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

Options

A. Zero
B. v
C. 2v
D. infinity

Answer

To solve the problem, we need to analyze the situation when the gravitational force acting on the satellite suddenly disappears. We'll use Newton's first law of motion to understand the behavior of the satellite in this scenario.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- A satellite is revolving around the Earth in a circular orbit at a uniform speed \( v \).
- The gravitational force provides the necessary centripetal force to keep the satellite in its circular path.

**Hint**: Remember that the gravitational force is what keeps the satellite in orbit.

2. **Gravitational Force**:
- The gravitational force acting on the satellite is given by Newton's law of gravitation:
\[ F_g = \frac{GMm}{r^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, and \( r \) is the distance from the center of the Earth to the satellite.

**Hint**: The gravitational force is crucial for maintaining the satellite's circular motion.

3. **Sudden Disappearance of Gravitational Force**:
- If the gravitational force suddenly disappears, the centripetal force that was keeping the satellite in circular motion is no longer acting on it.

**Hint**: Consider what happens to the forces acting on the satellite when gravity is no longer present.

4. **Application of Newton's First Law of Motion**:
- According to Newton's first law, if the net external force acting on an object is zero, the object will maintain its state of motion. This means:
- If the satellite was moving with a speed \( v \), it will continue to move with that speed in a straight line in the direction it was moving at the moment the force disappeared.

**Hint**: Newton's first law states that an object in motion stays in motion unless acted upon by an external force.

5. **Conclusion**:
- Therefore, when the gravitational force disappears, the speed of the satellite will remain \( v \). It will move tangentially to its circular path at that speed.

**Final Answer**: The speed of the satellite will be \( v \).