The escape velocity for a body of mass 1 kg from the earth surface is `11.2 "kms"^(-1)`. The escape velocity for a body of mass 100 kg would be

Options

A. `11.2 xx 10^(2) " kms"^(-1)`
B. `112 " kms"^(-1)`
C. `11.2 " kms"^(-1)`
D. `11.2 xx 10^(-2) " kms"^(-1)`

Explanation

To solve the problem, we need to understand the concept of escape velocity and how it relates to the mass of the projectile.

### Step-by-Step Solution:

1. **Understanding 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.

2. **Formula for Escape Velocity**:
The escape velocity \( v \) can be calculated using the formula:
\[ v = \sqrt{\frac{2GM}{R}} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the celestial body (in this case, Earth),
- \( R \) is the radius of the celestial body.

3. **Independence from Mass of the Projectile**:
It is important to note that escape velocity is independent of the mass of the object trying to escape. This means that whether the object has a mass of 1 kg or 100 kg, the escape velocity remains the same.

4. **Given Data**:
The problem states that the escape velocity for a body of mass 1 kg from the Earth's surface is \( 11.2 \, \text{km/s} \).

5. **Calculating Escape Velocity for 100 kg**:
Since escape velocity does not depend on the mass of the projectile, the escape velocity for a body of mass 100 kg will also be:
\[ v = 11.2 \, \text{km/s} \]

6. **Conclusion**:
Therefore, the escape velocity for a body of mass 100 kg is also \( 11.2 \, \text{km/s} \).

### Final Answer:
The escape velocity for a body of mass 100 kg is \( 11.2 \, \text{km/s} \).