Question

Question:A small piece of steel is tied to a block of wood. When the wood is placed in a tub of water with the steel on top, half of the block is submerged. Now the block is inverted so that the steel is under water. (i) Does the amount of the block submerged (a) Increase (b) Decrease (c) Remain the same? (ii) What happens to the water level in the tub when the block is inverted? (a) It rises. (b) It falls. (c) It remains the same.

Short answer

1. The amount of the block submerged will Decrease.
2. The water level in the bucket remains same.

Step-by-step solution

Step 1: Archimedes’ principle

When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force. According to Archimedes’s principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:

B =${\rho }_{Fluid}g{V}_{disp}$

Where V_disp the volume of fluid is displaced and ${\rho }_{Fluid}$is the density of the fluid.

Concept

Initial state: Since the wood steel combination floats, the buoyant force excreted on the water must be equaled to the weight. This buoyant force is equals to the weight is placed water. In this case the buoyant force is supplied only by the block.

Final state: Since the steel fully submerged into water, it supplies part of buoyant force and the wood block supplies the rest, therefore the block would float higher in water.

Step 3(i): Find the amount of the block does submerged

From initial and final state it is conclude that:

The block would float higher in the water.

The amount of the block submerged will Decrease.

Hence option (b) will become correct.