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 the areal velocity of the 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 correct answer from the options given below.

Question

Accepted Answer

(4) Both (A) and (R) are correct and (R) is the correct explanation of (A). The Sun's pull on a planet is always along the line joining them, so it is a central force and its torque about the Sun is zero. Zero torque means the angular momentum L⃗ of the planet about the Sun never changes. The area swept in time dt is dA=1/2|r⃗×v⃗|dt=L/(2m)dt. A constant L therefore forces a constant areal velocity, which is Kepler's second law. So both statements are true and (R) is the correct explanation of (A).

Step-by-step solution

Why the other options are wrong