A ball is dropped from an elevator moving upward with acceleration 'a' by a boy standing in it. The acceleration of ball with respect to [Take upward direction positive]

Options

A. Boy is - g
B. Boy is `-(g+a)`
C. Ground is `-g`
D. Both (2) & (3)

Answer

To solve the problem of a ball dropped from an elevator moving upward with acceleration 'a', we need to analyze the situation from two different frames of reference: the boy in the elevator (non-inertial frame) and the ground (inertial frame).

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Ball**:
- When the ball is dropped, it experiences two forces: the gravitational force acting downward (weight of the ball) and the pseudo force acting upward due to the acceleration of the elevator.
- The gravitational force is given by \( F_g = mg \) (where \( m \) is the mass of the ball and \( g \) is the acceleration due to gravity).
- The pseudo force, due to the upward acceleration of the elevator, is \( F_p = ma \) acting downward.

2. **Determine the Net Acceleration of the Ball with Respect to the Boy**:
- In the non-inertial frame of the boy, we must consider the pseudo force. The net acceleration \( a_{net} \) of the ball with respect to the boy is given by:
\[ a_{net} = g - a \]
- Here, \( g \) is positive (downward) and \( a \) is also considered positive (upward), thus the net acceleration is \( g - a \) downward.

3. **Determine the Acceleration of the Ball with Respect to the Ground**:
- In the inertial frame of the ground, the only force acting on the ball is the gravitational force. Therefore, the acceleration of the ball with respect to the ground is simply:
\[ a_{ground} = g \]
- This is because the ball is in free fall once it is released.

4. **Conclusion**:
- The acceleration of the ball with respect to the boy is \( g - a \) downward.
- The acceleration of the ball with respect to the ground is \( g \) downward.

### Final Answer:
- The acceleration of the ball with respect to the boy is \( g - a \) (downward).
- The acceleration of the ball with respect to the ground is \( g \) (downward).