Question

The correct statement of Newton’s third law is
A. The rate of change of momentum of an object is directly proportional to the applied force.
B. For every action there is an equal and opposite reaction.
C. An object at rest remains at rest and an object in motion remains in motion unless acted upon by a force.
D. None of these.

Answer 1

Hint: Newton proposed three laws of motion which describe the relation between the body and the forces acting on it and the motion due to these forces. The three laws of motion can also be expressed in the mathematical form. Here we will discuss the laws and its mathematical representation.

Complete step by step answer:
The Newton’s third law of motion states that the force \[{{F}_{A}}\] exerted on a body, say A, by another body, say B, will be equal to the force \[{{F}_{B}}\] exerted on body B by A, just the direction of the force will be opposite. In simple words every action has an equal and opposite reaction. Mathematically it can be represented as
\[{{F}_{A}}=-{{F}_{B}}\]

So, the correct answer is “Option B”.

Additional Information: The Newton’s first law states that the net force on the body will be zero and then the velocity will be constant. As velocity is constant its speed will be constant and so the direction of the motion.
Hence an object will remain in motion or at rest unless some force is applied on it.
The mathematical representation of the first law can be given as
\[\begin{align}
  & \sum{F=0} \\
 & \Rightarrow \dfrac{dv}{dt}=0 \\
\end{align}\]
Newton's second law states that the rate of change of momentum is equal to the force applied and the direction in which the force is applied, the change in momentum will take in the same direction. Mathematically it is represented as
\[F=\dfrac{dp}{dt}\]
On solving it, we get another form of second law of motion which says that the force acted on object is product of its mass and the acceleration and it is given as
\[F=ma\]

Note: The Newton’s third law was used to derive the laws of conservation and the third law also shows that a single isolated force is not possible. The example for Newton’s third law is wrestling in which both wrestlers exert equal and opposite forces, when one tries to exert more force the wrestler is pushed back.