question_answer

The X and Y components of a force F acting at \[{{30}^{o}}\] to x-axis are respectively

A)  \[\frac{F}{\sqrt{2}},F\]

B)  \[\frac{F}{2},\frac{\sqrt{3}}{2}F\]

C)  \[\frac{\sqrt{3}}{2}F,\frac{1}{2}F\]

D)  \[F,\frac{F}{\sqrt{2}}\]

Correct Answer: C

Solution :

:  The X component of force F is \[{{F}_{x}}=F\cos {{30}^{o}}=F\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}F\] The Y component of force F is \[{{F}_{y}}=F\sin {{30}^{o}}=F\times \frac{1}{2}=\frac{F}{2}\]