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 determine the escape velocity for a body of mass 100 kg from the Earth's surface, we can follow these steps:

### Step 1: Understand the concept of escape velocity
Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any further propulsion. It is given by the formula:

\[ v_e = \sqrt{\frac{2GM}{R}} \]

where:
- \( v_e \) is the escape velocity,
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the celestial body (Earth in this case),
- \( R \) is the radius of the celestial body (Earth in this case).

### Step 2: Recognize that escape velocity is independent of mass
From the formula, we can see that the escape velocity does not depend on the mass of the object trying to escape (the projectile). It only depends on the mass of the Earth and the radius of the Earth.

### Step 3: Apply the known escape velocity
We are given that the escape velocity for a body of mass 1 kg from the Earth's surface is 11.2 km/s. Since escape velocity is independent of the mass of the projectile, the escape velocity for any mass, including 100 kg, will remain the same.

### Step 4: State the final answer
Thus, the escape velocity for a body of mass 100 kg from the Earth's surface is also:

\[ v_e = 11.2 \text{ km/s} \]

### Summary
The escape velocity for a body of mass 100 kg from the Earth's surface is 11.2 km/s.

---