A cubical float, measuring 1.2 m on each side, weighs 182 kg and is anchored by a concrete block weighing 682 kg in air. When the chain connected to the concrete is taut, 22.5 cm of the float is submerged.

What rise in the water level will lift the concrete off the bottom? Note: Concrete has a density of 2400 kg/m³.

Question

20-04-2025
Engineering

College

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A cubical float, measuring 1.2 m on each side, weighs 182 kg and is anchored by a concrete block weighing 682 kg in air. When the chain connected to the concrete is taut, 22.5 cm of the float is submerged.

What rise in the water level will lift the concrete off the bottom? Note: Concrete has a density of 2400 kg/m³.

Answer :

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Final answer:

This physics problem uses Archimedes' principle to calculate the conditions under which a concrete block, anchored to a floating cube, is lifted off the bottom. It involves understanding the relationship between weight, volume, and density of the block and the displacing water.

Explanation:

The question involves the principles of buoyancy and Archimedes' principle to understand how a cubical float and a concrete block interact in water. When the float is submerged by 22.5 cm due to the weight of the concrete block, it displaces a certain volume of water equivalent to the weight of the submerged part of the float. The weight of the displaced water must equal the total weight of the float and block for the block to be lifted off the bottom. To calculate the rise in water level required to lift the concrete, we need to determine the volume of water that needs to be displaced, which is dictated by the weight of the concrete block compared to its volume (derived from its density) and understanding that the float itself has a limit to how much weight it can support without being completely submerged.