Gas escaps from the surface of a planet because it acquires an escape velocity. The escape velocity will depend on which of the following factors :
I. Mass of the planet
II. Mass pf the particle escaping
III. Temperature of the planet
IV. Radius of the planet
Select the correct answer from the codes given below.

Options

A. I and II
B. II and IV
C. I and IV
D. I, II and IV

Explanation

To determine the factors on which escape velocity depends, let's analyze the concept of escape velocity and the relevant equations.

### Step-by-Step Solution:

1. **Definition of Escape Velocity**:
Escape velocity is the minimum velocity an object must have to break free from the gravitational attraction of a planet without any further propulsion.

2. **Formula for Escape Velocity**:
The escape velocity (\(V_e\)) can be derived from the gravitational potential energy and kinetic energy principles. The formula is given by:
\[ V_e = \sqrt{\frac{2GM}{R}} \]
where:
- \(G\) is the universal gravitational constant,
- \(M\) is the mass of the planet,
- \(R\) is the radius of the planet.

3. **Analyzing the Factors**:
- **I. Mass of the Planet (M)**:
From the formula, we see that escape velocity is directly proportional to the square root of the mass of the planet. Therefore, this factor affects escape velocity.
- **II. Mass of the Particle Escaping**:
The escape velocity does not depend on the mass of the escaping particle. The formula shows that the mass of the escaping object cancels out when considering gravitational force and kinetic energy.
- **III. Temperature of the Planet**:
The escape velocity is not directly influenced by the temperature of the planet. However, temperature can affect the kinetic energy of gas particles, but it does not change the escape velocity itself.
- **IV. Radius of the Planet (R)**:
The escape velocity is inversely proportional to the square root of the radius of the planet. Thus, this factor also affects escape velocity.

4. **Conclusion**:
Based on the analysis:
- The escape velocity depends on:
- I. Mass of the planet (Yes)
- II. Mass of the particle escaping (No)
- III. Temperature of the planet (No)
- IV. Radius of the planet (Yes)

Therefore, the correct factors are I and IV.

### Final Answer:
The correct answer is: I and IV.

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