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Question: If the orbital velocity of the moon is increased by \(41.4\,\% \) of its present value, then (A) ...

If the orbital velocity of the moon is increased by 41.4 %41.4\,\% of its present value, then
(A) the moon will orbit around the earth with a double velocity
(B) the radius of the moon’s orbit will become double
(C) the moon will become a stationary satellite
(D) the moon will leave its orbit and escape into space

Explanation

Solution

The moon will rotate around the earth by means of the gravitational force between the earth and the moon. When the moon rotates around the earth it must keep the constant velocity for the rotation around the earth. If the velocity is changed then the gravitational force changes.

Complete step by step answer:
When the moon revolves around the earth, there is a gravitational force between the earth and the moon. The gravitational force attracts the moon and then by the velocity of the moon it keeps rotating around the earth by the imaginary circle called an orbit. During this rotation of the moon around the earth, the moon must keep the constant velocity for the rotation, it is also called as the uniform circular motion, which indicates that when the object wants to move in the fixed circular path or constant radius, then the velocity is constant. If the velocity of the revolving object changes, then the centripetal force will change and the radius of the path of the rotation will change.

As the orbital velocity of the moon is increased by the 41.4 %41.4\,\% , then the radius of the circular orbit will increase, if the gravitational force is capable of attracting the moon in the increased orbit radius, then the moon will rotate in the new circular orbit. If the gravitational force is not enough to attract the moon, then the moon will leave its orbit and escape into space.

Hence, the option (D) is the correct answer.

Note:
The solution to this question is also given by the analytical method by using the formula of the uniform circular motion. By this equation, the force is directly proportional to the velocity and the velocity is inversely proportional to the radius. By this equation also the solution can be determined.