A 9000 Kiogram boat floats in a lake. If half of the boat is submerged, which of the following is true:
1. The boat is less dense than the water in the lake.
2. The buoyant force is less than half the weight of the boat.
3. The buoyant force is greater than the total weight of the boat.
4. The buoyant force is equal to the weight of the water displaced by the boat or
5.all of the above statements a through d are all true
6. none of the above statements a through d are all false
1, true
2. the buoyant force EQUALS the weight if it floats. so false
3. same answer as 2
4. Yes
To answer this question, we need to understand the concept of buoyancy and the relationship between the weight of an object and the buoyant force acting on it.
1. To determine if the boat is less dense than the water, we need to compare their densities. Density is the ratio of an object's mass to its volume. Since the boat floats and only half of it is submerged, it means that the weight of the water displaced by the boat is equal to the buoyant force acting on it. This implies that the density of the boat is less than the density of the water, so statement 1 is true.
2. The buoyant force is the upward force exerted by a fluid on an object submerged or floating in it. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object. In this case, since only half of the boat is submerged, the buoyant force acting on it is equal to the weight of the water displaced by the half submerged boat. Therefore, statement 2 is true.
3. The buoyant force is not greater than the total weight of the boat. The buoyant force can never be greater than the weight of the object itself. It can only be equal to or less than the weight. So, statement 3 is false.
4. According to Archimedes' principle, the buoyant force is equal to the weight of the water displaced by the boat. Since half of the boat is submerged, the buoyant force acting on it is equal to the weight of the water displaced by the half submerged boat. Therefore, statement 4 is true.
Based on the explanations above:
- Statement 1 is true.
- Statement 2 is true.
- Statement 3 is false.
- Statement 4 is true.
Therefore, the correct answer to the question is option 6: none of the above statements a through d are all false.