A block of mass 4 kg and dimensions `10 cm xx 20 cm xx 30 cm` rests on the floor. If `g = 10 ms^(-2)`, then the maximum pressure the block can exert on the floor is:

Options

A. `2000 Nm^(-2)`
B. `1000 Nm^(-2)`
C. `4000 Nm^(-2)`
D. `1333 Nm^(-2)`

Explanation

To find the maximum pressure exerted by the block on the floor, we will follow these steps:

### Step 1: Calculate the Weight of the Block
The weight (force due to gravity) of the block can be calculated using the formula:
\[ F = m \cdot g \]
Where:
- \( m = 4 \, \text{kg} \) (mass of the block)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ F = 4 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 40 \, \text{N} \]

### Step 2: Determine the Area of Contact
The area of contact between the block and the floor will be the minimum area of the block's base. The dimensions of the block are \( 10 \, \text{cm} \times 20 \, \text{cm} \times 30 \, \text{cm} \). The minimum area will be:
\[ \text{Area} = 10 \, \text{cm} \times 20 \, \text{cm} \]

Calculating the area:
\[ \text{Area} = 200 \, \text{cm}^2 \]

To convert this to square meters:
\[ 200 \, \text{cm}^2 = 200 \times 10^{-4} \, \text{m}^2 = 0.02 \, \text{m}^2 \]

### Step 3: Calculate the Maximum Pressure
Pressure is defined as force per unit area:
\[ P = \frac{F}{A} \]

Substituting the values we have:
\[ P = \frac{40 \, \text{N}}{0.02 \, \text{m}^2} \]

Calculating the pressure:
\[ P = 2000 \, \text{N/m}^2 \]

### Final Answer
The maximum pressure the block can exert on the floor is:
\[ P = 2000 \, \text{N/m}^2 \]

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