Question

The components of force $F$ parallel and perpendicular to the incline are

• A. $(\frac{\sqrt{3}}{2}F,\frac{F}{2})$
• B. $(\frac{\sqrt{3}}{2}F,0)$
• C. $\frac{F}{2},0$
• D. $(\frac{F}{2},\frac{\sqrt{3}}{2}F)$

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 ${30}^{\circ }$
$F_{\text{parallel}}=F\cos \theta =F\cos {30}^{\circ }$
$F_{\text{parallel}}=\frac{\sqrt{3}}{2}F$
$F_{\text{perpendicular}}=F\sin \theta =F\sin {30}^{\circ }$
$F_{\text{perpendicular}}=\frac{F}{2}$