Correct Answer - Option 2 : the momentum of an isolated system with any number of objects is conserved.
CONCEPT:
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Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.
P = mv
where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.
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Newton's Second Law of Motion: It says that the net external force on a system or body is equal to the change in momentum of the system or body divided by the time over which it changes.
Mathematically:
\(F_{ext} = {Δ p \over Δ t}\)
where Fext is the external force on the system, Δp is the change in momentum, and Δt is the change in time.
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Momentum Conservation: When in a system, there is no external force then the total momentum (P) of the isolated system will be conserved.
EXPLANATION:
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Newton's Second Law of Motion says that the net external force on a system or body is equal to the change in momentum of the system or body divided by the time over which it changes.
\(F_{ext} = {Δ p \over Δ t}\)
- If the external force is zero i.e. Fext = 0
\(F_{ext} = {Δ p \over Δ t}=0\)
Δp = 0
Pinitial = Pfinal
Hence momentum is conserved.
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Option 4: For momentum conservation, it is necessary that external force is zero.
- So this is an incorrect statement.
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Option 2 and 3: If the system is not isolated, an external force may work.
- In an isolated system, there is no external force working. It is a closed system.
- So option 2 gives the correct statement while option 3 gives the incorrect one.
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Option 1: In the derivation, there is no restriction on the number of objects whether it is even or odd. Momentum will be conserved.
- So option 1 does not gives a correct statement regarding momentum conservation.
- So the correct answer is option 2.
