A small satellite is revolving near earth's surface. Its orbital velocity will be nearly

Options

A. 8 km/s
B. `11.2 ` km/s
C. 4 km/s
D. 6 km/s

Answer

To find the orbital velocity of a small satellite revolving near the Earth's surface, we can use the formula for orbital velocity:

### Step-by-Step Solution:

1. **Identify the formula for orbital velocity**:
The orbital velocity \( v_0 \) of a satellite near the Earth's surface is given by the formula:
\[ v_0 = \sqrt{g \cdot r_e} \]
where:
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( r_e \) is the radius of the Earth (approximately \( 6.4 \times 10^6 \, \text{m} \)).

2. **Substitute the values into the formula**:
Plugging in the values for \( g \) and \( r_e \):
\[ v_0 = \sqrt{9.8 \, \text{m/s}^2 \cdot 6.4 \times 10^6 \, \text{m}} \]

3. **Calculate the product inside the square root**:
First, calculate the product:
\[ 9.8 \cdot 6.4 \times 10^6 = 62.72 \times 10^6 \, \text{m}^2/\text{s}^2 \]

4. **Take the square root**:
Now, take the square root of the result:
\[ v_0 = \sqrt{62.72 \times 10^6} \approx 7920 \, \text{m/s} \]

5. **Convert to kilometers per second**:
To express this in kilometers per second:
\[ v_0 \approx 7.92 \, \text{km/s} \]
Rounding this value gives:
\[ v_0 \approx 8 \, \text{km/s} \]

### Final Answer:
The orbital velocity of a small satellite revolving near the Earth's surface is approximately \( 8 \, \text{km/s} \).

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