A ferry boat has an internal volume of 1 m ^3 and a weight of 50 kg . Neglecting the thickness of the wood, determine the fraction of the boat's volume that is immersed in water.

Step-by-step solution

By the principle of flotation, the weight of the boat is balanced by the buoyant force. mg = V_ in _w g where m = 50 kg is the mass of the boat, V_ in is the immersed volume, and _w = 1000 kg/m ^3 is the density of water. 50 = V_ in 1000 V_ in = 50 1000 = 1 20 m ^3 The total volume of the boat is V = 1 m ^3 . The fraction of the boat's volume immersed in water is V_ in V = 1/20 1 = 1 20 .