A block of weight 100 N and dimenions 50 cm x 30 cm x 10 cm rests on a table in three different positions with its base as (a) 50 cm x 30 cm, (b) 30 cm x 10 cm, (C) 50 cm x 10 cm. Calculate the pressure exerted in each case.

Answer

To solve the problem of calculating the pressure exerted by a block of weight 100 N on a table in three different positions, we will follow these steps:

### Step 1: Understand the formula for pressure
Pressure is defined as the force applied per unit area. The formula for pressure (P) is given by:
\[ P = \frac{F}{A} \]
where:
- \( P \) is the pressure,
- \( F \) is the force (weight of the block in this case),
- \( A \) is the area of contact with the surface.

### Step 2: Calculate the area for each position
We will calculate the area of the base in contact with the table for each of the three positions.

#### Case (a): Base dimensions 50 cm x 30 cm
- Area \( A_1 = 50 \, \text{cm} \times 30 \, \text{cm} = 1500 \, \text{cm}^2 \)
- Convert to square meters:
\[ A_1 = \frac{1500 \, \text{cm}^2}{10000} = 0.15 \, \text{m}^2 \]

#### Case (b): Base dimensions 30 cm x 10 cm
- Area \( A_2 = 30 \, \text{cm} \times 10 \, \text{cm} = 300 \, \text{cm}^2 \)
- Convert to square meters:
\[ A_2 = \frac{300 \, \text{cm}^2}{10000} = 0.03 \, \text{m}^2 \]

#### Case (c): Base dimensions 50 cm x 10 cm
- Area \( A_3 = 50 \, \text{cm} \times 10 \, \text{cm} = 500 \, \text{cm}^2 \)
- Convert to square meters:
\[ A_3 = \frac{500 \, \text{cm}^2}{10000} = 0.05 \, \text{m}^2 \]

### Step 3: Calculate the pressure for each case
Now we will use the pressure formula to calculate the pressure exerted in each case.

#### Case (a):
- Force \( F = 100 \, \text{N} \)
- Area \( A_1 = 0.15 \, \text{m}^2 \)
\[ P_1 = \frac{F}{A_1} = \frac{100 \, \text{N}}{0.15 \, \text{m}^2} = 666.67 \, \text{Pa} \]

#### Case (b):
- Area \( A_2 = 0.03 \, \text{m}^2 \)
\[ P_2 = \frac{F}{A_2} = \frac{100 \, \text{N}}{0.03 \, \text{m}^2} = 3333.33 \, \text{Pa} \]

#### Case (c):
- Area \( A_3 = 0.05 \, \text{m}^2 \)
\[ P_3 = \frac{F}{A_3} = \frac{100 \, \text{N}}{0.05 \, \text{m}^2} = 2000 \, \text{Pa} \]

### Summary of Results
- Pressure in Case (a): \( 666.67 \, \text{Pa} \)
- Pressure in Case (b): \( 3333.33 \, \text{Pa} \)
- Pressure in Case (c): \( 2000 \, \text{Pa} \)