Among the following physical quantities, which one is a vector quantity, that is, it has both magnitude and direction and obeys vector addition?

Introduction / Context:
This question tests your ability to distinguish between scalar and vector quantities in physics. A vector quantity has both magnitude and direction and follows the rules of vector addition, while a scalar has only magnitude. Many physical quantities may sound similar but differ in whether direction is an essential part of their definition. Correctly identifying vectors is important in mechanics and field theory.

Given Data / Assumptions:

• The quantities listed are pressure, impulse, gravitational potential and coefficient of friction.
• We are asked to pick the only vector quantity among them.
• No numerical data is provided; this is a concept based classification question.
• We assume standard definitions from classical mechanics.

Concept / Approach:
Impulse is defined as the change in momentum of a body when a force acts on it for a short time. Since momentum is a vector quantity (mass times velocity) and force is also a vector, impulse must be a vector quantity with both magnitude and direction. Pressure is force per unit area and is treated as a scalar in basic physics (in more advanced treatments it is part of a tensor but not a simple vector here). Gravitational potential is scalar energy per unit mass. Coefficient of friction is a dimensionless scalar constant. Therefore, impulse is the only vector quantity in the list.

Step-by-Step Solution:
Step 1: Recall that a vector quantity must have a direction that is physically meaningful and must obey vector addition rules. Step 2: Define impulse J as J = F * Δt, where F is the force vector and Δt is the time interval. Step 3: Recognise that impulse has the same direction as the force and represents the change in momentum, which is also a vector. Step 4: Consider pressure P, defined as normal force per unit area. In elementary physics, P is treated as a scalar because only its magnitude matters in basic problems. Step 5: Gravitational potential is energy per unit mass at a point in a field and is a scalar; it does not have a direction by itself. Step 6: The coefficient of friction is a dimensionless scalar describing the ratio of frictional force to normal reaction, not a vector. Step 7: Conclude that among the given options, impulse is the only vector quantity.

Verification / Alternative check:
An additional way to verify is to think about how these quantities combine. If you apply two impulses in different directions, the net effect on momentum is obtained by vector addition of the two impulses. On the other hand, pressures at different points are usually combined by arithmetic or weighted averages, not by vector addition. Similarly, gravitational potentials and coefficients of friction are added as scalars. This behaviour confirms that impulse behaves as a vector, while the others behave as scalars in typical problems.

Why Other Options Are Wrong:
Pressure is treated as a scalar quantity in basic mechanics, describing magnitude of normal force per unit area, without a direction that obeys vector addition rules at this level. Gravitational potential is a scalar field quantity; it provides a value of potential energy per unit mass at each point, not a direction. Coefficient of friction is a scalar constant between two surfaces and has no direction.

Common Pitfalls:
Students may confuse pressure with force because both involve the idea of push and area. While force is clearly a vector, pressure is defined as a scalar in basic courses. Another pitfall is to think of gravitational potential as a vector because gravity has a direction. However, gravitational field or acceleration is the vector quantity; gravitational potential is scalar. Focusing on definitions and how quantities add helps avoid these misunderstandings.

Final Answer:
The only vector quantity among the options is impulse.