Assertion (A): Angular speed,linear speed,and | vedclass

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(A) According to Kepler's second law,the areal velocity of a planet is constant,which implies that the angular momentum $(L)$ of the planet remains co

Vedclass · Accepted Answer

Both $A$ and $R$ are true and $R$ is a correct explanation for $A$.

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(A) According to Kepler's second law,the areal velocity of a planet is constant,which implies that the angular momentum $(L)$ of the planet remains constant.The torque $(	au)$ acting on a planet due to the gravitational force of the sun is given by $	au = r 	imes F$. Since the gravitational force is a central force acting along the line joining the planet and the sun,the torque is zero $(	au = 0)$.From the relation $	au = \frac{dL}{dt}$,if $	au = 0$,then $\frac{dL}{dt} = 0$,which means $L$ is constant.As the planet moves in an elliptical orbit,its distance from the sun changes,causing its linear speed,angular speed,and kinetic energy to vary with time.Therefore,both Assertion $(A)$ and Reason $(R)$ are true,and Reason $(R)$ is the correct explanation for Assertion $(A)$.

Assertion $(A)$: Angular speed,linear speed,and kinetic energy change with time,but angular momentum remains constant for a planet orbiting the sun.
Reason $(R)$: Angular momentum is constant as no external torque acts on the planet.

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Assertion $(A)$: Angular speed,linear speed,and kinetic energy change with time,but angular momentum remains constant for a planet orbiting the sun.Reason $(R)$: Angular momentum is constant as no external torque acts on the planet.