Question 04/01
BALL IN A BOX
A hollow cylinder, with its both ends closed, is filled
with a fluid and is at rest in the space. Inside the cylinder
there is a small hard
ball with a density equal to the density of the fluid.
The ball is initially at rest and is close to the center of
one of the lids (let's call it a "front lid"). The cylinder
suddenly gains an acceleration a and then moves with that
constant acceleration (the motion is non-relativistic although
the magnitude of the acceleration can be large). The direction
of the acceleration is along the axis of the
cylinder pointing from the "rear lid" to the "front lid".
If viewed from the reference frame of the cylinder at the very
first moment after the acceleration appears the ball will, of
course, start gaining speed in the direction toward the "rear lid".
The question is: will the ball hit the rear lid?
This question was created by Princeton Ph.D. students
Akakii Melikidze, Ilya Nemenman and Lesik Motrunich.
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