Question

Which of the following does not have a fundamental unit?
A) Mass
B) Time
C) Force
D) Length

Answer 1

Hint: The physical quantity which can be measured in terms of other physical quantities does not have fundamental units i.e. they are expressed as a combination of other physical units that have fundamental units. Fundamental units are also called derived units.

Complete solution:
A physical quantity that is expressed as a combination of the fundamental units does not have a fundamental unit. There are $7$ fundamental S.I. units: length, time, amount of substance, electric current, temperature, luminous intensity, and mass.
The unit of Force is Newton. According to the second law of motion, force is defined force as a product of mass and acceleration, therefore
${\text{F = m}} \times {\text{a}}$.
The S.I unit of mass is kilogram $(kg)$,
while the S.I unit for acceleration is $m/s^2$.
Therefore the S.I unit of force is $kg\cdot m/s^2$.
Since it is expressed as a combination of the units of mass, length, and time therefore it does not have a fundamental unit. While mass, time, and length cannot be expressed in terms of other units and have their own units, therefore they have fundamental units.
The fundamental S.I unit for mass is kilogram $(kg)$, for time is second $(s)$ and for length is meter $(m)$.

The correct answer is (C) Force.

Note: There are a fixed number of quantities that are assumed to be fundamental. We can consider our own sets of fundamental quantities but the seven quantities that were mentioned above are considered as fundamental quantities all over the world and other quantities are derived from them which are called derived quantities.