Eight particles are situated at the vertices of a regular octagon having side 10cm. they all start moving simultaneosuly with constant speed of 1 cm/s deading towards each other all the time. Choose the correct options

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Acceleration of each particle is directed perpendicular to tis velocity.

They will converge at the centroid

They will converge after time $\frac{10 \sqrt{2}}{\sqrt{2} - 1} s$

The distance travelled each particle is $\frac{\sqrt{2}}{\sqrt{2} - 1} m$

answer is A, B, D.

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Detailed Solution

They will always lie on a regular octagon but side of octagon will keep decreasing. Velocity of approach of two adjacent particle is
$V - V \cos (\frac{2 π}{8}) V_{a p p} = V (1 - \frac{1}{\sqrt{2}})$
Finally all will meet at the centroid,
$t = \frac{a}{V_{a p p}} = \frac{10}{1 - \frac{1}{\sqrt{2}}} = \frac{10 \sqrt{2}}{\sqrt{2} - 1} s$