Which will hit the ground first?

[Goongyae]

Which would hit the ground first if dropped from a certain height onto the moon, where there is no air resistance? A wooden ball 1 cm in radius, or a lead ball 1 cm in radius?

[berkeman]

Which would hit the ground first if dropped from a certain height onto the moon, where there is no air resistance? A wooden ball 1 cm in radius, or a lead ball 1 cm in radius?

What are your thoughts? Where is this question from?

[Goongyae]

Answer: the lead ball would hit first.

The moon's acceleration toward the lead ball would be greater than it would be toward the wooden ball. Thus the lead ball and the moon would collide in a shorter time.

[ashishsinghal]

Answer: the lead ball would hit first.

The moon's acceleration toward the lead ball would be greater than it would be toward the wooden ball. Thus the lead ball and the moon would collide in a shorter time.

Do you really need to go into so many considerations while solving a brainteaser?

[berkeman]

Do you really need to go into so many considerations while solving a brainteaser?

Well I for one did not think of that angle. What do brainteasers mean to you?

[BobG]

Answer: the lead ball would hit first.

The moon's acceleration toward the lead ball would be greater than it would be toward the wooden ball. Thus the lead ball and the moon would collide in a shorter time.

Not with the way the question was worded.

Both the lead ball and the wooden ball would accelerate towards the Moon at the same rate. The Moon's acceleration towards the two balls would depend on the combined mass of the wooden ball and the lead ball. The Moon can only have one net acceleration for any given instant of time. If the two balls are moving towards the Moon at the same rate, then the Moon can't move faster towards the lead ball than the wooden ball.

Unless.........

The two balls are dropped simultaneously from opposite sides of the Moon - something that wasn't specified and normally wouldn't be assumed from the original wording of the question. In the latter case, the Moon's net acceleration would be towards the lead ball and away from the wooden ball, meaning the Moon-lead ball collision would take place before the Moon-wooden ball collision.

[Gokul43201]

Unless.........

The two balls are dropped simultaneously from opposite sides of the Moon...They don't have to be dropped from opposite sides. Any sufficiently large separation between the balls will result in the moon's acceleration vector pointing just a little bit more towards the lead ball than the wooden one. With a cow-shaped moon (i.e., perfectly spherical), you could drop the balls from arbitrarily close initial positions and "see" the lead ball land first.

PS: One must, of course, neglect the curvature of the moon's orbit for this experiment, or account for it carefully.