Assuming you're using
this jug, you've got 1 litre of space. Balls don't space-fill, so they have to have less than a decilitre of volume each. The puzzle doesn't specify a minimum size beyond what can be read and manipulated, and doesn't rule out the use of a microscope to do this, so your minimum size may be around 10 microns in diameter. This gives us quite a range of possibilities, from 10 microns up to maybe 40 millimetres. We also don't know the density, but can make assumptions: the balls have higher density than air and are not undergoing radioactive decay at high enough rate to prevent you completing this weird activity you have invented. Let's call that 2 to 15 kg/m
3. This gives a mass range of 1*10
-15 to 5*10
-4 kg. The bottom-most ball in the jug has to move 250mm to be moved into the jug. The time available (
x) in which to do this is decreasing.
1kg of TNT yields 4184000 J of energy. Assuming that the jug is unable to withstand the release of this much energy within in, a point will come when:
4.184*10
6 < 0.5 * 1*10
-15 * (250mm/
x)
2 * c / ( c - (250mm/
x)) for the tiny "dust particle" balls
or
4.184*10
6 < 0.5 * 5*10
-4 * (250mm/
x)
2 * c / ( c - (250mm/
x)) for the larger "ping pong" balls
Determining the value range for
x is left as a rather dull exercise for the reader.
When
x is more than the time between insertions of ten balls into the jug, the jug explodes.
If the jug is stronger, the lower limit on
x will be smaller. Continuing to the point where
x reaches the reciprocal of 1.2 GHz is not recommended.
At
x = 1ns, for example,
0.5 * 1*10
-15 * (250mm/
x)
2 * c / ( c - (250mm/
x))
= 0.5 * 1*10
-15 * (250mm/1ns)
2 * c / ( c - (250mm/1ns))
= 5*10
-16 * (2.5*10
8)
2 * c / ( c - 2.5*10
8)
= 488498133082605467.9 J
= 116.754 MT TNT,
and at that point the jug doesn't really matter.
Disclaimer: I'm sober, so the maths is a load of bollocks and I'm out by several orders of magnitude, I know, but you still don't want to be throwing ten balls into a jug in under one nanosecond, do you?
Oh, Willie McBride, it was all done in vain.