Physical quantities Transitional Reasoning Download PDF

Questions

1. 1.

   A materials testing laboratory receives a uniform, homogeneous copper bar. An engineer cuts the bar into two unequal pieces: Piece 1 with a mass of 2 kg and Piece 2 with a mass of 6 kg, while maintaining both at the same uniform temperature. Based on the classification of physical quantities as intensive (independent of system size) or extensive (dependent on system size), which evaluation correctly compares the density, electrical resistivity, volume, and total thermal energy of the two pieces?

   • A) Because density and electrical resistivity are derived from bulk measurements, they are extensive quantities that are three times greater in Piece 2 than in Piece 1, whereas volume and total thermal energy remain identical.
   • B) Density and electrical resistivity are intensive quantities and remain identical for both pieces, whereas volume and total thermal energy are extensive quantities that are three times greater in Piece 2 than in Piece 1.
   • C) All four properties are extensive quantities because they characterize physical samples with different amounts of matter, meaning each property is three times greater in Piece 2 than in Piece 1.
   • D) Volume and density are intensive quantities that depend only on the substance type, whereas electrical resistivity and total thermal energy are extensive quantities that scale directly with sample mass.
2. 2.

   During a marine salvage operation, two auxiliary fuel tanks on a recovery vessel each have a mass of 2000 kg, yielding an exact combined fuel mass of 4000 kg regardless of their placement. Simultaneously, two tugboats pull the vessel, each exerting a horizontal towing force of 20 kN, yet the measured resultant force acting on the vessel is 28.3 kN rather than 40 kN. Based on the classification and fundamental properties of physical quantities, which statement correctly explains this difference in how these quantities combine?

   • A) Mass is a fundamental quantity whose combined total is conserved in isolated systems, whereas force is a derived quantity whose effective magnitude is reduced by mechanical transmission losses along the cables.
   • B) Mass is a scalar quantity measured directly against a reference standard, whereas force is an indirect quantity whose combined magnitude decreases with the physical separation between the tugboats.
   • C) Mass is an intrinsic property that follows ordinary addition only under static equilibrium, whereas force is a dynamic quantity whose net value is diminished by fluid resistance from the surrounding water.
   • D) Mass is a scalar quantity fully specified by magnitude and unit, combining via algebraic addition, whereas force is a vector quantity possessing direction, requiring vector addition that depends on the angle between the acting forces.
3. 3.

   A laboratory technician configures a spectrometer to record the wavelength of an optical emission line, initially displayed as 0.65 μm. To comply with a standard database format, the software switches the display unit to nanometers (nm) while the physical light wave remains completely unchanged. Based on the fundamental relationship between a physical quantity, its numerical value, and the size of the chosen measurement unit, which statement correctly explains how and why the displayed numerical value changes?

   • A) The numerical value becomes 1000 times larger because the unit size decreases by a factor of 1000, keeping the physical quantity invariant.
   • B) The numerical value becomes 1000 times smaller because switching to a smaller unit proportionally decreases the magnitude of the measurement.
   • C) The numerical value remains unchanged because the physical wavelength of the light wave is an invariant physical quantity.
   • D) The numerical value becomes 1000 times larger because a nanometer represents a unit size 1000 times larger than a micrometer.
4. 4.

   An autonomous rover analyzes a geological rock sample on Earth and then transports it to the Moon, where the local gravitational acceleration is approximately one-sixth of that on Earth. The rover uses an equal-arm balance to evaluate the sample's mass and a calibrated spring scale to determine its weight. Based on the classification of physical quantities and their physical behavior, which evaluation correctly compares mass and weight across these two locations?

   • A) Mass is a derived vector quantity that decreases on the Moon, whereas weight is a fundamental scalar quantity that remains constant across both locations.
   • B) Both mass and weight are fundamental scalar quantities, meaning both of their measured values remain identical regardless of the local gravitational acceleration.
   • C) Mass is an intrinsic fundamental scalar quantity that remains identical at both locations, whereas weight is a derived vector quantity whose magnitude decreases to one-sixth on the Moon.
   • D) Mass is a fundamental scalar quantity whose value decreases to one-sixth on the Moon, whereas weight is a derived vector quantity whose magnitude remains identical at both locations.
5. 5.

   An environmental engineering team models the mass $M$ of particulate matter accumulated in an air filtration unit over time $t$ using the relationship $M = A t^2 + B t$, where $M$ is measured in kilograms ($\text{kg}$) and $t$ is measured in seconds ($\text{s}$). According to the principle of dimensional homogeneity, all additive terms in a valid physical equation must represent the same physical quantity. Which evaluation correctly identifies the SI base units required for the parameters $A$ and $B$?

