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The question you uploaded asks for the correct expressions for centripetal acceleration \( a \) and speed \( v \) of a satellite in circular orbit around a planet of mass \( M \) at a radius \( r \). We are given four possible options (A to D) with different formulas for \( a \) and \( v \).

To solve this:

1. **Centripetal acceleration \( a \)** for a satellite in orbit is given by:
   \[
   a = \frac{v^2}{r}
   \]
   where \( v \) is the orbital speed, and \( r \) is the radius of the orbit.

2. The gravitational force provides the necessary centripetal force:
   \[
   \frac{GM}{r^2} = \frac{v^2}{r}
   \]
   Solving for \( v \), we get:
   \[
   v = \sqrt{\frac{GM}{r}}
   \]

3. Using this value of \( v \), we can plug it into the equation for acceleration:
   \[
   a = \frac{GM}{r^2}
   \]

Thus, the correct values are:

- \( a = \frac{GM}{r^2} \)
- \( v = \sqrt{\frac{GM}{r}} \)

These correspond to **Option B** in the table.

Would you like more details or explanations? Here are some related questions for deeper understanding:

1. What is the relationship between gravitational force and centripetal force in orbital motion?
2. How does the speed of the satellite change with an increase in orbital radius?
3. What are the units of centripetal acceleration in this context?
4. How does the mass of the planet affect the satellite's speed?
5. What are the limitations of using this model for orbits?

**Tip:** Remember, the mass of the satellite doesn't affect its orbital speed, only the mass of the planet and the orbital radius do.

A satellite X is in a circular orbit of radius r about the center of a spherical planet of mass M. Which line, A to D, in the table gives correct expressions for the centripetal acceleration a and the speed v of the satellite?

Find the correct expressions for the centripetal acceleration and speed of a satellite in a circular orbit around a planet. Understand the relationship between gravitational force and centripetal force, and learn to apply key formulas like a = GM/r^2 and v = √(GM/r). Suitable for high school physics students.

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