Problem-BP15 A log of radius R and uniform density lies half submerged in a lake, as shown at right. If the log is pushed very slightly down into the water and then re- leased, it will oscillate up and down. Find the frequency of this oscillation in terms of R and g. Hint: Archimedes showed that the buoyant (i.e., upward) force of a fluid on an object in the fluid is equal to the weight of fluid displaced by the object. For example, if half the log is submerged, the displaced water has weight Pwater (V/2)g where pwater is the density of water and V is the total vol- ume of the log. In equilibrium this upward force on the log must be balanced by the downward gravitational force Whogg = Plog Vg. Therefore ping = Pwater/2 in this exam- ple