The T.V.Transmission tower in Delhi has a height of 240m. The distnace up to which the broadcast can be received (taking the radius of earth to be `6.4xx 10^(6) is:

Options

A. 100km
B. 60km
C. 55km
D. 50km

Explanation

To solve the problem of finding the distance up to which the broadcast from a TV transmission tower can be received, we will use the formula that relates the height of the tower and the radius of the Earth.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Height of the tower (h) = 240 m
- Radius of the Earth (R) = 6.4 × 10^6 m

2. **Use the Formula for Distance:**
The distance (d) up to which the broadcast can be received is given by the formula:
\[ d = \sqrt{2 \cdot h \cdot R} \]
where:
- d = distance covered by the broadcast
- h = height of the tower
- R = radius of the Earth

3. **Substitute the Values into the Formula:**
Substitute the known values into the formula:
\[ d = \sqrt{2 \cdot 240 \, \text{m} \cdot (6.4 \times 10^6 \, \text{m})} \]

4. **Calculate the Product Inside the Square Root:**
First, calculate \(2 \cdot 240\):
\[ 2 \cdot 240 = 480 \]
Now calculate:
\[ 480 \cdot (6.4 \times 10^6) = 3.072 \times 10^9 \]

5. **Take the Square Root:**
Now, take the square root of \(3.072 \times 10^9\):
\[ d = \sqrt{3.072 \times 10^9} \approx 55,500 \, \text{m} \]

6. **Convert to Kilometers:**
To convert meters to kilometers, divide by 1000:
\[ d \approx 55.5 \, \text{km} \]

### Final Answer:
The distance up to which the broadcast can be received is approximately **55.5 km**.

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