The escape velocity of a particle of mass 'm'

Options

A. varies as `m^(2)`
B. varies as m
C. varies as `m^(-1)`
D. is independent of mass

Answer

To find the escape velocity of a particle of mass 'm', we can follow these steps:

### Step 1: Understand the Concept of Escape Velocity
Escape velocity is the minimum velocity required for an object to break free from the gravitational attraction of a celestial body without any additional propulsion.

### Step 2: Recall the Formula for Escape Velocity
The formula for escape velocity (v_e) from the surface of a planet is given by:
\[ v_e = \sqrt{\frac{2GM}{R}} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the celestial body (e.g., Earth),
- \( R \) is the radius of the celestial body.

### Step 3: Analyze the Dependency on Mass
From the formula, we can see that the escape velocity does not depend on the mass of the object (m) trying to escape. Instead, it depends on the mass of the celestial body (M) and its radius (R).

### Step 4: Conclusion
Since the escape velocity is independent of the mass of the escaping particle, we conclude that:
- The escape velocity does not vary with the mass of the particle (m).

Thus, the correct answer is that the escape velocity is independent of the mass of the particle.

### Final Answer
The escape velocity of a particle of mass 'm' is independent of the mass of the particle.

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