A force of `50N` is inclined to the vertical at an angle of `30^(@)` Find the acceleration it produes in a body of mass `2kg` which moves in the horizontal direction .

Explanation

To solve the problem, we need to find the horizontal component of the force and then use Newton's second law to find the acceleration of the body. Here’s a step-by-step solution:

### Step 1: Identify the Given Values
- Force (F) = 50 N
- Angle with the vertical (θ) = 30°
- Mass (m) = 2 kg

### Step 2: Determine the Horizontal Component of the Force
Since the force is inclined to the vertical, we need to find the horizontal component of the force. The horizontal component (F_horizontal) can be calculated using the sine function:
\[ F_{\text{horizontal}} = F \cdot \sin(θ) \]
Substituting the values:
\[ F_{\text{horizontal}} = 50 \cdot \sin(30°) \]

### Step 3: Calculate the Value of sin(30°)
We know that:
\[ \sin(30°) = \frac{1}{2} \]
So, substituting this value:
\[ F_{\text{horizontal}} = 50 \cdot \frac{1}{2} = 25 \text{ N} \]

### Step 4: Apply Newton's Second Law
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a). We can rearrange this to find acceleration (a):
\[ a = \frac{F_{\text{horizontal}}}{m} \]
Substituting the values we have:
\[ a = \frac{25 \text{ N}}{2 \text{ kg}} = 12.5 \text{ m/s}^2 \]

### Final Answer
The acceleration produced in the body is:
\[ \boxed{12.5 \text{ m/s}^2} \]

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