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. [cite: 55] Reason (R) For a central force field the angular momentum is a constant. [cite: 56] In the light of the above statements, choose the most appropriate answer from the options given below: [cite: 57]

### Related Formula fracdAdt = fracL2m$$\frac{dA}{dt} = \frac{L}{2m}$$ [cite: 684] ### Core Logic Kepler's Second Law state that the areal velocity fracdAdt$\frac{dA}{dt}$ is directly proportional to the angular momentum L$L$ of the planet[cite: 55, 684]. Because the gravitational force between the Sun and the planet acts strictly along the line joining their centers (a central force field), its torque vectau = vecr times vecF = 0$\vec{\tau} = \vec{r} \times \vec{F} = 0$[cite: 56, 686]. Since torque is zero, the angular momentum L$L$ remains completely constant over time[cite: 686]. As a consequence, fracdAdt = textconstant$\frac{dA}{dt} = \text{constant}$[cite: 55, 684]. Both statements are true and (R) is the correct explanation of (A)[cite: 63]. ### Pattern Recognition Areal velocity constancy is a direct geometric manifestation of the conservation of angular momentum under any central force field[cite: 55, 56, 686]. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Gravitation