A T.V. tower has a height 150m. What is the population density around the T.V. tower if the total population covered is 50 lakh? (Radius of earth `=6.4xx10^(6)m)`

Options

A. `82.6km^(_2)`
B. `800.6km^(-2)`
C. `826.6km^(-2)`
D. `876.6km^(-2)`

Answer

To solve the problem of finding the population density around a TV tower, we can follow these steps:

### Step 1: Understand the Given Data
- Height of the TV tower (h) = 150 m
- Total population covered = 50 lakh = 50 × 10^5
- Radius of the Earth (R) = 6.4 × 10^6 m

### Step 2: Calculate the Effective Radius for Signal Transmission
The effective radius (D) for the signal transmission from the tower can be calculated using the formula:
\[ D = \sqrt{2hR} \]
Where:
- h = height of the tower
- R = radius of the Earth

Substituting the values:
\[ D = \sqrt{2 \times 150 \times 6.4 \times 10^6} \]

### Step 3: Calculate the Area Covered
The area (A) covered by the signal can be calculated using the formula for the area of a circle:
\[ A = \pi \left(\frac{D}{2}\right)^2 \]
Since we have D, we can substitute it into the area formula.

### Step 4: Calculate Population Density
Population density (ρ) can be calculated using the formula:
\[ \rho = \frac{\text{Total Population}}{\text{Area}} \]
Substituting the total population and the area calculated in the previous step.

### Step 5: Final Calculation
After calculating the area and substituting it into the population density formula, we can find the population density in people per square kilometer.

### Step 6: Convert to Required Units
If necessary, convert the population density to the required units (e.g., per square kilometer).