What is the minimum pressure required to force the blood from the heart to the top of the head (vertical distance `0.5m` ) ? [density of blood is 1040 kg `m^(-3).` Fraction is to be neglected and `g=9.8ms^(-2)`]

Options

A. `1050N m^(-2)`
B. `2080 Nm^(-2)`
C. `5096Nm^(-2)`
D. `6096 Nm^(-2)`

Answer

To find the minimum pressure required to force blood from the heart to the top of the head, we can use the hydrostatic pressure formula. The pressure difference needed to lift a column of fluid can be calculated using the following equation:

\[ P = \rho g h \]

Where:
- \( P \) is the pressure difference (in Pascals),
- \( \rho \) is the density of the fluid (in kg/m³),
- \( g \) is the acceleration due to gravity (in m/s²),
- \( h \) is the height of the fluid column (in meters).

### Step-by-Step Solution:

1. **Identify the given values:**
- Density of blood, \( \rho = 1040 \, \text{kg/m}^3 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
- Height of the column, \( h = 0.5 \, \text{m} \)

2. **Substitute the values into the formula:**
\[ P = \rho g h = 1040 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \times 0.5 \, \text{m} \]

3. **Calculate the pressure:**
\[ P = 1040 \times 9.8 \times 0.5 \]
\[ P = 1040 \times 4.9 \]
\[ P = 5104 \, \text{Pa} \]

4. **Final Result:**
The minimum pressure required to force the blood from the heart to the top of the head is **5104 Pascals**.