To find the weight of a 120 kg body at a height of 2000 km above the surface of the Earth, we can follow these steps:
### Step 1: Determine the total distance from the center of the Earth
The radius of the Earth is given as 6000 km. When the body is taken to a height of 2000 km above the Earth's surface, the total distance from the center of the Earth (R + h) can be calculated as follows:
\[
\text{Total distance} = \text{Radius of the Earth} + \text{Height above the surface}
\]
\[
\text{Total distance} = 6000 \text{ km} + 2000 \text{ km} = 8000 \text{ km}
\]
### Step 2: Convert the distance into meters
Since the standard unit of measurement in physics is meters, we need to convert kilometers to meters:
\[
8000 \text{ km} = 8000 \times 1000 \text{ m} = 8,000,000 \text{ m}
\]
### Step 3: Use the formula for gravitational field intensity at height h
The gravitational field intensity (g') at a height h above the Earth's surface can be calculated using the formula:
\[
g' = \frac{G M}{(R + h)^2}
\]
Where:
- \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)
- \( M \) is the mass of the Earth, approximately \( 5.972 \times 10^{24} \, \text{kg} \)
- \( R \) is the radius of the Earth in meters, which is \( 6000 \, \text{km} = 6,000,000 \, \text{m} \)
### Step 4: Calculate the gravitational field intensity at the height
Substituting the values into the formula:
\[
g' = \frac{(6.674 \times 10^{-11}) \times (5.972 \times 10^{24})}{(8,000,000)^2}
\]
Calculating the denominator:
\[
(8,000,000)^2 = 64 \times 10^{12} = 6.4 \times 10^{13} \, \text{m}^2
\]
Now substituting back into the equation:
\[
g' = \frac{(6.674 \times 10^{-11}) \times (5.972 \times 10^{24})}{6.4 \times 10^{13}}
\]
Calculating the numerator:
\[
6.674 \times 10^{-11} \times 5.972 \times 10^{24} \approx 3.986 \times 10^{14} \, \text{N m}^2/\text{kg}
\]
Now substituting this into the equation for \( g' \):
\[
g' = \frac{3.986 \times 10^{14}}{6.4 \times 10^{13}} \approx 6.22 \, \text{m/s}^2
\]
### Step 5: Calculate the weight of the body at that height
The weight (W) of the body can be calculated using the formula:
\[
W = m \cdot g'
\]
Where \( m \) is the mass of the body (120 kg):
\[
W = 120 \, \text{kg} \times 6.22 \, \text{m/s}^2 \approx 746.4 \, \text{N}
\]
### Final Answer
The weight of the 120 kg body at a height of 2000 km above the surface of the Earth is approximately **746.4 N**.
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