Question

Find the components of force F parallel and perpendicular to the incline surface.

• A. $\frac{\sqrt{3}}{2}F,\frac{F}{2}$
• B. $\frac{F}{2},\frac{\sqrt{3}}{2}F$
• C. $F,\frac{\sqrt{3}}{2}F$
• D. $F,\frac{F}{2}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{2}F,\frac{F}{2}$

The angle made by $F$ with the surface of the incline is ${30}^{\circ }$
$F_{\text{parallel}}=\text{F cos}\theta =\text{F cos}{30}^{\circ }$
$F_{\text{parallel}}=\frac{\sqrt{3}}{2}F$
$F_{\text{perpendicular}}=F\sin \theta =F\sin {30}^{\circ }$
$F_{\text{perpendicular}}=\frac{F}{2}$