A body from the surface of a planet has a escape veloctiy of 8 km/s . If the mass of the body is made twice, then the escape velocity is

Options

A. 8 km/s
B. `2sqrt(2) km//s`
C. 16 km/s
D. 4 km/s

Answer

To solve the problem, we need to understand the concept of escape velocity and how it is derived. The escape velocity (v_escape) from the surface of a planet is given by the formula:

\[ v_{escape} = \sqrt{\frac{2GM}{R}} \]

Where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.

### Step-by-Step Solution:

1. **Identify the given values**:
- The escape velocity from the surface of the planet is given as \( v_{escape} = 8 \, \text{km/s} \).

2. **Understand the formula**:
- The escape velocity depends only on the mass of the planet and its radius, not on the mass of the object trying to escape.

3. **Analyze the effect of changing the mass of the body**:
- The problem states that the mass of the body is made twice. However, since the escape velocity does not depend on the mass of the object, this change will not affect the escape velocity.

4. **Conclude the result**:
- Therefore, regardless of the mass of the body, the escape velocity remains the same. Hence, the escape velocity will still be \( 8 \, \text{km/s} \).

### Final Answer:
The escape velocity remains \( 8 \, \text{km/s} \).

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