Fluid Mechanics: Conceptual Doubts Cleared (2)

Question

A block of wood floats half-submerged in water. If the same block is placed in a fluid of density $0.6$ g/cm³, will it float higher, lower, or sink? Many students answer “sink” because the new fluid is less dense than water. Why is that often wrong?

Solution — Step by Step

Why This Works

The rule for floating: a block floats if and only if its density is less than the fluid’s density. The new fluid is denser than the wood ($0.6 > 0.5$), so floating still happens — just with a larger submerged fraction.

The trap “less dense fluid → sink” is only true if the fluid becomes less dense than the wood. Here, the fluid is still denser than the wood.

Alternative Method — Force Balance Directly

Write the buoyant force $F_b = \rho_\text{fluid} \cdot V_\text{submerged} \cdot g$ and set it equal to weight $\rho_\text{wood} \cdot V \cdot g$. Cancel $g$, divide both sides by $V$, and we land on the same fraction formula.

This is the more general method — works even for objects with non-uniform density (as long as they are in equilibrium).

Common Mistake

The big mistake: assuming “less dense fluid means object sinks.” Sinking happens only when the fluid is less dense than the object — not just less dense than water.