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.