`2`kg ice block should be dropped form `'x'` km' height to melt completely. The `8` kg ice should be dropped from a height of

Options

A. `4x Km`
B. `x Km`
C. `2x Km`
D. `x//2 Km`

Explanation

To solve the problem, we need to understand the relationship between potential energy and the heat energy required to melt ice.

### Step-by-Step Solution:

1. **Understanding Potential Energy**:
The potential energy (PE) of an object at height \( h \) is given by the formula:
\[ PE = mgh \]
where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the height.

2. **Energy Required to Melt Ice**:
The energy required to melt ice is given by:
\[ Q = mL \]
where \( L \) is the latent heat of fusion of ice.

3. **Setting Up the Equation for the 2 kg Ice Block**:
For the 2 kg ice block dropped from height \( x \):
\[ mgh = mL \]
Substituting \( m = 2 \) kg, we get:
\[ 2g x = 2L \]
Simplifying this, we find:
\[ g x = L \quad \text{(1)} \]

4. **Setting Up the Equation for the 8 kg Ice Block**:
Now, for the 8 kg ice block, we set up a similar equation:
\[ mgh' = mL \]
Substituting \( m = 8 \) kg, we get:
\[ 8g h' = 8L \]
Simplifying this, we find:
\[ g h' = L \quad \text{(2)} \]

5. **Relating the Two Heights**:
From equations (1) and (2), we can relate \( x \) and \( h' \):
From (1):
\[ x = \frac{L}{g} \]
From (2):
\[ h' = \frac{L}{g} \]
Thus, we see that:
\[ h' = x \]

### Conclusion:
The height \( h' \) from which the 8 kg ice block should be dropped to melt completely is the same as the height \( x \) from which the 2 kg ice block was dropped. Therefore, the answer is:
\[ h' = x \text{ km} \]