inversely with the size of the unit. Reading only the number without the unit would make \(3\) and \(300\) look inconsistent even though both represent the same length.
20. A laboratory note says, “The mass of the object is \(0.25\,\text{kg}\).” If the same mass is expressed in \(\text{g}\), the numerical value becomes
ⓐ. \(25\)
ⓑ. \(250\)
ⓒ. \(0.025\)
ⓓ. \(2.5\)
Correct Answer: \(250\)
Explanation: \( \textbf{Given quantity:} \) Mass \(=0.25\,\text{kg}\).
\( \textbf{Required:} \) The numerical value when the unit is changed from \(\text{kg}\) to \(\text{g}\).
\( \textbf{Unit relation:} \) \(1\,\text{kg}=1000\,\text{g}\).
\( \textbf{Conversion:} \)
\[
0.25\,\text{kg}=0.25\times1000\,\text{g}
\]
\( \textbf{Calculation:} \)
\[
0.25\times1000=250
\]
So the same mass is \(250\,\text{g}\).
The unit \(\text{g}\) is smaller than \(\text{kg}\), so the numerical value must become larger.
\( \textbf{Final answer:} \) The numerical value is \(250\) when the mass is written as \(250\,\text{g}\).
