Floating Condition — Balance of Forces When a body is placed on or in a liquid, it will float if which of the following is true?

Introduction:
Floating and sinking are governed by Archimedes' principle and the force balance between weight and buoyant force (upthrust). Understanding this helps in ship design and stability assessments.

Given Data / Assumptions:

• Body partially or fully submerged in a static liquid.
• Forces considered: weight W and buoyant force B.
• Equilibrium, negligible wave motion.

Concept / Approach:
Archimedes: Upthrust equals weight of displaced liquid. A body floats in static equilibrium when net vertical force is zero and restoring moments are adequate for stability. That requires B = W for neutral vertical equilibrium.

Step-by-Step Solution:
Write vertical force balance: Sum F_z = B - W.For floating without acceleration, Sum F_z = 0 ⇒ B = W.If B > W, the body accelerates upward until displacement reduces so that B = W; if B < W, it sinks until new displacement restores B = W or it rests on bottom.

Verification / Alternative check:
Consider a block of density rho_b in water of density rho_w. Fraction submerged f ≈ rho_b / rho_w so that displaced water weight equals block weight; this reproduces B = W at floatation.

Why Other Options Are Wrong:
B > W: transient upward motion, not static float condition.
B < W: sinking occurs until support or new equilibrium is found.
None of the above: incorrect because B = W is the correct float criterion.

Common Pitfalls:
Confusing stability (metacentric height) with simple float condition; ignoring density variations with temperature/salinity; overlooking trapped air effects.

Final Answer:
gravitational force is equal to the upthrust of the liquid