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Question

# After a totally inelastic collision, two objects of the same masses and same initial speeds are found to move together at half of their initial speeds as shown in figure below. If α=30∘, then the angle between the initial velocities of the objects is

A
90
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B
60
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C
150
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D
45
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Solution

## The correct option is B 60∘Let the angle between initial velocities be 180−θ and the situation is as shown in figure. Momentum conservation along x− axis, mu−mucosθ=2mucosα2 ...(i) Momentum conservation along y− axis, musinθ=2musinα2 ...(ii) Dividing equation (ii) by eqaution (i) sinθ1−cosθ=tanα ⇒2sinθ2cosθ22sin2θ2=tanα ⇒cotθ2=tanα ⇒tan(90−θ2)=tanα ⇒θ=2×(90−α)=2×60∘=120∘ Therefore, angle between their velocities =180∘−θ=180∘−120∘=60∘

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