A satellite of the earth is revolving in a circular orbit with a uniform speed `v`. If gravitational force suddenly disappears, the satellite will

Options

A. continue to move speed `v` along the original orbit
B. move with the velocity `v` tangentially to the original orbit
C. fall downward with increasing velocity
D. ultimately come to rest somewhere on the original orbit

Explanation

To solve the problem, we need to analyze the motion of the satellite before and after the gravitational force disappears.

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- The satellite is in a circular orbit around the Earth, moving with a uniform speed `v`. This means that there is a centripetal force acting on it, which is provided by the gravitational force of the Earth.

2. **Centripetal Force Requirement**:
- For an object to move in a circular path, a centripetal force is required. This force is directed towards the center of the circular path (in this case, towards the Earth). The gravitational force provides this necessary centripetal force.

3. **Effect of Gravitational Force Disappearance**:
- If the gravitational force suddenly disappears, the centripetal force that keeps the satellite in a circular orbit is no longer acting on it.

4. **Motion After Gravitational Force Disappears**:
- In the absence of the gravitational force, the satellite will no longer be subjected to any inward force. According to Newton's first law of motion, an object in motion will continue in its state of motion unless acted upon by an external force.

5. **Path of the Satellite**:
- Since there is no longer any force acting towards the center, the satellite will move in a straight line in the direction of its velocity at the moment the gravitational force disappears. This straight-line path will be tangential to the circular orbit at the point where the gravitational force ceased to act.

6. **Conclusion**:
- Therefore, the satellite will move off in a straight line with a speed `v`, tangential to its original circular orbit.

### Final Answer:
The satellite will move in a straight line with a speed `v` tangential to its original orbit.

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