Question

Which one of the following is a scalar quantity?
a.)Displacement
b.)Electric field
c.)Acceleration
d.)work

Answer 1

Hint : All the measurable physical quantities can be grouped into two categories, Scalar and Vector quantities. Scalar quantities only require magnitude for their description while vector quantities need both magnitude and direction. We will consider each option and check whether that quantity is a scalar or a vector by applying the above criteria.

Complete step by step answer:
All the quantities which can be measured can be categorized into two groups – Scalar and vector quantities. Scalars are the quantities that are fully described by a magnitude, a numerical value only. Vectors are the physical quantities that are fully described by both magnitude and direction.

A scalar quantity is the one that only requires a single element of a number field for its description. Scalars are the physical quantities that only have magnitude, or a sign as well, and no other characteristics. A scalar is unchanged by any transformation in the coordinate system. Examples for scalar quantity are – volume, density, speed, energy, mass, and time.
A vector quantity is the one that has both of the characteristics, magnitude and direction. Vectors are typically demonstrated by an arrow whose direction is the same as that of the physical quantity and the length is proportional to the magnitude of that quantity. A vector has magnitude and direction, but it does not have a position. A vector is not altered by displacing it parallel to itself. Examples for vector quantity are – force, velocity, and torque.
In the given options, we have Displacement, Electric field, Acceleration, and Work.

Displacement is the difference between initial and final position of an object. It needs both magnitude and direction to describe it as a whole. Therefore, displacement is a vector quantity.

Electric field is the specific region around a charged particle. Its magnitude is expressed by the electric field strength. Its direction is the same as that of the electric force acting on a unit positive charge. Therefore, the electric field is a vector quantity.

Acceleration is the rate of change of velocity. Velocity is a vector quantity, and the rate of its change would also be a vector. An object is accelerating if its velocity is changing over time. Therefore, acceleration is a vector quantity.
Work is defined as the process of energy transfer. It is expressed as the dot product of force and displacement. As both the quantities, force and displacement, are vectors, their dot product would be a scalar. Therefore, work is a scalar quantity.
All the quantities mentioned above, displacement, electric field, and acceleration, are vectors except work. Work is a scalar quantity.

Hence, the correct option is D.

Note :
Scalar quantities are the one which are not associated with a particular direction. If a quantity is expressed in the terms of another quantity, it does not mean that all the quantities are of the same type, be it a scalar or a vector. Force and displacement are vector quantities, but their dot product Work is a scalar quantity since dot product always generates a scalar.