Question

State the physical quantity corresponding to each of the following units. (a) \(\mathrm{mm}\) (b) \(\mathrm{kg}\) (c) \(\mathrm{cm}^{3}\) (d) s (e) \({ }^{\circ} \mathrm{C}\) (f) \(k\) cal

Short answer

(a) Length, (b) Mass, (c) Volume, (d) Time, (e) Temperature, (f) Energy.

Step-by-step solution

Millimeters (mm)

The unit \(\mathrm{mm}\) stands for millimeters. Millimeters measure length or distance. Hence, the physical quantity for \(\mathrm{mm}\) is length.

Kilograms (kg)

The unit \(\mathrm{kg}\) stands for kilograms. Kilograms are used to measure mass or weight. Thus, the physical quantity for \(\mathrm{kg}\) is mass.

Cubic centimeters (cm³)

The unit \(\mathrm{cm}^{3}\) refers to cubic centimeters. Cubic centimeters are a measure of volume. Consequently, the physical quantity for \(\mathrm{cm}^{3}\) is volume.

Seconds (s)

The unit \(\mathrm{s}\) stands for seconds. Seconds are a measure of time. Therefore, the physical quantity for \(\mathrm{s}\) is time.

Degrees Celsius (°C)

The unit \(^{\circ} \mathrm{C}\) stands for degrees Celsius. It is a unit for measuring temperature. Thus, the physical quantity for \(^{\circ}\mathrm{C}\) is temperature.

Kilocalories (kcal)

The unit \(k\)cal stands for kilocalories. Kilocalories measure energy or heat. Hence, the physical quantity for \(k\)cal is energy.

Key concepts

Length

Length is one of the most fundamental physical units and is measured in units like meters, centimeters (cm), and millimeters (mm). It represents the measurement of distance or the amount of space between two points. For example, the length of a pencil might be measured in centimeters, while the thickness of a sheet of paper could be measured in millimeters. When we talk about measuring length, the basic tools include rulers, measuring tapes, and calipers. These tools help us quantify how long, wide, or tall an object is. This concept is crucial across various fields like construction, tailoring, and physics.

Mass

Mass is a measure of the amount of matter in an object. It is typically measured in units like grams (g) or kilograms (kg). While people often confuse mass with weight, they are not the same. Mass is a fundamental property that doesn't change with location, while weight is the force of gravity acting on that mass. Understanding mass is essential in the field of science, especially in physics where the relationship between mass, force, and acceleration is described by Newton's second law: \[ F = m imes a \] where \(F\) is the force, \(m\) is the mass, and \(a\) is acceleration. Knowing an object's mass helps us determine how much force is needed to move it.

Volume

Volume is the amount of space an object occupies and is measured in units such as cubic centimeters (cm³) and liters (L). It's particularly useful in understanding how much liquid a container can hold or the capacity of gas in an enclosed space. In practical terms, you can think of volume as the number of similar-sized cubes that can fit inside an object. Measuring volume is crucial in chemistry and cooking where precise amounts of liquids and gases are required. Often, graduated cylinders, beakers, and measuring cups are used to measure volume.

Temperature

Temperature is a measure of how hot or cold something is. The most commonly used unit for temperature is degrees Celsius (°C). It is a scalarly quantity that tells us about the kinetic energy of particles in a substance. Higher temperature means particles move faster, indicating more energy, while a lower temperature means particles move slower. This concept is vital in understanding weather patterns, cooking, and even how effective medication can be. Thermometers are a common tool used for measuring temperature, ranging from clinical thermometers to ambient sensors used in weather stations.

Energy

Energy is a measure of the ability to do work, often measured in units like joules (J) or kilocalories (kcal). It can exist in various forms such as kinetic energy, potential energy, thermal energy, and more. Kilocalories often relate to the energy content in food. Knowing the energy content helps us understand how much energy our body can obtain from nutrients. Energy transformation is a central theme in physics, where it changes from one form to another while abiding by the law of conservation of energy, which states that energy can neither be created nor destroyed. Our everyday activities, from driving a car to playing sports, involve some form of energy transformation.