To find the weight of a person of mass 50 kg revolving around the Earth in a satellite, we can follow these steps:
### Step 1: Understand the Concept of Weight
Weight is defined as the force exerted on an object due to gravity. It can be calculated using the formula:
\[
W = mg
\]
where:
- \( W \) is the weight,
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity.
### Step 2: Consider the Situation in a Satellite
When a person is in a satellite, they are in a state of free fall, which means they are accelerating towards the Earth due to gravity. However, because the satellite is also moving in a circular orbit, the person experiences a sensation of weightlessness.
### Step 3: Calculate the Acceleration Due to Gravity at the Height of the Satellite
The formula for the acceleration due to gravity at a height \( h \) above the Earth's surface is given by:
\[
g' = \frac{GM}{(R + h)^2}
\]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth,
- \( h \) is the height of the satellite above the Earth's surface.
### Step 4: Analyze the Condition of Weightlessness
In a satellite, the height \( h \) is significant compared to the radius of the Earth \( R \). As the height increases, the value of \( g' \) decreases. When the satellite is at a sufficient height, \( g' \) approaches zero.
### Step 5: Conclusion about Weight
Since the effective acceleration due to gravity \( g' \) in the satellite is nearly zero, the weight \( W \) of the person can be calculated as:
\[
W = mg'
\]
Given that \( g' \) is approximately zero at that height:
\[
W \approx 50 \, \text{kg} \times 0 \, \text{m/s}^2 = 0 \, \text{N}
\]
Thus, the weight of the person in the satellite is effectively zero, indicating a state of weightlessness.
### Final Answer
The weight of the person in the satellite is **0 N**.
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