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JEE Main 2025 Apr 7 Shift 2, Physics Q6: Satellite, Planetary Motion And Kepler’s Law

JEE Main2025Apr 7, Shift 2Physics
Q.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.

Reason (R) : For a central force field the angular momentum is a constant.

In the light of the above statements, choose the most appropriate answer from the options given below :

  1. A

    Both (A) and (R) are correct and (R) is the correct explanation of (A)

  2. B

    Both (A) and (R) are correct but (R) is not the correct explanation of (A)

  3. C

    (A) is correct but (R) is not correct

  4. D

    (A) is not correct but (R) is correct

Solution

Gravitational attraction from the Sun is a central force, always directed along the line joining the planet to the Sun, so its torque about the Sun is zero and the angular momentum of the planet is conserved. Reason (R) is correct.

The areal velocity is ; since both and are constants, the areal velocity is constant, which is exactly Kepler's second law stated in Assertion (A).

Thus the constancy of angular momentum, guaranteed by the central-force nature, directly implies constant areal velocity, so (R) is the correct explanation of (A).

Concept behind this question

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