A small, square plank of oak floats in a beaker half full of water. The piece of oak is...

A small, square plank of oak floats in a beaker half full of water. The piece of oak is 6.0 cm on a side and 3.0 cm thick and floats on its side as shown in Figure P10.80. (a) Find the location of the plank’s center of mass with respect to the water’s surface. (b) A very light vegetable oil is poured slowly into the beaker so that the oil floats on the water without mixing and until the oak plank is a few centimeters below the surface of the oil. If the density of the oil is what is the new position of the center of mass of the plank with respect to the water’s surface?