Question

What does the principle of conservation of linear momentum state?
(a). The linear momentum of a system cannot be changed.
(b). The linear momentum of a system cannot remain constant.
(c). The linear momentum of a system can be changed only if internal forces act.
(d). The linear momentum of a system can be changed only if external forces act on it.

Answer 1

Hint: In conservation we know that momentum before and after collision of objects should remain the same. So, by using this principle of conservation of momentum we will derive the mathematical expression and using it we will find our answer.

Formula used: $\overset{\to }{\mathop{p}}\,=m\overset{\to }{\mathop{v}}\,$

Complete step by step answer:
Before finding the law of conservation of momentum, we will first understand what momentum is, so momentum is defined as the product of mass of any object and its velocity in the direction of motion of the object. The law of conservation of momentum states that the momentum of the body remains constant until and unless any external force acts on it.
So, now, we know that conservation of momentum can be given by the formula,
$\overset{\to }{\mathop{p}}\,=m\overset{\to }{\mathop{v}}\,$,
Where, p is linear momentum, v is velocity and m is mass of object.
Now, taking derivation of the expression with respect to time the same expression is also expressed mathematically as,
$\dfrac{dp}{dt}=\dfrac{d\left( mv \right)}{dt}$
$=m\dfrac{d\left( v \right)}{dt}$
$=ma$
$=F_{net}$
Now, if net external force acting on the body is zero, then the rate of momentum is also zero which can be observed from the above equation.
Hence, we can say that the linear momentum of the system changes only if external force acts on the body.
Thus, option (d) is correct.

Note: This question can also be answered in a simple way if a student knows the principle of conservation of linear momentum which states that momentum is conserved when initial momentum is equal to final momentum which is only possible when no external force acts on the system.