   • A) $A$ has the unit $\text{kg}\cdot\text{s}^2$ and $B$ has the unit $\text{kg}\cdot\text{s}$
   • B) $A$ has the unit $\text{kg}\cdot\text{s}^{-2}$ and $B$ has the unit $\text{kg}\cdot\text{s}^{-1}$
   • C) $A$ has the unit $\text{kg}\cdot\text{s}^{-1}$ and $B$ has the unit $\text{kg}\cdot\text{s}^{-2}$
   • D) $A$ and $B$ are dimensionless scaling factors without physical units
6. 6.

   A student analyzing data from an automated transit vehicle categorizes four recorded quantities: mass, velocity, electric current, and momentum. The student seeks to identify which of these four quantities can be classified simultaneously as a fundamental (base) quantity and a vector quantity. Based on the classification principles of physical quantities in the International System of Units (SI), which evaluation is correct?

   • A) Velocity satisfies both conditions because it has an associated spatial direction and is measured directly using the vehicle's standard speedometer.
   • B) None of the four quantities satisfies both conditions, because all fundamental quantities in the SI are scalars, while velocity and momentum are derived quantities.
   • C) Electric current satisfies both conditions because it has a specific direction of flow through the circuit and is one of the seven base SI quantities.
   • D) Momentum satisfies both conditions because it depends directly on the fundamental property of mass and points in the direction of the vehicle's motion.
7. 7.

   During a laboratory investigation, students evaluate several physical properties of a solid metal cylinder. They measure its height using a metric ruler, determine its mass using a mechanical balance, and find its density by dividing the measured mass by the volume calculated from its dimensions. Based on the principles of measurement in physics, which evaluation correctly classifies these procedures as direct or indirect measurements?

   • A) Measuring height is an indirect measurement because it depends on scale alignment by the observer, whereas determining density is a direct measurement because it defines a characteristic property of the material.
   • B) Determining mass using a balance is an indirect measurement because gravitational force acts on the sample, whereas measuring height with a ruler is a direct measurement.
   • C) Measuring height and mass are direct measurements because they are obtained by direct comparison with a measuring tool, whereas determining density is an indirect measurement because it is calculated from mathematical relationships between other measured quantities.
   • D) All three procedures are indirect measurements because every measurement in a laboratory depends on calibrated reference standards and experimental uncertainty.
8. 8.

   A research group testing an electric vehicle measures the mechanical work delivered by a drive motor during acceleration. To ensure that their simulation software registers the data strictly in International System of Units (SI) base units rather than derived units, an engineer derives the fundamental unit combination for work. Based on the physical relationship between force and displacement, which expression correctly gives the derived quantity work in SI base units?

   • A) $\text{kg} \cdot \text{m} \cdot \text{s}^{-2}$
   • B) $\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}$
   • C) $\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-3}$
   • D) $\text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-2}$
9. 9.

   An automated weather station on a coastal research platform monitors several environmental parameters during a storm: atmospheric temperature, wind velocity, accumulated rainfall depth, and the net aerodynamic drag force exerted on the mast. The system classifies these records based on whether each physical quantity requires a spatial direction in addition to magnitude and unit for its complete physical description. Which evaluation correctly categorizes these monitored quantities into scalar and vector quantities?

   • A) Only net aerodynamic drag force is a vector quantity, while atmospheric temperature, wind velocity, and accumulated rainfall depth are all scalar quantities.
   • B) Wind velocity and net aerodynamic drag force are vector quantities, while atmospheric temperature and accumulated rainfall depth are scalar quantities.
   • C) Atmospheric temperature, wind velocity, and net aerodynamic drag force are vector quantities, while accumulated rainfall depth is the only scalar quantity.
   • D) Accumulated rainfall depth and net aerodynamic drag force are vector quantities, while atmospheric temperature and wind velocity are scalar quantities.
10. 10.

    During a laboratory test of an automated greenhouse system, a technician records the operating time of a pump, the electric current supplied to its motor, and the hydrostatic pressure inside the delivery pipe. When organizing these measurements into the International System of Units (SI), which evaluation correctly classifies the measured physical quantities as fundamental or derived?

    • A) Operating time and electric current are fundamental quantities, whereas hydrostatic pressure is a derived quantity.
    • B) Operating time is the only fundamental quantity, whereas electric current and hydrostatic pressure are both derived quantities.
    • C) Hydrostatic pressure and electric current are fundamental quantities, whereas operating time is a derived quantity.
    • D) Operating time, electric current, and hydrostatic pressure are all fundamental quantities because each is measured directly by a sensor.