Which one of the following physical quantities is a scalar quantity, having magnitude only and no associated direction?

Introduction / Context:
In physics, it is important to distinguish between scalar and vector quantities. Scalars have only magnitude, while vectors have both magnitude and direction. This distinction affects how we add quantities and how they behave in equations. The question asks you to identify the scalar quantity from a list that includes both vector and scalar physical quantities.

Given Data / Assumptions:

• Displacement describes change in position and has direction.
• Electric field describes the force per unit charge at a point and has direction.
• Acceleration describes the rate of change of velocity and has direction.
• Work is defined as force multiplied by displacement in the direction of the force.

Concept / Approach:
Displacement, electric field and acceleration are all defined with an inherent directional aspect. Displacement is a vector pointing from initial to final position. Electric field is a vector that shows the direction in which a positive test charge would be pushed. Acceleration is a vector indicating how the velocity vector changes. Work, however, is defined as W = F * s * cos(theta), where F and s are vectors and theta is the angle between them. The dot product of two vectors is a scalar, so work has magnitude but no inherent direction, making it a scalar quantity.

Step-by-Step Solution:
Step 1: Recall that scalars have magnitude only; vectors have both magnitude and direction.Step 2: Consider displacement: it indicates how far and in which direction an object has moved, so it is a vector.Step 3: Consider electric field: it specifies the direction and magnitude of the force per unit positive charge, so it is a vector.Step 4: Consider acceleration: as the rate of change of velocity, it must point in a specific direction, making it a vector.Step 5: Consider work: it is calculated as the dot product of force and displacement, giving a scalar value.Step 6: Conclude that work is the only scalar quantity among the given options.

Verification / Alternative check:
In textbook notation, displacement, electric field and acceleration are written in bold or with arrows above to indicate vector nature. Work is written as a plain symbol without vector notation and is measured in joules, a scalar unit. When adding works from different processes, we simply add their numerical values, unlike vector addition where directions matter. This confirms that work is scalar.

Why Other Options Are Wrong:
Displacement cannot be scalar because knowing only the distance is not enough to specify change in position; direction is required. Electric field must specify both how strong and in which direction it acts, so it is vectorial. Acceleration describes how velocity changes in direction and magnitude, making it clearly a vector. Therefore, these three cannot be the correct scalar quantity in this question.

Common Pitfalls:
Students sometimes confuse distance with displacement and may incorrectly think displacement is scalar. Others may treat any quantity without obvious directional wording as scalar, ignoring the formal definitions. To avoid such confusion, always check whether direction is essential to the definition of the quantity. If it is, you have a vector; if not, you likely have a scalar.

Final Answer:
Work is a scalar quantity, while displacement, electric field and acceleration are vector quantities.