The resultant of two forces is 20/3 N. If one of the force is 20 N and makes an angle of 30° with the resultant, the other force has a mangitude:

Options

A. 10 N
B. `20sqrt3 N`
C. `10sqrt3N`
D. `20 N`

Answer

d

Explanation

Let theta the angle between two forces `vecF_(1)`, and `vecF_(2)`Now sum of components of individual forces must be equal to component of resultant force along X-axis
:.` Fcos 30^(@) = F_(1) +F_(2) cos theta`

`implies20sqrt3xx(sqrt3)/(2)=20+F_(2)costheta=10`
`impliesF_(2)costheta=10...(i)`
Along y-direction`Fsin30^(@)=F_(1)cos90^(@)+F_(2)sintheta`
`20sqrt3xx(1)/(2)=0+F_(2)sintheta`
`impliesF_(2)sintheta=10sqrt3...(ii)`
Squaring and adding (i) and (ii)
`F_(2)^(2)(cos^(2)theta+sin^(2)theta)=100+300`
`F_(2)=20N`
Hence correct choice is (d).