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, let's analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions:**
- A satellite is in a circular orbit around the Earth with a uniform speed \( v \). This speed is maintained due to the gravitational force acting as the centripetal force.

2. **Gravitational Force:**
- The gravitational force acting on the satellite can be expressed as:
\[ F_g = \frac{G M m}{r^2} \]
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.

3. **Centripetal Force Requirement:**
- For the satellite to maintain its circular motion, the gravitational force must equal the required centripetal force:
\[ F_c = \frac{m v^2}{r} \]
- Therefore, we have:
\[ \frac{G M m}{r^2} = \frac{m v^2}{r} \]

4. **Effect of Disappearance of Gravitational Force:**
- If the gravitational force suddenly disappears, the force acting on the satellite becomes zero. According to Newton's first law of motion, an object in motion will continue to move in a straight line at a constant speed unless acted upon by an external force.

5. **Conclusion on Speed:**
- Since there is no longer any gravitational force acting on the satellite, it will not experience any change in speed. Therefore, the speed of the satellite will remain \( v \).

6. **Final Answer:**
- The speed of the satellite after the gravitational force disappears will be \( v \).

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