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Assertion : Angular momentum of a planet...

Assertion : Angular momentum of a planet is constant about any point
Reason : For acting on the planet is a central force.

A

If both Assertin and Reason are correct and Reason is the correct explanation of Assertion

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion

C

If Assertion is true but Reason is false

D

If Assertion is false but Reason is true

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AI Generated Solution

The correct Answer is:
To solve the assertion and reason question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "the angular momentum of a planet is constant about any point." - Angular momentum (L) is defined as \( L = r \times p \), where \( r \) is the position vector from the point about which we are calculating angular momentum, and \( p \) is the linear momentum of the planet. 2. **Analyzing Angular Momentum**: - For a planet moving in an orbit (like Earth around the Sun), the angular momentum can be affected by external forces. - The gravitational force acting on the planet is a central force, which means it acts along the line connecting the center of mass of the planet and the Sun. 3. **Effect of Central Force**: - A central force does not exert a torque about the center of mass of the planet. However, if we consider angular momentum about any point other than the center of mass, the gravitational force can create a torque. - Therefore, while the angular momentum about the center of mass remains constant (due to no net external torque), the angular momentum about any arbitrary point may change due to the torque created by the gravitational force. 4. **Conclusion on Assertion**: - Since the assertion claims that angular momentum is constant about any point, this is **incorrect**. Angular momentum is only constant about the center of mass when no external torques act on it. 5. **Understanding the Reason**: - The reason states that "the force acting on the planet is a central force." - This statement is **true** because the gravitational force between the planet and the Sun is indeed a central force. 6. **Final Evaluation**: - Since the assertion is false and the reason is true, the correct conclusion is that the assertion is incorrect while the reason is correct. ### Final Answer: - The assertion is false, and the reason is true.

To solve the assertion and reason question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that "the angular momentum of a planet is constant about any point." - Angular momentum (L) is defined as \( L = r \times p \), where \( r \) is the position vector from the point about which we are calculating angular momentum, and \( p \) is the linear momentum of the planet. ...
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DC PANDEY ENGLISH-GRAVITATION-(B) Chapter Exercises
  1. Assertion : The force between two finite rigid bodies is not necessari...

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  2. Assertion : Angular momentum of a planet is constant about any point ...

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  3. Assertion : Kepler's law for planetary motion are consequence of Newto...

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  4. Assertion : The field strength at the centre of a ring is zero Reaso...

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  5. Assertion : The binding energy of a satellite does not depend upon t...

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  6. Assertion : Plane of a satellite always passes through the centre of e...

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  7. Assertion : Gravitational potential and gravitational potentail energy...

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  8. Assertion : One two sides of a point mass, gravitational field strengt...

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  9. Assertion : If gravitational potential at some point is zero, then gra...

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  10. Assertion : If radius of earth suddenly shrinks to half its present wi...

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  11. Assertion : The centres of two cubes of masses m(1) and m(2) are separ...

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  12. Assertion : If a particle is projected from the surface of earth with ...

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  13. Assertion : On earth's satellite, we feel weightlessness. Moon is also...

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  14. Assertion : The centre of semicircular ring of mass m and radius R is...

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  15. Assertion : If the projuct of surface area and density is same for bot...

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  16. Assertion : Areal velocity of a planet around of surface area and dens...

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  17. Assertion : Mass of the rod AB is m(1) and of particle P is m(2). Dist...

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  18. Assertion : Four point masses each of mass m are placed at points 1, 2...

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  19. Assertion : Let W(1) be the work done in taking away a satellite from ...

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  20. Assertion : Two spherical shells have masses m(1) and m(2). Their radi...

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