Consider an object kept at the centre, in the XY-plane, on which five coplanar forces act as shown in the figure. The resultant forces on the object is

Options

A. 6.5 N, `330^(@)`
B. 6.5 N, `300^(@)`
C. 6.5 N, `30^(@)`
D. 5.7 N, `331^lt(@)`

Answer

A

Explanation

The total force in X- direction,
`sumF_(x)= 15cos 60^(@)+19-11cos 30^(@)- 16 cos 45^(@)`
`sum F_(x) = 5.66 N `
The total force in Y- direction,
`sumF_(y)=-22+ 15 sin 60^(@) + 16 cos 45^(@)-11sin 30^(@)`
`sum F_(y)=-3.196N`
Then, resultant force
`rArr R=sqrt(F_(x)^(2)+F_(y)^(2))=sqrt((5.66)^(2)+(3.196)^(2))`
R = 6.5 N
Direction of resultant,
`rArr tan theta= F_(y)//F_(x)= (-3.196)/(5.66)`
`rArr theta = 330^(@)`