Question

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 :

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

Hint:

When dealing with Assertion-Reason type questions, first verify the correctness of each statement individually. Then, try to establish a causal link between the Reason and the Assertion. Ask yourself: "Does the Reason logically explain why the Assertion is true?" In this case, the conservation of angular momentum (due to the central nature of gravity) is the direct cause of the constant areal velocity.

Answer 1

The Correct Option is A

To address the provided assertion and reason, we will analyze each statement individually and then their relationship:

1. Assertion (A) Analysis: "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."
   • This assertion is a direct consequence of Kepler's Second Law of Planetary Motion. This law posits that a line connecting a planet to the Sun covers equivalent areas in equivalent time durations. Consequently, the rate at which area is swept (areal velocity) remains constant for a planet in orbit. Therefore, Assertion (A) is valid.
2. Reason (R) Analysis: "For a central force field the angular momentum is a constant."
   • A central force field is defined by forces acting along the line connecting two bodies, with magnitude dependent solely on their separation distance, exemplified by the gravitational force between a planet and the Sun.
   • Within a central force field, angular momentum is conserved because no external torque acts upon the system. This conservation principle validates Reason (R).
3. Assertion and Reason Connection:
   • The constancy of areal velocity, as stated in Assertion (A), is directly attributable to the conservation of angular momentum, as outlined in Reason (R). Consequently, Reason (R) accurately explains Assertion (A).

The accurate conclusion is: Both (A) and (R) are correct, and (R) provides the correct explanation for (A).