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(D) Let the particles be at vertices $A, B,$ and $C$ of an equilateral triangle with side $L$. Each particle moves towards the next one. The velocity

Vedclass · Accepted Answer

$2L/3$

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(D) Let the particles be at vertices $A, B,$ and $C$ of an equilateral triangle with side $L$. Each particle moves towards the next one. The velocity of particle $A$ is directed towards $B$,and the velocity of particle $B$ is directed towards $C$. The component of the velocity of $A$ along the line $AB$ is $v$,and the component of the velocity of $B$ along $AB$ is $-v \cos(60^{\circ}) = -v/2$. The relative velocity of approach between $A$ and $B$ is $v_{rel} = v - (-v/2) = 3v/2$. The time taken for the particles to meet at the centroid is $t = L / v_{rel} = L / (3v/2) = 2L / (3v)$. Since each particle moves with a constant speed $v$,the distance covered by each particle is $s = v 	imes t = v 	imes (2L / 3v) = 2L/3$.

Three particles,located initially on the vertices of an equilateral triangle of side $L$,start moving with a constant speed $v$ towards each other in a cyclic manner,forming spiral loci that converge at the centroid of the triangle. The length of one such spiral locus will be

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