Question

Which of the following does not have a fundamental unit?
A. Mass
B. Time
C. Force
D. Electric current

Answer 1

Hint: Fundamental quantities are some basic quantities using which other physical quantities are derived or explained. Fundamental quantities are measured in fundamental units. Fundamental units are defined using some natural easily reproducible phenomenon. Fundamental quantities cannot be defined using any other physical quantities.
One can look at the options and determine whether the quantity is a fundamental quantity or not.

Complete Step-by-Step solution:
There are some physical quantities which are basic to the study of physics and they cannot be defined using any other quantities but have an arbitrary definition of their own. These quantities are known as fundamental quantities. Using these basic quantities other physical quantities are derived or explained. Fundamental quantities are measured in fundamental units.
The definition for fundamental units is given by some natural, easily reproducible phenomenon.
For example, length and time are fundamental units which are used to define the speed of an object. The speed of an object is defined as the ratio of the distance covered (length) by a body to the time taken.
There are seven fundamental quantities, with their respective units. They are mass, length, time, temperature, electric current, luminous intensity and number of particles.
All other physical quantities can be defined as some combination of one or many of these seven fundamental quantities.
Hence, from the options given clearly, force is not a fundamental quantity and does not have a fundamental unit.
Force can be defined as the product of the mass and the rate of change in displacement (length) of the body per unit.
Hence, the dimensions of force are
$\left| \text{Force} \right|=\text{Mass}\times \dfrac{\text{length}}{\text{tim}{{\text{e}}^{2}}}$
Since, force is not a fundamental quantity, it does not have a fundamental unit.
Hence, the correct option is C) force.

Additional information:
Fundamental quantities have their respective fundamental units. These units are defined by using some easily reproducible naturally occurring phenomenon. However, the definitions of these fundamental units have constantly been evolved and changed over the years for obtaining greater accuracy.

Note: The fundamental units stated above are for the SI system of units. For other systems, fundamental quantities may change. However, the SI system of units is universally recognized and considered the official system of measurements for all scientific measurements.
In this question one could get confused upon thinking that electric current can be defined in terms of charge passing per unit time and so it must not be a fundamental quantity and not have a fundamental unit. In fact, in many systems, electric charge instead of electric current is considered to be a fundamental quantity. However, in the SI system, electric current is considered to be a fundamental quantity and this should also be followed by the student.