The escape velocity of 10g body from the earth is 11.2 `km s^(-1)`. Ignoring air resistance, the escape velocity of 10 kg of the iron ball from the earth will be

Options

A. `0.0112 kms^(-1)`
B. `0.112 kms^(-1)`
C. `11.2 kms^(-1)`
D. `0.56 kms^(-1)`

Explanation

To find the escape velocity of a 10 kg iron ball from the Earth, we can use the information provided in the question and the principles of escape velocity.

### Step-by-Step Solution:

1. **Understanding Escape Velocity**:
The escape velocity (VE) is the minimum velocity required for an object to break free from the gravitational attraction of a celestial body without any additional propulsion. The formula for escape velocity is given by:
\[ V_E = \sqrt{2gR_e} \]
where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)) and \( R_e \) is the radius of the Earth (approximately \( 6400 \, \text{km} \) or \( 6.4 \times 10^6 \, \text{m} \)).

2. **Given Escape Velocity**:
The problem states that the escape velocity for a 10 g body is \( 11.2 \, \text{km/s} \). This value is a constant for any object regardless of its mass.

3. **Mass Independence**:
It is important to note that escape velocity does not depend on the mass of the object. This means that whether the object is 10 g or 10 kg, the escape velocity remains the same.

4. **Conclusion**:
Therefore, the escape velocity for the 10 kg iron ball will also be \( 11.2 \, \text{km/s} \).

### Final Answer:
The escape velocity of a 10 kg iron ball from the Earth is **11.2 km/s**.

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