Question

If force (F), velocity v and time (T) are taken as fundamental units then the dimensions of mass are____.

Answer 1

Here we have to find out the dimension value of mass by using the newton’s second law. Then we use the acceleration and velocity formula to solve the dimension of the mass value. On some simplification we get the required answer.
Formula Used:
$F = MA$

Complete step by step answer:
As newton’s second law of motion, states as the product of acceleration and mass is equal to the force $F = MA$
Where, F is force, m is mass of the product and $a$ is acceleration.
Hence we can write it as $A = \dfrac{L}{{{T^2}}}$
Where L is length and T is Time taken
Now putting $A = \dfrac{L}{{{T^2}}}$ in $F = MA$and we get,
$\Rightarrow F = M \times \dfrac{L}{{{T^2}}}$
$\Rightarrow F = \dfrac{M}{L} \times \dfrac{L}{T}$
Since velocity $= \dfrac{L}{T}$
So, we can write it as, $F = \dfrac{{MV}}{T}$
To find value of M, we have to bring M on right hand side
$M = FT{V^{ - 1}}$
Mass is proportional to force and time and inversely proportional to velocity.

Additional information:
Newton's second law is the acceleration of a body is inversely related to its mass and directly related to the net force. It implies that the conservation of momentum, the momentum of the body, is constant, when the net force on the body is zero.
Acceleration depends on two things: the force and mass of the object.
Applications of Newton's second law are kicking the ball, pushing the loaded box, etc. Newton’s second law is also called the law of force and acceleration. Newton’s second law is applied for rockets. The lighter the rocket's acceleration will be faster.

Note: Force is the ability of changing the state of rest or motion of a particular object. It has both direction and magnitude. It is measured with spring balance. The SI unit is newton. Dimension is $LM{T^{ - 2}}$ Net force that acts upon any object is equal to the rate of momentum that changes with the time. Force is the dot product of mass and acceleration.
The rate of change of the position is called velocity. It is a physical vector quantity. SI unit of velocity is $m{s^{ - 1}}$ Dimension of velocity is $L{\text{ }}{T^{ - 1}}$ . Magnitude and direction are required to explain velocity. Average velocity calculated by $\overline V = \dfrac{{\Delta x}}{{\Delta t}}$ , where $\Delta x$ is changed in position and $\Delta t$ is changed in time. Time is defined as the value which the clock shows. It is the scalar quantity. $s$ is the SI unit of time.