Newton's second law of motion is
- $ F=dp/dt $
- $ F=mv $
- $F=mv^{2}$
- $F=m^{2}v$
The Correct Option is A
Approach Solution - 1
$ F=\frac{dp}{dt} $
Approach Solution -2
Newton’s 2nd law of motion is about the acceleration of any object produced by a total force which is directly proportional to the magnitude of the total force, in a similar direction as the net force, and is inversely proportional to the mass of the object.
Mathematically it is given as,
F ∝ \(\frac{DP}{dt}\)
⇒F ∝ \(\frac{mv-mu}{t}\)
⇒F ∝ \(\frac{m(v-u)}{t}\)
⇒F∝ma
⇒F=kma
Here, ‘k’ is known as the constant of proportionality, it is equal to 1 when we consider those values in SI units.
Thus, the final expression is given as,
F=ma
Therefore, Newton’s 2nd law of motion represents the magnitude of force.
Hence, option (A) is the correct answer.
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Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.