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The X and Y components of force F acting at $30^{0}$ to x-axis respectively

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$\sqrt{\frac{3}{2}} F, \frac{1}{2} F$

$\frac{F}{\sqrt{2}}, \sqrt{\frac{3}{2}} F$

$F, \frac{F}{\sqrt{2}}$

$\frac{F}{\sqrt{2}}, F$

answer is C.

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Detailed Solution

$\vec{F} = F x \hat{i} + F y \hat{j} = (F \cos θ) \hat{i} + (F \cos θ) \hat{j}$
$F = F (\cos 30) \hat{i} + F \sin 30 \hat{j}$
$\vec{F} = \sqrt{\frac{3}{2}} F \hat{i} + \frac{1}{2} F \hat{j}$

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