Question

Which of the following physical quantity is fundamental? (a) viscosity (b) velocity (c) force (d) time

Short answer

Among the given options, time (option d) is the fundamental physical quantity, as it cannot be expressed as a combination or product of other physical quantities.

Step-by-step solution

Understand the definition of fundamental and derived quantities

Fundamental quantities are basic quantities that cannot be defined in terms of other physical quantities. Derived quantities can be expressed as a combination or product of fundamental quantities.

Analyze each option

Now, let's analyze each of the given options to see which one is a fundamental quantity: (a) Viscosity: It is a measure of a fluid's resistance to flow and depends on factors like temperature and pressure. It is a derived quantity since it can be expressed as a combination of mass (M), length (L), and time (T). (b) Velocity: It is a vector quantity representing the rate of change of an object's position with respect to time. It is a derived quantity, as it can be expressed as length (L) divided by time (T). (c) Force: It is a vector quantity that represents the interaction between two objects and causes acceleration. According to Newton's second law, force is equal to mass (M) times acceleration (L/T^2). Hence, it is a derived quantity. (d) Time: It is a scalar quantity that represents the duration or interval between two events. It cannot be expressed as a combination or product of other physical quantities. Therefore, time is a fundamental quantity.

Conclude which is the fundamental quantity

Based on the analysis of each option, we can conclude that among the given physical quantities, time (option d) is the fundamental quantity.

Key concepts

Derived Quantities

In the world of physics, quantities can be divided into fundamental and derived categories. Derived quantities are those that are expressed as a function of fundamental quantities. They are basically dependent variables. For instance, various physical phenomena and properties derive from basic elements.Derived quantities often involve measurements like:

• Velocity: This refers to the speed of something in a given direction. It is derived using distance, a fundamental quantity, and time, another fundamental quantity, combined to form the ratio \( \text{velocity} = \frac{\text{length}}{\text{time}} \).
• Force: Measured by mixing mass and acceleration. The fundamental equation \( \text{force} = \text{mass} \times \text{acceleration} \) roots back to fundamental units of mass (M), length (L), and time (T).
• Viscosity: This involves factors like mass, length, and time in expressing resistance in fluids.

Vector Quantity

Quantities in physics can also be classified based on their directional properties. Vector quantities are those that have both magnitude and direction. This is akin to saying they have a size and a direction in which they act. Thus, vectors are inherently directional. Some common examples of vector quantities include:

• Velocity: Not only does it tell how fast something is moving, but also the direction it’s heading towards.
• Force: Shows how one object influences another, indicating the direction of the exerted influence along with the magnitude.

Representing vector quantities involves arrows. The length of the arrow denotes the magnitude, and the arrowhead points in the direction of the quantity. Vectors play a crucial role in understanding objects in motion under forces.

Scalar Quantity

In contrast to vector quantities, scalar quantities have only magnitude. This means they are purely numerical, without any indication of direction. Scalars are straightforward numbers that define how much of something there is. Key examples of scalar quantities include:

• Time: It merely measures the duration of events and does not involve direction.
• Mass: Defines the amount of matter in an object without specifying where it's pointing.
• Temperature: Indicates how hot or cold something is without any direction.

Scalars simplify many calculations in physics as they do not require the consideration of direction, unlike vectors. They are essential in calculating energy, power, and many more activities where direction isn’t a focus.

Newton's Second Law

Newton's second law is a cornerstone in classical physics, describing how the velocity of an object changes when it is subjected to an external force. This law introduces the concept of force as it dictates motion.In formula terms, it's represented as:\[ F = ma \]Where:

• \( F \) is the force applied to an object.
• \( m \) is the mass of the object.
• \( a \) is the acceleration produced.

This equation not only establishes the relationship between force, mass, and acceleration but also helps in understanding how objects behave under different force conditions. Mass is constant in this equation, while force and acceleration are variables.Understanding this law is crucial as it applies to nearly all physical systems, explaining why objects accelerate (change their velocity) when subjected to forces.