Assertion : For the planets orbiting around t | vedclass

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(A) The net torque acting on the planet orbiting the sun is zero because the gravitational force is a central force,i.e.,$	au = 0$.According to the p

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If both $Assertion$ and $Reason$ are correct and the $Reason$ is a correct explanation of the $Assertion$.

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(A) The net torque acting on the planet orbiting the sun is zero because the gravitational force is a central force,i.e.,$	au = 0$.According to the principle of conservation of angular momentum,$\frac{dL}{dt} = 	au$.Since $	au = 0$,the angular momentum $L$ remains constant.Thus,the $Reason$ statement is correct.For a planet,$L = mvr = 	ext{constant}$. As the distance $r$ between the sun and the planet changes (elliptical orbit),the linear speed $v$ must change to keep $L$ constant. Consequently,the kinetic energy $K.E. = \frac{1}{2}mv^2$ also changes.Similarly,$L = mr^2\omega = 	ext{constant}$. As $r$ changes,the angular speed $\omega$ must change.Therefore,the $Assertion$ statement is correct,and the $Reason$ provides a correct explanation for it.

Column-$I$	Column-$II$
$(1)$ Kepler's first law	$(a)$ Law of periods
$(2)$ Kepler's second law	$(b)$ Law of orbits
$(3)$ Kepler's third law	$(c)$ Law of areas

$Assertion$ : For the planets orbiting around the sun,angular speed,linear speed and $K.E.$ change with time,but angular momentum remains constant.
$Reason$ : No torque is acting on the rotating planet. So its angular momentum is constant.

Similar Questions

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Kepler's first law $(a)$ Law of periods

$(2)$ Kepler's second law $(b)$ Law of orbits

$(3)$ Kepler's third law $(c)$ Law of areas

If the radius of the Earth's orbit is made $\frac{1}{4}$ of its original value,the duration of a year will become:

$A$ planet has an orbital radius twice that of the Earth's orbital radius. The time period of the planet is .......... $years$.

If a satellite orbiting the Earth is $9$ times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $= 27 \text{ days}$ and gravitational attraction between the satellite and the moon is neglected.

The figure shows an elliptical orbit of a planet of mass $m$ about the sun $S.$ The shaded area $SCD$ is twice the shaded area $SAB.$ If $t_1$ is the time taken for the planet to move from $C$ to $D$ and $t_2$ is the time taken to move from $A$ to $B,$ then:

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$Assertion$ : For the planets orbiting around the sun,angular speed,linear speed and $K.E.$ change with time,but angular momentum remains constant.$Reason$ : No torque is acting on the rotating planet. So its angular momentum is constant.