A rectangular wooden block has length, breadth and height of 50 cm, 25 cm, and 10 cm, respectively. This wooden block is kept on ground in three different ways, turn by turn. Which of the following is the correct statement about the pressure exerted by this block on the ground?

Options

A. the maximum pressure is exerted when the length and breadth form the base.
B. the maximum pressure is exerted when length and height form the base
C. the maximum pressure is exerted when bredth and height form the base.
D. the minimum pressure is exerted when length and height form the base.

Answer

To solve the problem of determining the pressure exerted by a rectangular wooden block on the ground when placed in three different orientations, we can follow these steps:

### Step 1: Understand the Dimensions of the Block
The dimensions of the wooden block are:
- Length (L) = 50 cm
- Breadth (B) = 25 cm
- Height (H) = 10 cm

### Step 2: Calculate the Weight of the Block
The weight (W) of the block acts as the force (F) exerted on the ground. For simplicity, we can assume a uniform density and that the weight is constant regardless of the orientation.

### Step 3: Determine the Area of the Base for Each Orientation
We will calculate the area of the base for each of the three orientations:

1. **Orientation 1 (Length and Breadth as Base)**:
- Area (A1) = Length × Breadth = 50 cm × 25 cm = 1250 cm²

2. **Orientation 2 (Breadth and Height as Base)**:
- Area (A2) = Breadth × Height = 25 cm × 10 cm = 250 cm²

3. **Orientation 3 (Length and Height as Base)**:
- Area (A3) = Length × Height = 50 cm × 10 cm = 500 cm²

### Step 4: Calculate the Pressure for Each Orientation
Pressure (P) is defined as the force (F) divided by the area (A) of the base. Since the weight of the block is constant, we can express the pressure for each orientation as follows:

1. **Pressure in Orientation 1 (P1)**:
- \( P1 = \frac{F}{A1} = \frac{F}{1250 \, \text{cm}^2} \)

2. **Pressure in Orientation 2 (P2)**:
- \( P2 = \frac{F}{A2} = \frac{F}{250 \, \text{cm}^2} \)

3. **Pressure in Orientation 3 (P3)**:
- \( P3 = \frac{F}{A3} = \frac{F}{500 \, \text{cm}^2} \)

### Step 5: Compare the Pressures
To determine which orientation exerts maximum and minimum pressure, we compare the denominators:

- For Orientation 1 (Length and Breadth): 1250 cm²
- For Orientation 2 (Breadth and Height): 250 cm²
- For Orientation 3 (Length and Height): 500 cm²

### Step 6: Identify Maximum and Minimum Pressure
- The maximum pressure occurs when the area is the smallest, which is in Orientation 2 (Breadth and Height).
- The minimum pressure occurs when the area is the largest, which is in Orientation 1 (Length and Breadth).

### Conclusion
The correct statement about the pressure exerted by the block on the ground is:
- **Maximum pressure is exerted when the breadth and height form the base (Orientation 2)**.
- **Minimum pressure is exerted when the length and breadth form the base (Orientation 1)**.

### Final Answer
The correct option is that the maximum pressure is exerted when the breadth and height form the base.

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