# Principle of conservation of momentum is deduced from

(a) Newton’s first law

(b) Newton’s second law

(c) Newton’s third law

(d) Law of inertia

Answer

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**Hint:**In order to solve this question, we are first going to state the principle of conservation of momentum, then, stating the law from which it is deduced and then we will represent the mathematical deduction of the principle of conservation of momentum from the law.

**Formula used:**

The Newton’s second law of motion is expressed as:

\[{F_{net}} = \dfrac{{dP}}{{dt}}\]

**Complete answer:**

According to the principle of conservation of momentum, “the net linear momentum is constant when there is no external force applied to it.”

The law of conservation of momentum is deduced from Newton's second law of motion. Mathematically, the Newton’s second law of motion is expressed as:

\[{F_{net}} = \dfrac{{dP}}{{dt}}\]

Now, if the external force is zero, i.e. \[{F_{net}} = 0\]

This implies,

$ \dfrac{{dP}}{{dt}} = 0 \\

\Rightarrow P = constant \\

$

Now, we can see that if the net external force is zero, then there is no change in the linear momentum, i.e. the momentum remains constant hence the principle of conservation of momentum.

Thus, we have seen here that the law of conservation of momentum has been deduced from the equation \[{F_{net}} = \dfrac{{dP}}{{dt}}\], which is exactly the Newton’s second law of motion. Hence, option (b) Newton’s second law is the correct answer.

**Note:**Newton’s second law of motion says that “The rate of change of linear momentum of a body is equal to the net external force applied to it.” This law is stated as the Universal law of Newton’s laws of motion because a number of laws can be deduced from this very law of motion so as the conservation of momentum.

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