A body of mass 2kg is acted by two forces each of magnitude 1 newton, making an angle of `60^(@)` with each other. The net acceleration of the body `("in" m//s^(2)`) is

Options

A. 0.5
B. 1
C. `sqrt(3)//2`
D. `sqrt(2)//3`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the Forces
We have two forces \( F_1 \) and \( F_2 \), both with a magnitude of \( 1 \, \text{N} \), acting at an angle of \( 60^\circ \) with respect to each other.

### Step 2: Use the Formula for Resultant of Two Forces
The resultant force \( F_{\text{net}} \) can be calculated using the formula for the resultant of two vectors:
\[ F_{\text{net}} = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos \theta} \]
Where:
- \( F_1 = 1 \, \text{N} \)
- \( F_2 = 1 \, \text{N} \)
- \( \theta = 60^\circ \)

### Step 3: Substitute the Values
Substituting the values into the formula:
\[ F_{\text{net}} = \sqrt{(1)^2 + (1)^2 + 2 \cdot 1 \cdot 1 \cdot \cos(60^\circ)} \]
Since \( \cos(60^\circ) = \frac{1}{2} \), we can simplify:
\[ F_{\text{net}} = \sqrt{1 + 1 + 2 \cdot 1 \cdot 1 \cdot \frac{1}{2}} \]
\[ F_{\text{net}} = \sqrt{1 + 1 + 1} = \sqrt{3} \]

### Step 4: Apply Newton's Second Law of Motion
According to Newton's second law:
\[ F_{\text{net}} = m \cdot a_{\text{net}} \]
Where:
- \( m = 2 \, \text{kg} \)
- \( a_{\text{net}} \) is the net acceleration we want to find.

### Step 5: Rearrange to Find Net Acceleration
Substituting \( F_{\text{net}} \) into the equation:
\[ \sqrt{3} = 2 \cdot a_{\text{net}} \]
Now, solve for \( a_{\text{net}} \):
\[ a_{\text{net}} = \frac{\sqrt{3}}{2} \]

### Final Answer
Thus, the net acceleration of the body is:
\[ a_{\text{net}} = \frac{\sqrt{3}}{2} \, \text{m/s}^2 \]

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