In physics, which of the following best defines scalar quantities?

Introduction / Context:
In mechanics and other branches of physics, quantities are broadly classified as scalars or vectors. This classification is crucial because vectors require special addition rules and include direction information, while scalars can be added algebraically. This question asks you to recall the correct definition of scalar quantities and distinguish it from the definition of vectors and other incorrect statements.

Given Data / Assumptions:
- The question is about scalar quantities in basic physics.
- Options describe different combinations of magnitude and direction properties.
- We assume standard definitions from introductory physics courses.

Concept / Approach:
A scalar quantity is completely specified by a numerical value (magnitude) and appropriate units, without any associated direction in space. Examples include mass, temperature, energy and time. A vector quantity has both magnitude and direction and follows vector addition laws. It is not possible for a physical quantity to have direction without magnitude in the usual sense. A statement that a quantity has neither magnitude nor direction does not describe a meaningful measurable physical quantity. Therefore, the correct definition is that scalars have magnitude only and no direction.

Step-by-Step Solution:
Step 1: Recall that scalars are quantities like mass and time that do not require direction for their description. Step 2: Note that the defining feature of a scalar is having magnitude only. Step 3: Recognise that vectors, such as velocity and force, have both magnitude and direction and are not scalars. Step 4: Option A states that scalar quantities have magnitude only and no direction, which matches the standard definition. Step 5: Options B, C and D either talk about direction without magnitude, or combine magnitude and direction, or have neither, none of which matches the definition of scalar quantities. Step 6: Therefore, choose option A as the correct answer.

Verification / Alternative check:
Reviewing examples can confirm this. Mass of 5 kg, temperature of 30 C and time interval of 10 seconds are all fully described without mentioning direction. In contrast, a velocity of 20 m/s east or a force of 5 N upward clearly includes direction and is treated as a vector. This practical check aligns with the theoretical definition and supports option A.

Why Other Options Are Wrong:
Physical quantities which have no magnitude and only direction: Direction without magnitude does not represent a measurable physical quantity; such a definition is not used in physics.
Physical quantities which have magnitude and direction and obey vector addition: This is the definition of vector quantities, not scalar quantities.
Physical quantities which have no magnitude and no direction: Such a description does not correspond to any meaningful physical measurement in standard physics.

Common Pitfalls:
Some students confuse “having a sign” with “having a direction.” Negative temperature differences or negative charges can still be scalars even though they can be positive or negative. Direction in the vector sense means a specific orientation in space, not just a sign. Being clear about this distinction helps avoid misclassifying quantities as vectors when they are actually scalars.

Final Answer:
Scalar quantities are physical quantities which have magnitude only and no direction.