If suddenly the gravitational force of attraction between earth and satellite revolving around it becomes zero, then the satellite will

Options

A. Both the bodies always have equal acceleration
B. move tangentially to the original orbit with the same velocity.
C. become stationary in its orbit
D. move towards the earth

Explanation

To solve the question, we need to analyze the situation when the gravitational force between the Earth and a satellite suddenly becomes zero. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding the Initial Conditions
The satellite is initially in orbit around the Earth due to the gravitational force acting on it. This gravitational force provides the necessary centripetal force for the satellite's circular motion.

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

For the satellite to maintain its circular orbit, this gravitational force must equal the centripetal force \( F_c \) required to keep the satellite moving in a circle:
\[ F_c = \frac{m v^2}{r} \]
where \( v \) is the orbital velocity of the satellite.

### Step 3: Setting the Forces Equal
At equilibrium (when the satellite is in stable orbit), we have:
\[ \frac{G M m}{r^2} = \frac{m v^2}{r} \]
By simplifying this equation, we can cancel \( m \) (the mass of the satellite) from both sides:
\[ \frac{G M}{r^2} = \frac{v^2}{r} \]
Multiplying both sides by \( r \) gives:
\[ \frac{G M}{r} = v^2 \]
Thus, the orbital velocity \( v \) can be expressed as:
\[ v = \sqrt{\frac{G M}{r}} \]

### Step 4: Sudden Loss of Gravitational Force
If the gravitational force suddenly becomes zero, the satellite will no longer experience any centripetal 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.

### Step 5: Conclusion on the Satellite's Motion
Since there is no longer any gravitational force acting on the satellite, it will continue to move in a straight line at the velocity it had at the moment the gravitational force became zero. This motion will be tangential to its original circular orbit.

### Final Answer
Therefore, the satellite will move tangentially to its original orbit and will escape into space.

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