Unit of Mass

In the given scenario where force (F), length (L), and time (T) are considered fundamental units, we need to determine the unit of mass. To do so, we can analyze Newton's second law of motion and derive the unit of mass based on its equation.

Newton's Second Law of Motion
According to Newton's second law of motion, the force acting on an object is directly proportional to its mass and the acceleration produced. Mathematically, it is represented as:

F = ma

Where:
F = Force (in newtons)
m = Mass (in kilograms)
a = Acceleration (in meters per second squared)

Deriving the Unit of Mass
To determine the unit of mass, we can rearrange the equation and isolate the mass:

m = F/a

Since the force (F) is measured in newtons (N) and the acceleration (a) is measured in meters per second squared (m/s^2), we can substitute their respective units into the equation:

m = N / (m/s^2)

Simplifying further, we can rewrite the equation as:

m = N * (s^2/m)

Now, let's break down the units:

N = kg * m/s^2 (by definition of newton)
s^2 = (s * s) (square of seconds)
m = m (meter)

Substituting the units into the equation, we have:

m = (kg * m/s^2) * (s^2/m)

Simplifying the equation, we find:

m = kg

Thus, the unit of mass in this scenario is kilogram (kg).

Since M=FT²/L Hence,in CGS its unit will be dyne sec²cm-¹ and in SI it'll be Newton sec²m-¹.