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 prependicular, then the particle remains stationary. If the force `F_(1)` is now rejmoved then the acceleration of the particle is

Options

A. `F_(1)//m`
B. `F_(2)F_(3)//mF_(1)`
C. `F_(2)-F_(3)//m`
D. `F_(2)//m`

Explanation

To solve the problem step by step, we can follow the reasoning laid out in the video transcript:

### Step 1: Understand the Forces Acting on the Particle
We have three forces acting on a particle of mass \( m \): \( F_1 \), \( F_2 \), and \( F_3 \). It is given that \( F_2 \) and \( F_3 \) are mutually perpendicular.

### Step 2: Condition for the Particle to be Stationary
For the particle to remain stationary, the net force acting on it must be zero. This can be expressed mathematically as:
\[ F_1 + F_2 + F_3 = 0 \]
From this equation, we can rearrange it to find:
\[ F_1 = - (F_2 + F_3) \]

### Step 3: Magnitude of Forces
Since \( F_2 \) and \( F_3 \) are perpendicular, we can find the magnitude of their resultant using the Pythagorean theorem:
\[ |F_2 + F_3| = \sqrt{|F_2|^2 + |F_3|^2} \]
However, since the particle is stationary, we also know:
\[ |F_1| = |F_2 + F_3| \]

### Step 4: Removing Force \( F_1 \)
Now, if we remove \( F_1 \), the net force acting on the particle will be:
\[ F_{\text{net}} = F_2 + F_3 \]
This net force is now equal to the resultant of \( F_2 \) and \( F_3 \).

### Step 5: Calculate the Acceleration
Using Newton's second law, the acceleration \( a \) of the particle can be calculated as:
\[ a = \frac{F_{\text{net}}}{m} \]
Substituting \( F_{\text{net}} = F_2 + F_3 \):
\[ a = \frac{F_2 + F_3}{m} \]
Since we established earlier that \( |F_2 + F_3| = |F_1| \), we can write:
\[ a = \frac{|F_1|}{m} \]

### Conclusion
Thus, the acceleration of the particle after removing \( F_1 \) is:
\[ \boxed{\frac{|F_1|}{m}} \]