Question

Write the mathematical form of Newton’s second law of motion.
A) $ F = m/g $
B) $ F = 0 $
C) $ F = ma $
D) $ v = u + at $

Answer 1

Hint : Newton’s second law relates the force acting on a body with its acceleration. The acceleration gained by an object when subjected to the same magnitude of the force depends on the mass of the object. This means that the acceleration gained by an object is proportional to the force acting on it and inversely proportional to the mass of the object.

Complete step by step answer
Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.
Option (A) talks about force mass and gravitational acceleration which is irrelevant to the law and is a more general case so option (A) is incorrect.
Option (B) is incorrect since the net force on any object can be non-zero and is not always zero.
Option (D) is also incorrect as it is a law of kinematics that relates the initial and final velocity of an object that experiences an amount of consonant acceleration in a given amount of time.
In equation form, Newton’s second law of motion can be written as
 $ a = \dfrac{F}{m} $
Which can also be written as,
 $ F = ma $
This corresponds to option (C).

Note
Newton’s second law is often also stated as the force acting on a body is proportional to the rate of change of momentum of the body. This can be mathematically written as
 $ F = \dfrac{{dp}}{{dt}} $
Since the momentum of an object is equal to the mass times its velocity that is $ p = mv $ , assuming that the mass is constant, we can write
 $ F = m\dfrac{{dv}}{{dt}} $
And since $ \dfrac{{dv}}{{dt}} = a $ , we can write the net force as
 $ F = ma $ .
Newton’s second law also leads to Newton’s first law as if the net force acting on a system is zero, the rate of change of momentum is zero which means that the system will continue its motion if it is in motion or it will remain at rest if that was its original state.