In non inertial frames,Newton's second law of motion is written as
where `a=` acceleration of the body, relative to the non-inertial fram and `F_(p)` is the pseudo force.

Options

A. `vecF=mveca`
B. `vecF=mveca+vecF_(p)`
C. `vecF=mveca-vecF_(p)`
D. `vecF=2ma`

Explanation

To express Newton's second law of motion in a non-inertial frame, we need to consider the effects of pseudo forces that arise due to the acceleration of the frame itself. Here's a step-by-step breakdown of how this is done:

### Step-by-Step Solution:

1. **Understanding Non-Inertial Frames**:
- A non-inertial frame is one that is accelerating. For example, if you are in a lift (elevator) that is accelerating upwards, you are in a non-inertial frame.

2. **Identifying the Forces**:
- In a non-inertial frame, the forces acting on an object include not only the real forces (like gravity) but also a pseudo force that appears due to the acceleration of the frame itself.

3. **Defining the Pseudo Force**:
- The pseudo force \( F_p \) acts in the opposite direction to the acceleration of the non-inertial frame. If the frame is accelerating upwards with an acceleration \( A \), then the pseudo force acting on a mass \( m \) is given by:
\[ F_p = -mA \]

4. **Applying Newton's Second Law**:
- In an inertial frame, Newton's second law states:
\[ F = ma \]
- In a non-inertial frame, we modify this to account for the pseudo force:
\[ F_{\text{net}} = ma + F_p \]
- Substituting the expression for the pseudo force:
\[ F_{\text{net}} = ma - mA \]

5. **Rearranging the Equation**:
- We can rearrange this equation to express the net force in terms of the acceleration of the object relative to the non-inertial frame:
\[ F_{\text{net}} = m(a - A) \]
- This shows that the effective acceleration of the object in the non-inertial frame is \( a - A \).

6. **Final Expression**:
- Thus, in a non-inertial frame, Newton's second law can be expressed as:
\[ F_{\text{net}} = m a + m A \]
- Where \( a \) is the acceleration of the body relative to the non-inertial frame and \( A \) is the acceleration of the frame itself.

### Summary:
In non-inertial frames, Newton's second law is modified to include a pseudo force that accounts for the acceleration of the frame. The final expression is:
\[ F_{\text{net}} = ma + mA \]