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Statement-1: The plane of the orbit of a...

Statement-1: The plane of the orbit of an artificial satellite must contain the centre of the Earth.
Statement-2: For an artificial satellite, the necessary centripetal force is provided by gravity.

A

Statement-1 is true, statement-2 is true: Statement-2 is a correct explanation for statement-1

B

Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false.

D

Statement-1 is false, Statement-2 is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we will analyze both statements and determine their validity and relationship. ### Step-by-Step Solution: 1. **Understanding Statement 1**: - The statement claims that "The plane of the orbit of an artificial satellite must contain the center of the Earth." - For any object in orbit around a planet, the gravitational force acts towards the center of the planet. Therefore, the orbiting object must have its orbital plane containing the center of the planet (in this case, the Earth). This is true because the gravitational force acts along the line connecting the center of the Earth to the satellite. **Conclusion**: Statement 1 is true. **Hint**: Think about how gravity works and the geometry of orbits. 2. **Understanding Statement 2**: - The statement claims that "For an artificial satellite, the necessary centripetal force is provided by gravity." - In the case of an artificial satellite, the gravitational force acting on it provides the necessary centripetal force required to keep it in orbit. The gravitational force can be expressed as \( F_g = \frac{G \cdot m \cdot M}{r^2} \), where \( m \) is the mass of the satellite, \( M \) is the mass of the Earth, \( r \) is the distance from the center of the Earth to the satellite, and \( G \) is the gravitational constant. This gravitational force is indeed what keeps the satellite in circular motion, providing the required centripetal force \( F_c = \frac{mv^2}{r} \). **Conclusion**: Statement 2 is also true. **Hint**: Consider the relationship between gravitational force and centripetal force in circular motion. 3. **Analyzing the Relationship Between Statements**: - While both statements are true, we need to determine if Statement 2 is a correct explanation for Statement 1. - Statement 1 discusses the geometric aspect of the orbit (the plane containing the center of the Earth), while Statement 2 discusses the dynamics of the satellite (the role of gravity as centripetal force). Therefore, Statement 2 does not explain why the plane of the orbit must contain the center of the Earth; it only describes the forces acting on the satellite. **Conclusion**: Statement 2 is not a correct explanation for Statement 1. **Hint**: Think about whether one statement logically explains the other. ### Final Answer: - Statement 1 is true. - Statement 2 is true. - Statement 2 is not a correct explanation for Statement 1. Thus, the correct option is that both statements are true, but Statement 2 does not explain Statement 1.
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ALLEN-GRAVITATION-Exercise 3 (Miscellaneous Type Questions)
  1. Statemet-1: Two satellites A & B are in the same orbit around the eart...

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  2. Statement-1: The acceleration of a particle near the earth surface dif...

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  3. Statement-1: Kepler's law of areas is equivalent to the law of conserv...

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  4. Statement-1: A satellite is moving in a circular orbit of the earth. I...

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  5. Statement-1:A personfeels weightlessness in an artificial satellite of...

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  6. Statement-1: Moon cannot be used as a satellite for communication. S...

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  7. Statement-1: There is not atmosphere on the moon. Statement-2: The r...

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  8. Statement-1: Pendulum clock stops working on the spaceship Statement...

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  9. Statement-1: Escape velocity is independent of the angle of projection...

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  10. Statement-1: The plane of the orbit of an artificial satellite must co...

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  11. Statement-1:When a planet approches the point which is farthest from t...

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  12. When a particle is projected from the surface of earth, its mechanical...

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  13. When a particle is projected from the surface of earth its mechanical ...

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  14. A solid sphere of mass M and radius R is surrounded by a spherical she...

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  15. It is easier to draw up a wooden block along an inclined plane than ha...

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  16. A solid sphere of mass M and radius R is surrounded by a spherical she...

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  17. For circular orbits the potential energy of the companion star is cons...

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  18. If temperature of ideal black body is decreased from T to T/2 than fin...

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  19. In the picture below the planet orbits around the sun with a period of...

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  20. In the picture below the planet orbits around the sun with a period of...

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