A lead piece is fastened to the top surface of a cubical block of wood weighing 200 g . Determine the mass of the lead piece if the block floats with its upper surface just dipping into water. The specific gravity of wood is 0.8 and that of lead is 11.3 .

Step-by-step solution

Let the mass of the wood block be m_w = 200 g . The specific gravity of wood is 0.8 , so its density is _w = 0.8 g/cm ^3 . The volume of the wood block is: V_w = m_w _w = 200 0.8 = 250 cm ^3 The block floats with its upper surface just dipping into the water. This means the entire volume of the wood block is submerged in the water. Since the lead piece is fastened to the top surface, it remains above the water level and does not displace any water. The buoyant force is provided entirely by the submerged wood block.