In x-y plane, a force `10 N` acts at an angle `30^(@)` to the positive direction of x-axis. The force can be written as

Options

A. `5hat(i)+5hat(j)`
B. `5sqrt(3)hat(i)+5hat(j)N`
C. `5hat(i)+5sqrt(3)hat(j)N`
D. None of these

Answer

B

Explanation

Let `vec(F)= xhat(I)+yhat(j)`
Now `F= sqrt(x^(2)+y^(2))= 10`
`implies x^(2)+y^(2)=100`….(i)
`tan 30^(@)= y/ximplies y=1/(sqrt(3))x`….(ii)
Solving, (i) and (ii)
`y= 5 N, x= 5sqrt(3) N`