As astronaut orbiting the earth in a circular orbit \(120 \mathrm{~km}\) above the surface of earth, gently drops a spoon out of space-ship. The spoon will (A) Fall vertically down to the earth (B) move towards the moon (C) Will move along with space-ship (D) Will move in an irregular wav then fall down to earth

When the astronaut gently drops the spoon, it experiences the same gravitational force as the astronaut and the spaceship, since they are in the same orbit. There is no other significant force acting on the spoon.

Gravity curves the path of the spoon due to the attractive force between the Earth and the spoon. Since both the astronaut and the spoon are in the same orbit, they continue to experience the same gravitational force. This means that their motion will be affected by gravity in a similar way.

(A) Fall vertically down to the earth: This is incorrect because, although gravity is pulling the spoon towards the Earth, the centripetal force due to the circular orbit prevents it from falling directly down to the surface. (B) Move towards the moon: This is incorrect because the moon's gravity does not have a significant impact on the spoon's motion in this case. (C) Will move along with space-ship: This is correct because the spoon continues to experience the same gravitational force as the spaceship, which keeps it in the same orbit and parallel to the motion of the spaceship. (D) Will move in an irregular wave then fall down to earth: This is incorrect because the spoon does not experience any other force that would make its movement irregular, or cause it to fall down to the Earth.

Based on our analysis, the correct answer is (C): The spoon will move along with the spaceship. This is because the spoon and the spaceship are in the same orbit and experience the same gravitational force, causing them to have the same motion.