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Question

Three points are located at the vertices of an equilateral triangle having each side as α. All the points move simultaneously with speed u such that first point continually heads for second, the second for the third and the third for the first. Time taken by the points to meet at the centre is

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A
α3u
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B
2α3u
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C
α2u3
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D
3α2u
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Solution

The correct option is B 2α3u
All three points were initially at same distance from the centroid of the original equilateral triangle of the side α
At any time t, the three points still form an equilateral triangle, moving with the same speed
The distance between two points is decreasing at the same rate as at the beginning.
The total amount of time taken for the points to meet is α divided by the inital rate at which two points approach each other
Taking any two points it shows first point moves in the direction of the second at speed μ
While the second moves in direction of first (taking component along one of the triangle edges) at μcos60°=μ2
The rate at which the distance between two points is decreasing is 3μ2
The time taken by the three points to meet is thus 2α 3μ

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