Question

The pair containing a scalar and a vector quantity is:
A) Impulse and angular momentum.
B) Work and frequency.
C) Electromagnetic force and force.
D) Current density and current.

Answer 1

A vector quantity is a quantity which has both magnitude as well as direction whereas the scalar quantities are those quantities which only have magnitude and no direction. All those physical quantities which have magnitude as well as direction are called vector quantities and those with only magnitude are known as scalar quantities.

Complete step by step answer:
It is asked in the problem to find out whether the option has the pair of a scalar quantity and vector quantity. We can consider each option and find out which option is correct. Let us consider the first option.

Impulse and angular momentum.

Impulse is defined as the product of force and time and impulse is a vector quantity whereas angular momentum is defined as the product of mass linear velocity and radius and it is not a scalar quantity nor a vector quantity it is expressed as a matrix.

Option B.

Work and frequency,

The work is defined as the product of force and displacement and work is a scalar quantity as the dot product of force and displacement is always a scalar quantity. Frequency is defined as the number of oscillations made per second. Frequency is a scalar quantity.

Option C.

Electromagnetic force and force.

Electromagnetic force is defined as the energy per unit charge and is a scalar quantity. Electromagnetic force is a scalar quantity. Force is defined as the product of mass and acceleration and force is a vector quantity. This is the pair in which one physical quantity is scalar and other is vector. The correct answer is electromagnetic force and force.

Option D.

Current density and current.

Current is defined as a moving stream of charged particles ions and electrons from one point to another point. Current is a scalar quantity.

Current density is defined as the amount of charge per unit time that flows through a unit area of cross section. The current density is vector quantity.

The correct option for this problem is option C.

Note: It is important for students to remember that whenever it is asked about the physical quantities being scalar or vector we only consider that the physical quantity has only direction or direction along with the magnitude and this is enough to categories whether the physical quantity is scalar or vector.