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Three particles start from origin at the...

Three particles start from origin at the same time: one with velocity `v_(1)` along positive x - axis, the second along the positive y-axis with a velocity `v_(2)` and the third along the line `y=x` with such a speed that all the three always stay in a straight line, then the velocity of the third particle is `(sqrt(k) V_(1)V_(2))/((V_(1)+V_(2)))`.

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Knowledge Check

  • Three particles A, B & C start from the origin at the same time, A with a velocity 'a' along x-axis, B with a velocity 'b' along y-axis and C with velocity 'c' in XY plane along the line x = y. The magnitude of 'c' so that the three always remain collinear is:

    A
    `(a + b)/2`
    B
    `sqrt(ab)`
    C
    `(ab)/(a+ b)`
    D
    `(sqrt(2)ab)/(a +b)`

  • Three particles A, B & C start from the origin at the same time, A with a velocity 'a' along X-axis, B with a velocity 'b' along y-axis and C with velocity 'c' in XY plane along the line x = y. The magnitude of 'c' so that the three always remain collinear is:

    A
    `(a+b)/(2)`
    B
    `sqrt(ab)`
    C
    `(ab)/(a+b)`
    D
    `(sqrt2 ab)/(a+b)`

  • Three particles A, B & C start from the origin at the same time, A with a velocity 'a' along X-axis, B with a velocity 'b' along y-axis and C with velocity 'c' in XY plane along the line x = y. The magnitude of 'c' so that the three always remain collinear is:

    A
    `(a+b)/(2)`
    B
    `sqrt(ab)`
    C
    `(ab)/(a+b)`
    D
    `(sqrt2 ab)/(a+b)`

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