Buoyant beaker balls

The January 2016 “Figuring Physics” column¹ compares the weight of two beakers containing the same amount of water, with a Ping-Pong ball tethered to the bottom of the left one and a lead ball held submerged in the right one by a string tied to an external support. The solution² can be used to show that the weight of the right beaker would be the same as that of a beaker filled to the same depth of water having no ball in it. Consequently that would also be the weight of the left beaker if, rather than being tethered to the bottom, the Ping-Pong ball were tethered to an externally supported arm that dips into the water below the ball as in Fig. 1. (A simple way to understand this fact is that in all three illustrated cases the scale reads the weight of the glass plus...