Question

Which of the following physical quantities is different from others?
(A) Displacement
(B) Velocity
(C) Force
(D) Kinetic energy

Answer 1

Hint Vectors are the quantities that have both, a magnitude and a direction. Two vectors can be only added using the properties of vector addition, and a vector can also have negative values which generally define its direction relative to a reference point.

Complete Step by step solution
In the given options, there are some physical properties which are either vector or scalar. On analyzing each option based on the definition of a vector, we have-
Option A) Displacement is defined as the shortest distance that can be covered to reach from one point to the other. When both of the points are joined via a straight line, this line gives the displacement of the object. No matter what path is traveled by the object its displacement remains the same, and its direction is towards the endpoint of the path. If an object moves in any path but ends up at the same spot, its displacement is zero. Thus, displacement is a vector quantity.
Option B) Velocity is defined as the displacement of an object per unit of time. Thus the average velocity of an object is given by the length of the shortest path between two points divided by the total time taken to cover that length. We know that displacement is a vector quantity, therefore velocity is also a vector quantity.
Option C) Force is defined as a type of interaction with an object, which can cause a change in its motion. The force is the product of the mass of an object with the acceleration produced in it. The mass of an object is a scalar quantity, while the acceleration is a vector quantity. This makes force a vector quantity as well.
Option D) Kinetic energy is defined as the energy carried by moving objects. It is the dot product or scalar product of the velocity of a body and a very small change in its momentum. Both velocity and momentum are vector quantities, but their dot product gives out a scalar quantity. Thus kinetic energy is a scalar quantity.

Hence option (D) is a different physical quantity than the other options and is the correct option.

Note When a vector is multiplied to a scalar quantity, its product remains a vector. When two vectors are multiplied with each other, the product can either be a vector or a scalar quantity. A dot product is the only way to create a scalar quantity from a given vector quantity.