A raft of density 700 kg/m³ has a surface area of 7.0 m² and a volume of 0.7 m³.What depth does it sink into water of density 1000 kg/m³? A)10 cm B)0.7 cm C)0.7 m D)7 m E)7 cm

Question

Quizplus · Accepted Answer

The buoyant force on the raft is equal to the weight of the water displaced by the raft. The weight of the water displaced is equal to the density of the water times the volume of the water displaced. The volume of the water displaced is equal to the volume of the raft. Therefore, the buoyant force on the raft is equal to the density of the water times the volume of the raft. The weight of the raft is equal to the density of the raft times the volume of the raft. Therefore, the raft will sink into the water until the buoyant force on the raft is equal to the weight of the raft. The depth to which the raft sinks is equal to the volume of the raft divided by the surface area of the raft. Therefore, the depth to which the raft sinks is 0.7 m / 7.0 m^2 = 0.1 m = 10 cm.

A Raft of Density 700 Kg/m3 Has a Surface Area

A Raft of Density 700 Kg/m³ Has a Surface Area