A metal cuboid of mass M kg rests on a table surface area of `40cm^2` is in contact with the table the pressure exerted by the cuboid on the table surface is 10000Pa value of M is (given that,g=`10ms^-2`)

Options

A. 20kg
B. 5kg
C. 4kg
D. 2.5kg

Answer

To solve the problem, we need to use the formula for pressure, which 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 in Pascals (Pa),
- \( F \) is the force in Newtons (N),
- \( A \) is the area in square meters (m²).

### Step 1: Convert the area from cm² to m²
The area given is \( 40 \, \text{cm}^2 \). We need to convert this to square meters:

\[ 1 \, \text{cm}^2 = 10^{-4} \, \text{m}^2 \]

So,

\[ A = 40 \, \text{cm}^2 = 40 \times 10^{-4} \, \text{m}^2 = 0.004 \, \text{m}^2 \]

### Step 2: Use the pressure formula to find the force
We know the pressure \( P = 10000 \, \text{Pa} \) and the area \( A = 0.004 \, \text{m}^2 \). We can rearrange the pressure formula to find the force \( F \):

\[ F = P \times A \]

Substituting the values:

\[ F = 10000 \, \text{Pa} \times 0.004 \, \text{m}^2 = 40 \, \text{N} \]

### Step 3: Relate the force to the mass of the cuboid
The force exerted by the cuboid on the table is equal to its weight, which can be expressed as:

\[ F = m \cdot g \]

Where:
- \( m \) is the mass in kilograms (kg),
- \( g \) is the acceleration due to gravity, given as \( 10 \, \text{m/s}^2 \).

### Step 4: Solve for the mass \( m \)
We can rearrange the equation to solve for mass:

\[ m = \frac{F}{g} \]

Substituting the values we found:

\[ m = \frac{40 \, \text{N}}{10 \, \text{m/s}^2} = 4 \, \text{kg} \]

### Final Answer
The mass \( M \) of the cuboid is \( 4 \, \text{kg} \).

---