On which quantity the escape velocity for earth does not depend on

Options

A. mass of the earth
B. mass of the projectile
C. point of projection relative to the earth
D. gravitational constant

Answer

To determine the quantity on which the escape velocity for Earth does not depend, we start with the formula for escape velocity:

### Step 1: Write down the formula for escape velocity.
The escape velocity \( v_e \) is given by the formula:
\[ v_e = \sqrt{\frac{2GM}{R}} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth.

### Step 2: Identify the variables in the formula.
From the formula, we can see that escape velocity depends on:
- \( G \) (the universal gravitational constant),
- \( M \) (the mass of the Earth),
- \( R \) (the radius of the Earth).

### Step 3: Analyze the mass of the projectile.
The escape velocity formula does not include the mass of the projectile (the object trying to escape Earth's gravity). This means that the escape velocity is independent of the mass of the object.

### Step 4: Conclusion.
Thus, the quantity on which the escape velocity for Earth does not depend is the mass of the projectile.

### Final Answer:
The escape velocity for Earth does not depend on the mass of the projectile.

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