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:
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:
- (A)Both (A) and (R) are correct and (R) is the correct explanation of (A)✓ Correct
- (B)Both (A) and (R) are correct but (R) is not the correct explanation of (A)
- (C)(A) is correct but (R) is not correct
- (D)(A) is not correct but (R) is correct
Answer: (A)
Solution
For a central force the torque about the centre vanishes, so the angular momentum stays constant. The areal velocity of the planet is , which is therefore also constant; this is Kepler's law of equal areas. Both statements are correct, and the constancy of angular momentum is precisely why the areal velocity is constant, so the reason correctly explains the assertion.
JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Single correct option