Question

If the unit of force is 100N, unit of length is 10m and unit of time is 100s, what is the unit of mass in this system of units?

Answer 1

Hint: To answer this question, the given unit of force should be broken down into the fundamental units of those systems of units. Thus, the definition of force must be known in order to break down the units of force.

Complete step-by-step answer:
A unit of measurement is the magnitude of a property of a physical system, known as quantity that is adopted by convention or by law.
The units of measurement for several physical quantities in nature are bundled into a system of units. The major systems of units are: i) MKS or SI system ii) CGS system iii) FPS or Imperial system
Out of the three, the universally accepted standard system of units, that are applied in scientific notations as per the International System of units, is the MKS system or simply, the metric system.
These systems are defined by the units of the three most fundamental quantities i.e. length, mass and time. The units in the same order in these systems are given as follows: i) MKS – metre, kilogram, second ii) CGS – centimetre, gram, second iii) FPS – foot, pound, second
Every other physical quantity can be derived from these fundamental units.
The unit of force in the SI system is newton.
The force is defined as the product of mass and the acceleration as per Newton’s second law of motion.
$F = ma$
1 newton is defined as the product of force applied by 1 kilogram of mass, causing an acceleration of 1 meter per second square.
$1N = 1kg \times 1m{s^{ - 2}}$
So, in the system where newton is the unit of force, second is the unit of time, metre is the unit of length, the unit for mass in the SI system is kilogram.

Note:
In the CGS or the centimetre-gram-second system of units, the unit of force is called dyne.
1 dyne = $1g \times 1cm{s^{ - 2}}$
The relationship between newton and dyne is given by –
1 newton = 100000 dynes.