Longer the size of the key ............... it is to open a safe vault.

Options

A. easier
B. lesser the force required by
C. convenient
D. all of the above

Explanation

To solve the question, "Longer the size of the key ............... it is to open a safe vault," we need to analyze how the size of the key affects the effort required to open a safe vault.

### Step-by-Step Solution:

1. **Understanding the Concept of Moment of Force**:
- The action of turning a key to open a safe vault involves the concept of moment of force (also known as torque). The moment of force is the rotational effect produced by a force acting at a distance from the pivot point (in this case, the lock).

2. **Formula for Moment of Force**:
- The moment of force (τ) can be expressed mathematically as:
\[ τ = r \times F \]
where:
- \( τ \) is the moment of force,
- \( r \) is the distance from the pivot point (length of the key),
- \( F \) is the force applied.

3. **Effect of Increasing the Key Size**:
- If the size of the key (length \( r \)) increases, the distance from the pivot point increases. This means that for the same amount of force \( F \), the moment of force \( τ \) will increase.

4. **Implication of Increased Moment of Force**:
- A larger moment of force means that it becomes easier to turn the key. Therefore, less force is required to achieve the same rotational effect needed to open the vault.

5. **Conclusion**:
- As the size of the key increases, it becomes easier to open the safe vault because:
- It requires less force to achieve the necessary moment of force.
- It is more convenient to use a longer key.

Thus, the completed statement is: "Longer the size of the key, easier it is to open a safe vault."

### Answer Options:
- Option 1: Easier
- Option 2: Lesser the force required
- Option 3: Convenient
- Option 4: All of the above

The correct answer is **Option 4: All of the above**.

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