Which one of the following is a scalar quantity?
(i) distance (ii) displacement (iii) velocity (iv) Gravity
Answer (2)
Distance is a scalar quantity because it only has magnitude.
Displacement is a vector quantity because it has both magnitude and direction.
Velocity is a vector quantity because it has both magnitude and direction.
Gravity is a vector quantity because it is a force with both magnitude and direction.
Therefore, the scalar quantity is d i s t an ce .
Explanation
Identifying Scalar Quantities We need to identify which of the given options is a scalar quantity. A scalar quantity is defined by its magnitude only, whereas a vector quantity is defined by both magnitude and direction. Let's analyze each option:
Analyzing Distance (i) Distance: Distance is the total length of the path traveled. It only has magnitude and no specific direction. Therefore, distance is a scalar quantity.
Analyzing Displacement (ii) Displacement: Displacement is the shortest distance between the initial and final positions and has a specific direction. Therefore, displacement is a vector quantity.
Analyzing Velocity (iii) Velocity: Velocity is the rate of change of displacement and has a specific direction. Therefore, velocity is a vector quantity.
Analyzing Gravity (iv) Gravity: Gravity is a force, and force is a vector quantity because it has both magnitude and direction.
Conclusion Therefore, the scalar quantity among the given options is distance.
Examples
Understanding the difference between scalar and vector quantities is crucial in physics. For example, when planning a road trip, knowing the distance you'll travel helps you estimate fuel consumption. However, if you're navigating using GPS, the displacement (shortest distance and direction to your destination) is more relevant. Similarly, understanding gravity as a vector helps in calculating projectile motion, like the trajectory of a ball thrown in the air.
The scalar quantity among the options is distance, as it only possesses magnitude. Displacement, velocity, and gravity are all vector quantities since they include both magnitude and direction.
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