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Standard VII

Mathematics

Major Arc, Minor Arc and Semicircular Arc

A circle of r...

Question

A circle of radius unity is centred at origin. Two particles start moving at the same time from the point $(1, 0)$ and move around the circle in opposite direction. One of the particle moves counterclockwise with constant speed v and the other moves clockwise with constant speed $3 v$ . After leaving $(1, 0)$ , the two particles meet first at a point $P$ , and continue until they meet next at point $Q$ . The coordinates of the point $Q$ are

(1, 0)

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(0, 1)

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(0, - 1)

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(- 1, 0)

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Solution

The correct option is D $(- 1, 0)$
The particle which moves clockwise is moving three times as fast as the particle moving anticlockwise. This means the clockwise particle travels (3/4)th of the way around the circle, the anticlockwise particle will travel (1/4)th of the way around the circle and so the second particle will meet at P(0, 1).
Using the same logic they will meet at Q(-1, 0) when they meet the second time.

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