Three forces `vecF_(1),vecF_(2)` and `vecF_(3)` are simultaneously acting on a particle of mass `'m'` and keep it in equlibrium. If `vecF_(1)` force is reversed in direction only, the acceleration of the particle will be.

Options

A. `barF_(1)//m`
B. `2barF_(1)//m`
C. `-barF_(1)//m`
D. `-2barF_(1)//m`

Explanation

To solve the problem step by step, we will analyze the forces acting on the particle and how reversing the direction of one of the forces affects the net force and consequently the acceleration of the particle.

### Step 1: Understand the Initial Condition
Initially, the particle is in equilibrium under the action of three forces: \( \vec{F}_1 \), \( \vec{F}_2 \), and \( \vec{F}_3 \). In equilibrium, the net force acting on the particle is zero.

**Equation:**
\[ \vec{F}_1 + \vec{F}_2 + \vec{F}_3 = 0 \]

### Step 2: Rearranging the Forces
From the equilibrium condition, we can express one of the forces in terms of the others. Rearranging the equation gives us:

\[ \vec{F}_1 = -(\vec{F}_2 + \vec{F}_3) \]

### Step 3: Reverse the Direction of \( \vec{F}_1 \)
Now, we reverse the direction of \( \vec{F}_1 \). The new force can be represented as \( -\vec{F}_1 \). Therefore, the new net force acting on the particle becomes:

\[ -\vec{F}_1 + \vec{F}_2 + \vec{F}_3 \]

### Step 4: Substitute for \( \vec{F}_1 \)
Substituting \( \vec{F}_1 \) from our earlier equation into the new net force equation gives:

\[ -\left(-(\vec{F}_2 + \vec{F}_3)\right) + \vec{F}_2 + \vec{F}_3 \]

This simplifies to:

\[ \vec{F}_2 + \vec{F}_3 + \vec{F}_2 + \vec{F}_3 = 2\vec{F}_2 + 2\vec{F}_3 \]

### Step 5: Calculate the Net Force
The net force acting on the particle after reversing \( \vec{F}_1 \) is:

\[ \vec{F}_{net} = 2(\vec{F}_2 + \vec{F}_3) \]

### Step 6: Apply Newton's Second Law
According to Newton's second law, the acceleration \( \vec{a} \) of the particle is given by:

\[ \vec{a} = \frac{\vec{F}_{net}}{m} \]

Substituting the expression for net force:

\[ \vec{a} = \frac{2(\vec{F}_2 + \vec{F}_3)}{m} \]

### Final Result
Thus, the acceleration of the particle when the direction of \( \vec{F}_1 \) is reversed is:

\[ \vec{a} = \frac{2(\vec{F}_2 + \vec{F}_3)}{m} \]