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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

t = 2 sec

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B

t = 1 sec

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C

t = 4 sec

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D

t = 4±142 sec

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Solution

The correct option is A

t = 2 sec


ωangularaccelerationParticleAπ radsecπ2radsec2ParticleB2π radsec0Particle B with respect to particle A2ππ;πradsec0π2;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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