Question

The motion of planets in the solar system is an example of conservation of
A. Mass
B. Linear momentum
C. Angular momentum
D. Energy

Answer 1

Angular momentum is the rotational analogue of linear momentum. From Newton's second law we know that the rate of change of momentum is equal to the force applied. If force acting is zero then the rate of change of momentum will be zero. Similarly, we can say that when torque acting on a system is zero then the rate of change of angular momentum will be zero. That is angular momentum will be a constant if net torque acting on it is zero. In equation form it can be written as
$\tau = \dfrac{{dL}}{{dt}}$
Where, $\tau$ is the torque and $L$ is the angular momentum.
We know the sun and the planets together form a closed system. Energy is always conserved in a closed system.

Complete step by step answer:
In the motion of planets around the sun the angular momentum is conserved. That is the total angular momentum of the system is constant. This is because there is no external torque acting on the system.
Angular momentum is the rotational analogue of linear momentum. From Newton's second law we know that the rate of change of momentum is equal to the force applied. If force acting is zero then the rate of change of momentum will be zero. Which means linear momentum is a constant in that case.
Similarly, we can say that when torque acting on a system is zero then the rate of change of angular momentum will be zero. That is angular momentum is a constant. In equation form it can be written as
$\tau = \dfrac{{dL}}{{dt}}$
Where, $\tau$ is the torque and $L$ is the angular momentum.
When, $\tau = 0$
$\dfrac{{dL}}{{dt}} = 0$
So, angular momentum is a constant.
Kepler’s second law is a manifestation of the conservation of angular momentum. Kepler's second law or the law of equal areas says that the line joining the planet and sun sweeps the same area in equal intervals of time. This is to conserve angular momentum. Angular momentum is given as the product of mass, velocity and the radius.
$L = mvr$
Where $m$ is the mass, $v$ is the velocity and $r$ is the radius. So, if radius decreases velocity must increase to make the value of angular momentum remain the same. Similarly, when radius increases velocity must decrease. That is why the planets move faster when they are closer to the sun and slower when they are away from the sun.

A closed system is a system in which there is no exchange of matter. In a closed system there will be no outside forces. We know that according to the law of conservation of energy the total mechanical energy in a closed system will always be constant. Since, the sun along with its planets together forms a closed system we can say that total energy of the solar system is also conserved.

So the correct options are option C and option D

Note: The law of conservation of energy is not applicable in cases where the system is an open system. That is, in a system where both exchange of matter and energy takes place total mechanical energy will not be conserved. Here, we considered the solar system as closed because there is no exchange of matter from the system with the surrounding and there is no external force acting on the system.