Mark the correct statement (i) Escape velocity does not depend on mass of body
(ii) If total energy of a satellite becomes positive , it escape from earth .
(iii) Orbit of geostationary orbit is called parking orbit

Options

A. (i) only
B. (i),(ii) only
C. (i),(ii) and (iii)
D. (i),(iii) only

Answer

To determine which statements are correct regarding escape velocity and related concepts, let's analyze each statement step by step.

### Step 1: Analyze Statement (i)
**Statement (i): Escape velocity does not depend on mass of body.**

The formula for escape velocity (v) is given by:
\[ v = \sqrt{\frac{2GM}{R}} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth (or the celestial body),
- \( R \) is the radius of the Earth (or the distance from the center of the celestial body to the point of escape).

From the formula, we can see that escape velocity depends only on the mass of the Earth (M) and the radius (R). It does not depend on the mass of the object trying to escape. Therefore, this statement is **correct**.

### Step 2: Analyze Statement (ii)
**Statement (ii): If total energy of a satellite becomes positive, it escapes from Earth.**

The total mechanical energy (E) of a satellite in orbit is given by:
\[ E = K + U \]
where:
- \( K \) is the kinetic energy,
- \( U \) is the potential energy.

For a satellite in a gravitational field, the potential energy is negative (since it is bound to the gravitational field), and the total energy is negative when the satellite is in a stable orbit. If the total energy becomes positive, it means that the kinetic energy exceeds the gravitational potential energy, allowing the satellite to escape the gravitational influence of the Earth. Therefore, this statement is also **correct**.

### Step 3: Analyze Statement (iii)
**Statement (iii): Orbit of geostationary orbit is called parking orbit.**

A geostationary orbit is one where a satellite orbits the Earth at the same rotational speed as the Earth, meaning it remains fixed over one point on the equator. This orbit is indeed often referred to as a "parking orbit" because satellites placed in this orbit appear to be stationary relative to the Earth's surface. Therefore, this statement is also **correct**.

### Conclusion
All three statements are correct:
1. Escape velocity does not depend on mass of the body. **(Correct)**
2. If total energy of a satellite becomes positive, it escapes from Earth. **(Correct)**
3. Orbit of geostationary orbit is called parking orbit. **(Correct)**

Thus, the correct answer is that all statements are correct.

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