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Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v₁ while body B is at rest before collision. The velocity of the system after collision is v₂. The ratio v₁ : v₂ is:
m v_1 = (m + m) v_2 = 2m v_2 -> v_1 = 2 v_2 -> v_1 : v_2 = 2 : 1!
Before the collision, body A of mass m moves with velocity v_1 while body B of identical mass m is at rest. The total initial linear momentum of the system is:
In a completely inelastic one-dimensional collision, coefficient of restitution e = 0. The two bodies coalesce into a single combined mass of 2m moving together with common velocity v_2:
In the absence of external impulsive forces, linear momentum is conserved:
Dividing both sides by m v_2 gives the ratio v_1 : v_2:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Incorrectly squares the mass ratio.
Inverted and squared.
Inverts the ratio (gives v_2 : v_1 instead of v_1 : v_2).
Exact momentum conservation: m v_1 = 2m v_2 -> v_1/v_2 = 2/1.
The velocity after collision is halved (v_2 = v_1 / 2), so students often think "half" and impulsively pick 1 : 2.
"In a completely inelastic collision of two identical masses with one initially at rest, final velocity is halved and momentum is conserved."
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