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Answer :
The explanation involves using Archimedes' principle to calculate the mass of the load on the barge by considering the change in submerged depths caused by the load.
Archimedes' principle states that the buoyant force acting on a body submerged in a fluid is equal to the weight of the fluid displaced by the body. To calculate the mass of the load on the barge, we can use the difference in submerged depths caused by the load. The mass of the load can be calculated by considering the change in buoyancy forces due to the increased submersion depth.
For example, consider the rectangular barge problem. Given the barge's dimensions and the depth to which it is submerged when empty versus when loaded, we can calculate the volume of water displaced in each case, and from that calculate the load mass by using the density of water.
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