Question

Newton’s second law of motion gives a measurement of:
A. Inertia
B. Momentum
C. Force
D. Acceleration

Answer 1

Hint: According to Newton’s second law of motion the rate of change of linear momentum of a body is directly proportional to the external force applied on the body in the direction of applied force. Using this relation, we need to derive the equation of motion of a body.

Complete step by step answer:
Let us take a body of mass m and velocity v.
The linear momentum of the body would be:
$\overrightarrow{p}=m\overrightarrow{v}$
The rate of change of linear momentum with respect to time would be:
$\dfrac{d\overrightarrow{p}}{dt}$
According to the second law:
$\overrightarrow{F}\propto \dfrac{d\overrightarrow{p}}{dt}$
$\overrightarrow{F}=k\dfrac{d\overrightarrow{p}}{dt}$
$\overrightarrow{F}=k\dfrac{d(m\overrightarrow{v})}{dt}$
$\overrightarrow{F}=km\dfrac{d(\overrightarrow{v})}{dt}$
$\overrightarrow{F}=km\overrightarrow{a}$
Taking a proportionality constant k=1
$\overrightarrow{F}=m\overrightarrow{a}$
This equation represents the equation of motion of a body of mass m and acceleration a. The direction of force and acceleration is the same. Here mass is a scalar quantity and acceleration is a vector quantity the product of a scalar and a vector gives a vector.
Thus, magnitude of force can be calculated by taking the product of mass and acceleration of the body. Hence the second law of motion gives us the measure of force and acceleration.
The correct answer is option C. Force. and option D. acceleration.

Note: Students should not get confused with inertia and momentum since the first law is the law of inertia and in the second law Force has a direct proportionality with rate of change of momentum and not just momentum.