One of the following is a scalar quantity?

Analysis

The question asks us to identify which of the given physical quantities is a scalar quantity.

Concept Explanation

In physics, quantities are categorized into two main types based on their properties:

1. Scalar Quantities: These are physical quantities that have magnitude only. They do not have a specific direction. Examples include mass, time, temperature, distance, speed, and energy.
2. Vector Quantities: These are physical quantities that have both magnitude and direction. Examples include force, velocity, acceleration, displacement, momentum, and weight.

Step-by-Step Evaluation

Let’s examine each option:

• A. Weight: Weight is the force of gravity acting on an object ($W = mg$). Since force is a vector quantity (it always acts downwards towards the center of the Earth), weight is a vector.
• B. Momentum: Momentum is the product of mass and velocity ($p = mv$). Since velocity is a vector, momentum is also a vector.
• C. Potential Energy: Energy is the capacity to do work. It is defined by its magnitude (the amount of energy) and does not have a direction associated with it. Therefore, potential energy is a scalar.
• D. Displacement: Displacement is the shortest distance between two points in a specified direction. Because it requires a direction, it is a vector.

Conclusion

Comparing our analysis to the options, only potential energy fits the definition of a scalar quantity.

Exam Tip: A simple trick to remember the difference is the "Direction Test." Ask yourself, "Does it make sense to say '5 meters to the North'?" If yes, it's a vector (like displacement). If you ask, "Does it make sense to say '5 Joules to the North'?" it sounds nonsensical, which confirms it is a scalar!