A boat containing some pieces of material is floating in a pond. What will happen on the level of waer in the pond, if out unloading the pieces in the pond, the pieces (a) float (b) sink?

A boat containing some pieces of material is floating in a pond. What

1.	A boat containing some pieces of material is floating in a pond. What will happen on the level of waer in the pond, if out unloading the pieces in the pond, the pieces (a) float (b) sink?
Answer» Solution :If M is the mas of boat and m is the mass of pieces in it, then initially as the system in floating, `m+m=v_(D)rho_(w)` i.e. the system displaces water `V_(D)=M/(rho_(w))+m/(rho_(w))` ….1 When the pieces are dropped in the POND, the boat will still float, so it displaces water `M=V_(1)rho_(w)` i.e. `V_(1)=(M//rho_(w))` a. Now if the uploaded pieces floats in the pond, the water displaced by them `m=V_(2)rhio_(w)` i.e. `V_(2)=(m//rho_(w))` So the total water displaced by the boat and the floating pieces `V_(1)+V_(2)=M/(rho_(w))+m/(rho_(w))` .......2 which is same as the water displaced by the floating system initially (EQN, 1) so the LEVEL of waterin the pond will remain unchanged. b. NOw if the unloaded pieces sik the water displaced by them will be equal to their own volume, i.e. `V_(2)^(1)=m/(rho)""\|"as" rho=m/V\|` and so in this situation the total volume of water diaplced by boat and siking pieces will be `V_(1)+V_(2)^(1)=(M/(rho_(w))+m/(rho))` ........3 Now as the pieces are sinking `4hogtrho_(w)` so this volume will belesser than initial water displaced by the floating system (Eqn 1) so the level of water in the pond will GO down (or fall).