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The earth revolves around the sun in an elliptical orbit. Its speed is
(A) going on decreasing continuously
(B) greatest when it is closest to the sun
(C) greatest when it is farthest from the sun
(D) constant at all the points on the orbit.

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Last updated date: 22nd Feb 2024
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IVSAT 2024
Answer
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Hint We know that in physics, angular velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time. There are two types of angular velocity: orbital angular velocity and spin angular velocity. However, the momentum of the pendulum is not conserved, because a condition for momentum conservation is that no external force should act on the system. Thus, momentum is not conserved because of gravity's action. Angular and linear momentum are not directly related; however, both are conserved. Angular momentum is a measure of an object's tendency to continue rotating. A rotating object will continue to spin on an axis if it is free from any external torque. Linear momentum is an object's tendency to continue in one direction.

Complete step by step answer
We know that angular momentum is defined as the property of any rotating object given by moment of inertia times angular velocity. It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object. It is a vector quantity that is a measure of the rotational momentum of a rotating body or system, that is equal in classical physics to the product of the angular velocity of the body or system and its moment of inertia with respect to the rotation axis, and that is directed along the rotation axis.
We know that the angular moment of the planet revolving around the sun is constant.
Now, the angular moment is given by $mvr$.
So as r is maximum v will be minimum as m is always constant.
and if r is minimum then v is maximum.

Option B is the correct option.

Note: We call this quantity angular momentum. The symbol $\pm $ indicates that angular momentum has a positive or negative sign to represent the direction of rotation; for example, in a given problem, we could choose to represent clockwise angular momenta as positive numbers, and counter clockwise ones as negative. Angular velocity and angular momentum are vector quantities and have both magnitude and direction. The direction of angular velocity and angular momentum are perpendicular to the plane of rotation. The angular momentum of an object moving in a circle with radius 'r' is the product of the mass, velocity or speed of rotation, and the radius of the circle. Newton's first law tells us that unless there is a net torque, or twisting force, on the body that is rotating, angular momentum will be conserved.