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

Options

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

Answer

A

Explanation

`"tan" beta=(B tan theta)/(A+B cos theta) .....(1) :. oo=(B tan theta)/(A+B cos theta) :. A+B cos theta=0`
`rArr 20 sqrt(3)=-B cos theta .....(2)`
`R^(2)=A^(2)+B^(2)+2AB cos theta` and substituting (2) in (1) we get
`400-1200+2400=B^(2) rArr =40 N`