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(A) Kepler's second law states that the radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time. This implies that th

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

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(A) Kepler's second law states that the radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time. This implies that the areal velocity $\frac{dA}{dt}$ is constant.The areal velocity is given by the formula $\frac{dA}{dt} = \frac{L}{2m}$,where $L$ is the angular momentum and $m$ is the mass of the planet.Since the gravitational force exerted by the Sun on the planet is a central force,the torque $	au$ acting on the planet about the Sun is zero $(	au = \vec{r} 	imes \vec{F} = 0)$.Because the torque is zero,the angular momentum $L$ remains constant over time.Since $L$ and $m$ are constant,the areal velocity $\frac{dA}{dt}$ is also constant.Therefore,Assertion $(A)$ is correct,and Reason $(R)$ provides the correct physical explanation for it.

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