I’m sitting in a boat in a pool. In the boat with me is a cannonball. What happens to the level of the pool if I take the cannonball out of the boat and drop it into the pool? Does the level increase, decrease or stay the same?
The level decreases.
Let Mb be the mass of the boat and Mc be the mass of the cannonball. Let the density of water be Dw. An object floating in water displaces its own mass in water. So the volume of the water displaced is initially (Mb + Mc)/Dw. If the cannonball is dropped out of the boat, the amount of water displaced is Mb/Dw + Vc, where Vc is the volume of the cannonball. Vc can be calculated as the mass of the cannonball divided by its density, or Vc = Mc/Dc. This means that the amount of water displaced after the cannonball is thrown out is Mb/Dw + Mc/Dc. This is almost the same as the formula we had for when the boat contained the cannonball, except that we have Dc instead of Dw. Dc is much higher than Dw because we know that cannonballs sink in water. Thus, a boat with an overboard cannonball displaces less water than a boat containing a cannonball, so the water level must decrease.
Solution
