A research satellite of mass `200 kg` circles the earth in an orbit of average radius `3 R//2`, where `R` is the radius of the earth. Assuming the gravitational pull on the mass of `1 kg` on the earth's surface to be `10 N`, the pull on the satellite will be a) 1212 N b) 889 N c) 1280 N d) 960 N

Options

A. `1212 N`
B. `889 N`
C. `1280 N`
D. `960 N`

Explanation

To find the gravitational pull on the satellite, we can follow these steps:

### Step 1: Understand the gravitational force formula
The gravitational force \( F \) between two masses is given by the formula:
\[ F = \frac{G \cdot M \cdot m}{r^2} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( m \) is the mass of the object (satellite in this case),
- \( r \) is the distance from the center of the Earth to the object.

### Step 2: Calculate the gravitational force on 1 kg at the Earth's surface
We know that the gravitational pull on a mass of 1 kg at the Earth's surface is given as \( 10 \, N \). This can be represented as:
\[ F = \frac{G \cdot M}{R^2} = 10 \, N \]
where \( R \) is the radius of the Earth.

### Step 3: Determine the radius of the satellite's orbit
The satellite orbits at an average radius of \( \frac{3R}{2} \). Thus, the distance \( r \) from the center of the Earth to the satellite is:
\[ r = \frac{3R}{2} \]

### Step 4: Calculate the gravitational force on the satellite
Now, we will calculate the gravitational force \( F' \) acting on the satellite of mass \( 200 \, kg \):
\[ F' = \frac{G \cdot M \cdot 200}{\left(\frac{3R}{2}\right)^2} \]

### Step 5: Simplify the expression for \( F' \)
Substituting \( r = \frac{3R}{2} \) into the equation:
\[ F' = \frac{G \cdot M \cdot 200}{\left(\frac{9R^2}{4}\right)} = \frac{G \cdot M \cdot 200 \cdot 4}{9R^2} \]

### Step 6: Relate \( F' \) to the known force \( F \)
From Step 2, we know:
\[ F = \frac{G \cdot M}{R^2} = 10 \, N \]
Thus, we can express \( F' \) in terms of \( F \):
\[ F' = \frac{200 \cdot 4}{9} \cdot F = \frac{800}{9} \cdot 10 \]
\[ F' = \frac{8000}{9} \, N \]

### Step 7: Calculate the numerical value of \( F' \)
Now, we can calculate:
\[ F' \approx 889 \, N \]

### Conclusion
The gravitational pull on the satellite will be approximately \( 889 \, N \).

### Final Answer
The correct option is **b) 889 N**.

---