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 Components
The force \( F \) can be resolved into two components: the X component (horizontal) and the Y component (vertical). The angle given is \( 30^\circ \) with respect to the x-axis.

### Step 2: Use Trigonometric Functions
To find the components, we use the following trigonometric relationships:
- The X component is given by \( F_x = F \cos(\theta) \)
- The Y component is given by \( F_y = F \sin(\theta) \)

Where \( \theta \) is the angle with respect to the x-axis.

### Step 3: Substitute the Angle
In this case, \( \theta = 30^\circ \):
- \( F_x = F \cos(30^\circ) \)
- \( F_y = F \sin(30^\circ) \)

### Step 4: Calculate the Cosine and Sine Values
Using known values:
- \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \)
- \( \sin(30^\circ) = \frac{1}{2} \)

### Step 5: Substitute the Values
Now substituting these values into the equations:
- \( F_x = F \cdot \frac{\sqrt{3}}{2} \)
- \( F_y = F \cdot \frac{1}{2} \)

### Step 6: Write the Components
Thus, the X and Y components of the force \( F \) can be expressed as:
- \( F_x = \frac{\sqrt{3}}{2} F \)
- \( F_y = \frac{1}{2} F \)

### Final Answer
The X and Y components of the force \( F \) acting at \( 30^\circ \) to the x-axis are:
- \( F_x = \frac{\sqrt{3}}{2} F \)
- \( F_y = \frac{1}{2} F \)