If a ladder is not in balance against a smooth vertical wall, then it can be made in balance by :-

Options

A. Decreasing the length of ladder
B. Increasing the length of ladder
C. Increasing the angle of inclination
D. Decreasing the angle of inclination

Explanation

To solve the problem of balancing a ladder against a smooth vertical wall, we can analyze the forces acting on the ladder and how they relate to its angle of inclination. Here’s a step-by-step solution:

### Step 1: Understand the Forces Acting on the Ladder
The ladder experiences a gravitational force acting downwards due to its weight (mg), where m is the mass of the ladder and g is the acceleration due to gravity. This force acts at the center of mass of the ladder.

**Hint:** Identify the forces acting on the ladder and their directions.

### Step 2: Identify the Role of the Angle of Inclination
The angle of inclination (θ) is the angle between the ladder and the ground. The gravitational force can be resolved into two components: one perpendicular to the ground (mg cos θ) and one parallel to the ground (mg sin θ).

**Hint:** Consider how the angle of inclination affects the components of the gravitational force.

### Step 3: Analyze the Conditions for Balance
For the ladder to be in balance, the net torque about any point (usually the base of the ladder) must be zero. If the angle of inclination is too steep or too shallow, the ladder will either slide down or fall over.

**Hint:** Think about how changing the angle of inclination affects the stability of the ladder.

### Step 4: Evaluate the Options Given
1. **Decreasing the length of the ladder**: This does not affect the gravitational force acting on the ladder and will not help in balancing it.
2. **Increasing the length of the ladder**: Similar to decreasing the length, this will not change the gravitational force and will not help in balancing.
3. **Increasing the angle of inclination**: This decreases the component of the gravitational force acting parallel to the ground (mg sin θ), which can help in balancing the ladder.
4. **Decreasing the angle of inclination**: This increases the component of the gravitational force acting parallel to the ground, making it less stable.

**Hint:** Analyze each option to see how it affects the balance of the ladder.

### Step 5: Conclusion
The correct option to make the ladder balance against the smooth vertical wall is to **increase the angle of inclination**. This reduces the component of the gravitational force that could cause the ladder to slide down.

**Final Answer:** Increasing the angle of inclination (Option C) will help balance the ladder.