When forces `F_1`, `F_2`, `F_3`, are acting on a particle of mass m such that `F_2` and `F_3` are mutually perpendicular, then the particle remains stationary. If the force `F_1` is now removed then the acceleration of the particle is

Options

A. (a) `F//m`
B. (b) `F_2F_3//mF_1`
C. (c) `(F_2-F_3)//m`
D. (d) `F_2//m`

Explanation

To solve the problem, we need to analyze the forces acting on a particle of mass \( m \) and determine the acceleration when one of the forces is removed.

### Step-by-Step Solution:

1. **Understanding the Forces**:
- We have three forces acting on a particle: \( F_1 \), \( F_2 \), and \( F_3 \).
- It is given that \( F_2 \) and \( F_3 \) are mutually perpendicular to each other.

2. **Condition for Stationarity**:
- The particle remains stationary when the net force acting on it is zero. This means that the vector sum of the forces must equal zero:
\[ F_1 + F_2 + F_3 = 0 \]

3. **Removing \( F_1 \)**:
- If we remove \( F_1 \), the remaining forces are \( F_2 \) and \( F_3 \).
- Since \( F_2 \) and \( F_3 \) are perpendicular, we can find the resultant force \( R \) using the Pythagorean theorem:
\[ R = \sqrt{F_2^2 + F_3^2} \]

4. **Applying Newton's Second Law**:
- According to Newton's second law, the acceleration \( a \) of the particle can be expressed as:
\[ F = m \cdot a \]
- The net force acting on the particle after removing \( F_1 \) is \( R \):
\[ R = m \cdot a \]
- Therefore, we can express the acceleration as:
\[ a = \frac{R}{m} \]

5. **Substituting for \( R \)**:
- Now substituting the expression for \( R \):
\[ a = \frac{\sqrt{F_2^2 + F_3^2}}{m} \]

6. **Relating \( F_1 \) to \( F_2 \) and \( F_3 \)**:
- From the initial condition where the forces were balanced, we know:
\[ F_1 = \sqrt{F_2^2 + F_3^2} \]
- Thus, we can substitute \( F_1 \) into the equation for acceleration:
\[ a = \frac{F_1}{m} \]

### Final Answer:
The acceleration of the particle after removing \( F_1 \) is:
\[ a = \frac{F_1}{m} \]