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Calculate the angle between20 N force an...

Calculate the angle between`20 N` force and a `30 N` force so thea ther resultant is `40 N`.

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Here, ` A =20 N, B=30 N, `
`R=40 N , theta =?`
As, `R= sqrt(A^(2) + B^(2) + 2 AB cos theta)`
:. Cos theta =(R^(2) -A^(2) -B^(2))/(2 A B)`
`=((40)^(2) -(20)^(2) -(30^(2))/(2xx 20 xx 30) =(300)/(2 xx 20 xx 30)`
`= 0. 25 =cos 75 ^(@) 31'` gtbrgt :. theta =75 ^(@) 31'` .
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Knowledge Check

  • Six forcees, 9.81 N each, acting at a point are coplaner. If the angles between neighbouring forces are equal, then the resultant is

    A
    0 N
    B
    9. 81 N
    C
    `2 xx 9.81 N`
    D
    `3 xx 9.81 N`

  • The square of the resultant of two forces 4 N and 3N exceeds the square of the resultant of the two forces by 12 when they are mutually perpendicular.The angle between the vectors is.

    A
    `30^(@)`
    B
    `60^(@)`
    C
    `90^(@)`
    D
    `120^(@)`

  • Five equal forces each of 20N are acting at a point in the same plane. If the angles between them are same, the resultant of these forces is

    A
    0
    B
    `40N`
    C
    `20N`
    D
    `20sqrt2N`
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