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Question

# Two particle A and B move on a circle. Initially Particle A and B are diagonally opposite to each other. Particle A moves with angular velocity π radsec, angular acceleration π2radsec2 and particle B moves with constant angular velocity 2π radsec. Find the time after which both the particle A and B will collide.

A

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B

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C

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D

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Solution

## The correct option is A ωangularaccelerationParticleAπ radsecπ2radsec2ParticleB2π radsec0Particle B with respect to particle A2π−π;πradsec0−π2;−π2 radsec2 If I keep A constant and see the motion of B, B will look like coming towards me and in the process will have to cover an angular displacement of π rad. ⇒ θ = π rad θ = ω0 t + 12α t2 θ = ω t + 12α t2 ⇒ π = πt + 12(−π2)t2 ⇒ t2 − 4t + 4 = 0 ⇒ t = 2 sec

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