(a) Newton’s first law of motion gives a qualitative definition of force. Justify.
(b) Which would require a greater force for accelerating – a $2kg$ of mass at $4m.{{s}^{-2}}$ or a $3kg$ of mass at $2m.{{s}^{-2}}$?

Hint: Newton’s first law of motion relates the state of motion of a body with the presence or absence of a net force acting on the body. The second part of the problem can be solved by using the mathematical equation for Newton’s second law of motion.

Formula used:
$F=ma$

Complete step by step answer:
(i) Newton’s first law of motion states that a body at uniform motion or rest remains in the same state until and unless a net external unbalanced force acts on it. This is due to a property of the body termed as its inertia. Hence, this is also known as the law of inertia. The greater the inertia of a body, the greater is its tendency to remain in the same state of the motion and hence, the greater is the net force required to change its state of motion.
Therefore, this provides a qualitative definition of force. Qualitatively, force can be defined as the physical quantity that is required to act upon a body to change its state of motion.
(ii) The magnitude of force $F$ acting on a body is the product of the mass $m$ of the body and the magnitude of the acceleration $a$ produced in the direction of that force.
$F=ma$ --(1)
Now, let us analyze the question.
Let the mass of the first body be ${{m}_{1}}=2kg$.
The acceleration of the first body is ${{a}_{1}}=4m/{{s}^{2}}$.
Let the force acting on the first body be ${{F}_{1}}$.
Hence, using (1), we get,
${{F}_{1}}={{m}_{1}}{{a}_{1}}$
$\therefore {{F}_{1}}=2\times 4=8N$ --(2)
Let the mass of the second body be ${{m}_{2}}=3kg$.
The acceleration of the second body is ${{a}_{2}}=2m/{{s}^{2}}$.
Let the force acting on the second body be ${{F}_{2}}$.
Hence, using (1), we get,
${{F}_{2}}={{m}_{2}}{{a}_{2}}$
$\therefore {{F}_{2}}=3\times 2=6N$ --(3)
Hence, comparing (2) and (3), we see that
${{F}_{1}} > {{F}_{2}}$
Hence, the body of mass $2kg$ requires a greater force for acceleration.

Note: From this question, students will understand that Newton’s first law of motion provides a qualitative definition for the force acting on a body while Newton’s second law of motion provides a quantitative definition for the force acting on a body. In fact, the second law of motion can serve as the proof for the validity of the first law. That is, in the second law, if the force is zero in the equation, the acceleration will also be zero which means that there is no change in the state of motion of the body.