Five forces `2 N, sqrt(3)N, 5 N, sqrt(3) and 2 N` respectively act at a particel `P` as shown in figure.

The resultant force on the particle `P` is

Options

A. `10 N` making angle `60^(@)` with X-axis
B. `10 N` making angle `60^(@)` with Y-axis
C. `20 N` along Y-axis
D. None of these

Answer

A

Explanation

`SigmaF_(x)=` sum of x-ax is-compon ents of force
`= 2+sqrt(3) cos 30^(@)+5 cos 60^(@)-2 sin 30^(@)`
`= 2+3/2+5/2-1= 5N`

`SigmaF_(y)=` sum of y-ax is-compon ents of force
`=sqrt(3)sin30^(@)+5 sin 60^(@)+sqrt(3)+2 cos 30^(@)`
`=(sqrt(3))/(2)+(5sqrt(3))/(2)+sqrt(3)+sqrt(3)= 5sqrt(3)N`
`:. sqrt((SigmaF_(x))^(2)+(SigmaF_(y))^(2))=sqrt(5^(2)+(5sqrt(3))^(2))`
`=sqrt(100)=10N`
`:. tan theta= (Sigma_(y))/(SigmaF_x)=(5sqrt(3))/(5)= sqrt(3)implies theta= 60^(@)`