Which one of the following physical quantities is not a vector quantity and therefore has magnitude only with no associated direction?

Introduction / Context:

In physics, it is crucial to distinguish between scalar and vector quantities. Scalars have magnitude only, while vectors have both magnitude and direction and follow specific rules for addition and subtraction. Many basic mechanics questions test whether you can correctly classify common quantities like force, work, displacement and velocity. This question asks you to pick the quantity that is not a vector from the list given.

Given Data / Assumptions:

• Work is defined as the product of force and displacement in the direction of the force.
• Force is defined as a push or pull that can cause acceleration.
• Displacement is a change in position from one point to another.
• Velocity is the rate of change of displacement with time.
• Momentum is defined as mass multiplied by velocity.

Concept / Approach:

A vector quantity must have both magnitude and direction and obey vector addition. Force has a definite direction of action, so it is a vector. Displacement points from the initial position to the final position, so it is a vector. Velocity has both speed and direction, making it a vector. Momentum is mass times velocity, so it inherits the direction of velocity. Work, however, is defined as the scalar product of force and displacement, W = F * s * cos(theta), and the result is a scalar value. It can be positive, negative or zero, but it does not have a direction in space.

Step-by-Step Solution:

Verification / Alternative check:

One way to check is to think about how these quantities are added. Forces can be added using head to tail vector addition; so can displacements, velocities and momenta. However, when you add work done by multiple forces, you simply add the numerical values (with sign), not using vector diagrams. Furthermore, work does not change direction when you change your coordinate system, while vectors do. These considerations confirm that work is a scalar.

Why Other Options Are Wrong:

Option B (force): It has direction and magnitude and obeys vector addition rules, so it is a vector.

Option C (displacement): It is a directed distance from initial to final point, clearly a vector.

Option D (velocity): It combines speed with direction, thus a vector.

Option E (momentum): Since momentum is mass times velocity, and velocity is a vector, momentum is also a vector.

Common Pitfalls:

Students sometimes confuse work and force because they appear together in the equation W = F * s * cos(theta). The presence of vectors in the formula does not make the result a vector. Remember that the dot product of two vectors is a scalar. Work is a scalar quantity that can be positive or negative depending on the angle between force and displacement, but it does not have a direction in space. Keeping this in mind helps when deciding whether a quantity is scalar or vector.

Final Answer:

The quantity that is not a vector is work.