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Question

Two particles A and B are moving in opposite direction on a circle. Initially particle A and B are diagonally opposite to each other. Particle A move with angular velocity π rad/s, angular acceleration π2 rad/s2 and particle B moves with constant angular velocity 2π rad/s. Find the time after which both the particles A and B will collide.

A
3.2 sec
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B
2 sec
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C
3.6 sec
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D
4.5 sec
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Solution

The correct option is B 2 sec

Let us consider the motion of B w.r.t A

ωrel=2ππ=π rad/s

Similarly, angular acceleration of B w.r.t A will be

αrel=0π2=π2 rad/s2

When the two bodies collide, the relative angular displacement will be,

Δθ=180=π

Applying kinetic equation in relative terms:

(Δθ)rel=ωrelt+12αrel t2

π=πt+12(π2)t2

π=πt14πt2

t24t+4=0(t2)2=0

t=2 sec

Hence, option (b) is right.
Why this question?
Tip: When two bodies are in motion simultaneously, then it's always advisable to solve from relative frame. Use of relative motion technique will make one body come to rest and problem will become simple.

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