A rectangular "boat" (the horizontal sides are L each, the depth is h = L/2) is made of a think weightless walls and partially filled with mercury. The height of mercury is such that the boat is floating with two-thirds (2/3) of the boat above the water level. The specific gravity of mercury is 13.6.
(a). Determine the depth h of the mercury inside the box.
(b). If the box is shaken, the waves appear. If the wavelength id the waves is L/3, determine the speed of the waves.
(c). A very small circular hole (diameter d)appears at the bottom of the boat (assuming that the hole is located right at the bottom. Determine the flow rate.
(d). If the boat (without the hole) is pushed down below the equilibrium position and released, describe the motion of the boat.