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 most appropriate answer from the options given below:
Answer: (A) Both (A) and (R) are correct and (R) is the correct explanation of (A)
A central force has no torque about the centre, so the planet's angular momentum $L$ is constant. The areal velocity is
$$\frac{dA}{dt} = \frac{L}{2m}$$
so it is constant too (Kepler's second law). Both statements are correct and R explains A.
Solution by Sreeraj P, M.Sc Physics