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The resultant of two forces has magnitud...

The resultant of two forces has magnitude 20 N. One of the forces is of magnitude `20sqrt(3)` N and makes an angle of `90^(@)` with the resultant. Then, the other force must be of magnitude

A

40N

B

20N

C

`20sqrt(3)N`

D

`10sqrt(3)N`

Text Solution

Verified by Experts

The correct Answer is:
A
`tan beta=(B tan)/(A+B cos theta)`………1 `:.oo=(B tan theta)/(A+Bcos theta):.A+Bcos theta=0`
`implies20sqrt(3)=-Bcos theta` ……..
`R^(2)=A^(2)+B^(2)+2ABcos theta` and substituting 2 in 1 we get
`400-1200+2400=B^(2)impliesB=40N`
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Knowledge Check

  • The resưltant of two forces has magnitude 20 N. One of the forces is of magnitude sqrt(20) N and makes an angle of 90^(@) with the resultant. Then, the other force must be of magnitude

    A
    40 N
    B
    20 N
    C
    `20 sqrt(3)N`
    D
    `10 sqrt(3)N`

  • The sum of magnitudes of two forces acting at a point is 16 N and their resultant 8sqrt(3)N is at 90^(@) with the force of smaller magnitude. The two forces (in N) are

    A
    a)11, 5
    B
    b)9, 7
    C
    c)6, 10
    D
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  • The sum of the magnitudes of two forces acting at a point is 18 N and the magnitude of their resultant is 12 N. If the resultant is at 90^(@) with the smaller force, the magnitude of the forces in N are

    A
    6, 12
    B
    11, 7
    C
    5, 13
    D
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