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

Options

A. 890 N
B. 889 N
C. 885 N
D. 892 N

Explanation

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

### Step 1: Understand the gravitational force on the surface of the Earth
The gravitational force acting on a mass of 1 kg on the surface of the Earth is given as \( F = 10 \, \text{N} \). This force can be expressed using the formula for gravitational force:

\[ F = \frac{G \cdot M_E \cdot m}{R_E^2} \]

Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( M_E \) is the mass of the Earth,
- \( m \) is the mass of the object (1 kg in this case),
- \( R_E \) is the radius of the Earth.

### Step 2: Calculate the gravitational force on the satellite
The satellite has a mass of \( 200 \, \text{kg} \) and orbits at a radius of \( \frac{3R}{2} \) (where \( R \) is the radius of the Earth). The gravitational force acting on the satellite can be expressed as:

\[ F' = \frac{G \cdot M_E \cdot m_s}{r^2} \]

Where:
- \( F' \) is the gravitational force on the satellite,
- \( m_s = 200 \, \text{kg} \) (mass of the satellite),
- \( r = \frac{3R}{2} \) (radius of the orbit).

Substituting \( r \) into the equation gives:

\[ F' = \frac{G \cdot M_E \cdot 200}{\left(\frac{3R}{2}\right)^2} \]

### Step 3: Simplify the expression
Now, we simplify the denominator:

\[ \left(\frac{3R}{2}\right)^2 = \frac{9R^2}{4} \]

Thus, the force becomes:

\[ F' = \frac{G \cdot M_E \cdot 200}{\frac{9R^2}{4}} = \frac{G \cdot M_E \cdot 200 \cdot 4}{9R^2} = \frac{800G \cdot M_E}{9R^2} \]

### Step 4: Relate it to the gravitational force on the surface
We know from Step 1 that:

\[ \frac{G \cdot M_E}{R_E^2} = 10 \, \text{N} \]

Thus, we can substitute this into our expression for \( F' \):

\[ F' = \frac{800}{9} \cdot 10 = \frac{8000}{9} \, \text{N} \]

### Step 5: Calculate the numerical value
Now we can calculate \( \frac{8000}{9} \):

\[ F' \approx 889 \, \text{N} \]

### Final Answer
The gravitational pull on the satellite is approximately \( 889 \, \text{N} \).

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