The velocity with which a projectile must be fired to escape from the earth does not depend upon

Options

A. mass of earth
B. mass of projectile
C. radius of earth
D. None of these

Explanation

To solve the question regarding the escape velocity of a projectile from the Earth, we can follow these steps:

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

### Step 2: Use the Escape Velocity Formula
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, and
- \( R \) is the radius of the Earth.

### Step 3: Analyze the Formula
From the formula, we can see that:
- Escape velocity depends on \( G \), \( M \), and \( R \).
- It does not include the mass of the projectile itself.

### Step 4: Conclusion
Thus, the velocity with which a projectile must be fired to escape from the Earth does not depend upon the mass of the projectile.

### Final Answer
The correct option is that the escape velocity does not depend on the mass of the projectile.

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