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Difficulty: MediumNewton's Laws of Motion and Linear Momentum

In an isolated system of colliding bodies where no net external force acts, total linear momentum is conserved only if the collision is perfectly elastic.

Answer: Answer

Answer

The statement is False. Total linear momentum is conserved in all isolated collisions regardless of whether the collision is elastic or inelastic.
Linear momentum conservation depends strictly on the absence of net external forces. Internal forces, such as those causing deformation or heat release in inelastic collisions, cancel out in equal and opposite pairs according to Newton's Third Law and therefore do not change total linear momentum.

Step-by-Step Solution

1
Analyze the condition for linear momentum conservation.
Linear momentum is conserved whenever the net external force acting on the system is zero (∑Fext=0∑ F_{\text{ext}} = 0).
By Newton's Second Law written in terms of momentum (Fnet=ΔpΔtF_{\text{net}} = \frac{\Delta p}{\Delta t}), if Fnet=0F_{\text{net}} = 0, then Δp=0\Delta p = 0, meaning initial total momentum equals final total momentum.
2
Differentiate between momentum conservation and kinetic energy conservation.
Total linear momentum is conserved in both elastic and inelastic collisions, whereas total kinetic energy is conserved only in elastic collisions.
In inelastic collisions, internal forces convert kinetic energy into heat, sound, or mechanical deformation, but internal forces cannot alter the net momentum of the system.

Key Concept

Conservation of Linear Momentum in Collisions
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Topics

Newton's Laws of Motion and Linear Momentum

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