Question

# Two particles A and B are moving in same direction on a circular path. Initially particle A and B are diametrically opposite to each other. Particle A moves with angular velocity π rad/s and angular acceleration π2rad/s2 and particle B moves with constant angular velocity 2π rad/s. Find the time after which both particles A and B collides.

A
1 s
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B
2 s
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C
3 s
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D
4 s
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Solution

## The correct option is B 2 sSuppose the angle between OA and OB=θ then the rate of change of θ is wθ wθ=wB−wA=2π−π=π rad/sec αθ=αB−αA=−π2 rad/sec2 It the angular displacement is Δθ then Δθ=wθt+12αθt2 A and B collides after angular displacement Δθ=π, ⇒π=πt−12×π2×t2 ⇒t2−4t+4=0 ⇒t=2 s

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