A cylindrical log of wood, length 1.50m and radius 12cm, has a uniform density of 0.60gcm−3. A narrow, vertical cavity (initially filled with air) is drilled completely through the center of the log along its axis. Lead shot of density 11.3gcm−3 is gradually poured into the cavity until the log, with the cavity now sealed, is just neutrally buoyant in fresh water.
(a) Calculate the original mass of the undrilled log.
(b) Determine the mass of lead shot that must be added so that the modified log is neutrally buoyant in fresh water.
(c) After sealing the cavity, the log–lead system is placed in seawater of density 1.025gcm−3. Calculate the percentage of the log’s volume that will be submerged at equilibrium in seawater.
(d) Suppose the same amount of lead shot had been fastened to the exterior of the undrilled log instead of being placed inside. Qualitatively discuss one practical reason why placing the shot inside the cavity is preferable for achieving stable neutral buoyancy.