Question

An earth's satellite is moving in a circular orbit with a uniform speed v. If the gravitational force of the earth suddenly disappears, the satellite will: -
(A)vanish into outer space and continue to move with velocity v in original orbit.
(B)continue to move with velocity v in original orbit
(C)fall down with increasing velocity
(D)fly off tangentially from the orbit with velocity v

Answer 1

Hint: Satellite moves in the orbit due to the influence of gravitational force. It is a text-book example of a body in a uniform circular motion although the orbits are not spherical in reality, they are elliptical but the motion can be considered as a circular motion.

Complete step by step answer:
When the satellite is moving in the orbit the motion is dragged by centripetal force and in such a motion the satellite has a constant velocity that can be found at any place in the orbit by drawing the tangent at that time. Thus, the velocity is always tangential. The body wants to go off tangentially but the gravitational force is binding it. Now if suddenly the gravitational force disappears then there is no force binding it and hence as such the body is free to move tangentially. Hence the body will move tangentially.

So, the correct answer is “Option D”.

Note:
All heavenly bodies move under the influence of mutual gravitational forces which are an example of conservative forces. The analogy of this problem is a stone tied to a circle and whirled in a vertical circle and when the thread breaks the stone flies away tangentially.