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Three particles A,B, and C are situated ...

Three particles `A,B, and C` are situated at the vertices of an equilateral triangle of side `r` at `t = 0`. The particle `A` heads towards `B`, `B` towards `C`, `C` towards `A` with constant speeds `v`. Find the time of their meeting.

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To find the time of meeting of the three particles A, B, and C, we can follow these steps: ### Step 1: Understand the setup We have three particles A, B, and C located at the vertices of an equilateral triangle with side length \( r \). Each particle moves towards the next particle: A moves towards B, B moves towards C, and C moves towards A, all with a constant speed \( v \). ### Step 2: Analyze the motion As each particle moves towards the next, they will spiral inward towards a common point. We need to determine how long it will take for them to meet at that point. ...
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Knowledge Check

  • Three particles of equal mass 'm' are situated at the vertices of an equilateral triangle of side L . The work done in increasing the side of the triangle to 2L is

    A
    `(2G^(2)m)/(2L)`
    B
    `(Gm^(2))/(2L)`
    C
    `(3Gm^(2))/2L`
    D
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  • Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side d at time t=0. Each of the particles moves with constant speed v. A always has its velocity along AB, B along BC and C along CA. At what time will the particles meet each other?

    A
    `t=d/v`
    B
    `t=(3d)/(2v)`
    C
    `t=(2d)/(3v)`
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    `t=0`

  • Three particles A, B and C situated at vertices of an equilateral triangle, all moving with same constant speed such that A always move towards B, B always towards C and C always towards A . Initial seperation between each of the particle is a. O is the centroid of the triangle. Distance covered by particle A when it completes one revolution around O is

    A
    `2a(1-e^(-2sqrt(3pi)))`
    B
    `(2a)/(3)(1-e^(-2sqrt(3pi)))`
    C
    `a(1+e^(-2sqrt(3pi)))`
    D
    `(2a)/(3)(1-e^(-sqrt(3pi)))`

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