it is interesting that this question has attracted so many responses. I have two ways of answering this.
Firstly, the string has no relevance to the balance. The balance does not "see" anything else except weight in the set-up. The ping pong ball on the left side adds only its own weight as far as the balance is concerned. The steel ball displaces its volume of water (this weight equals the boyance force). Hence, there is a greater downward force on the RHS. This means that the right side will tip.
Secondly, one can view the situation in terms of added water. On the left side, the ping pong ball would float without the string which is just a distractor in this situation (the forces due to the string are internal to the system). The ping pong ball displaces the amount of water which equals its weigh. This is "under the water" volume if the ping pong ball were floating. So one can image that this the amount of water is poured to the LHS whereas the water poured to the RHS is equal to the volume of the steel ball. Since there is more water added to the RHS, the right side will tip.
Cheers,
Antti
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