The X and Y components of a force F acting at `30^(@)` to x-axis are respectively :

Options

A. `(F)/(sqrt(2)), F`
B. `(F)/(2), (sqrt(3))/(2) F`
C. `(sqrt(3))/(2)F, (1)/(2)F`
D. `F,(F)/(sqrt(2))`

Answer

To find the X and Y components of a force \( F \) acting at an angle of \( 30^\circ \) to the x-axis, we can follow these steps:

### Step 1: Understand the Force Components
The force \( F \) can be resolved into two components:
- The X component, which lies along the x-axis.
- The Y component, which lies along the y-axis.

### Step 2: Use Trigonometric Functions
The components can be calculated using trigonometric functions:
- The X component is given by:
\[ F_x = F \cos(30^\circ) \]
- The Y component is given by:
\[ F_y = F \sin(30^\circ) \]

### Step 3: Calculate the X Component
Now, we need to calculate \( F_x \):
- We know that \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \).
- Therefore, substituting this value, we get:
\[ F_x = F \cos(30^\circ) = F \cdot \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{2} F \]

### Step 4: Calculate the Y Component
Next, we calculate \( F_y \):
- We know that \( \sin(30^\circ) = \frac{1}{2} \).
- Therefore, substituting this value, we get:
\[ F_y = F \sin(30^\circ) = F \cdot \frac{1}{2} = \frac{1}{2} F \]

### Step 5: Final Results
Thus, the components of the force \( F \) acting at \( 30^\circ \) to the x-axis are:
- X component: \( F_x = \frac{\sqrt{3}}{2} F \)
- Y component: \( F_y = \frac{1}{2} F \)

### Conclusion
The X and Y components of the force \( F \) are respectively \( \frac{\sqrt{3}}{2} F \) and \( \frac{1}{2} F \).

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