A body is dropped by a satellite in its geo-stationary orbit :

Options

A. it will burn on entering in to the atmosphere
B. it will remain in the same place with respect to the earth
C. it will reach the earth is 24 hours
D. it will perform uncertain motion

Answer

To solve the problem of a body dropped by a satellite in a geostationary orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Geostationary Orbit**:
- A geostationary satellite orbits the Earth at a height where its orbital period matches the Earth's rotation period (24 hours). This means that the satellite appears stationary to an observer on the ground.

2. **Initial Conditions of the Dropped Body**:
- When a body is dropped from the satellite, it initially has the same velocity as the satellite. Therefore, its initial velocity (u) in the horizontal direction is equal to the orbital velocity of the satellite.

3. **Motion of the Dropped Body**:
- Upon being dropped, the body does not fall straight down towards the Earth. Instead, it continues to move forward with the same horizontal velocity as the satellite. This is due to Newton's first law of motion, which states that an object in motion will stay in motion unless acted upon by an external force.

4. **Effect of Gravity**:
- While the body is influenced by Earth's gravity, it will not simply fall to the Earth. Instead, it will begin to follow a trajectory that is a combination of its initial horizontal motion and the downward pull of gravity.

5. **Resulting Motion**:
- As the body continues to move forward while being pulled down by gravity, it will enter into a new orbit around the Earth. However, since it started with the same velocity as the satellite, it will continue to revolve around the Earth in such a way that its orbital period matches that of the Earth.

6. **Conclusion**:
- Therefore, the body will not fall directly to the Earth but will instead remain in a geostationary orbit, appearing stationary relative to the surface of the Earth. The answer to the question is that the body will remain in the same place with respect to the Earth.

### Final Answer:
The body will remain in the same place with respect to the Earth.