Buoyant Force and Archimedes' Principle in Fluids

Physics · Mechanical Properties Of Fluids · NEET

When you put an object in a fluid, the fluid pushes it up with a force called the buoyant force (upthrust). Archimedes' principle says this upthrust equals the weight of the fluid the object pushes aside (displaces): F_buoyant = rho_fluid x V_displaced x g. Memory hook: "an object feels lighter in water because water pays back the weight it had to move out of the way."
Buoyant Force and Archimedes' Principlefluid surfaceobjectWeight W (down)Buoyant F_b (up)F_b = rho_fluid x V_displaced x gApparent weight = W - F_bFloat: rho_object <= rho_fluid
The deeper bottom face feels more pressure than the top, giving a net upward buoyant force F_b equal to the weight of displaced fluid; the object's apparent weight is its real weight minus this upthrust.

Your doubts, answered

Why does a body feel lighter when it is inside water?

Two forces act on it. Its real weight W pulls it down. The fluid pushes it up with the buoyant force F_b. Your hand or the spring balance only has to support the difference. So apparent weight = W minus F_b. The body did not lose mass, it just gets an upward help from the fluid, so it feels lighter.

Does the buoyant force depend on the object's weight or on the fluid?

It does not depend on the object's own weight or what the object is made of. From F_b = rho_fluid x V_displaced x g, it depends only on the fluid's density (rho_fluid), the submerged volume (V_displaced), and g. A steel block and a wooden block of the same submerged volume in the same water feel the same upthrust, even though their weights are very different.

What exactly is the 'volume of fluid displaced'?

It is the volume of the object that is actually inside the fluid. If the object is fully submerged, V_displaced equals the object's full volume. If it floats, V_displaced is only the part under the surface, not the whole object. This is why a floating ship displaces water equal to its own weight, not equal to its full volume.

How do I decide if an object will float or sink?

Compare densities. If the object's density is less than the fluid's density, it floats (like ice in water). If it is more, it sinks (like a coin). If they are equal, it stays wherever you put it. For a floating body the rule is: weight of object = weight of fluid displaced, so rho_object x V_object = rho_fluid x V_submerged.

Is upthrust the same as buoyant force?

Yes. Upthrust, buoyancy, and buoyant force all mean the same upward push a fluid gives to any object placed in it. It comes from pressure being larger at the bottom of the object than at the top, because pressure increases with depth (P = P0 + rho g h).

⚠️ The NEET trap
Buoyant force depends on the weight or density of the object, so a heavier object gets more upthrust.
Buoyant force depends only on the fluid density, the submerged volume, and g: F_b = rho_fluid x V_displaced x g. Two objects with the same submerged volume in the same fluid get the same upthrust, whatever their mass.
🧠 NTA loves giving a 'heavy iron' vs 'light aluminium' pair of the same size fully dipped in water and asking which feels more upthrust. Trap answer: the heavy one. Correct answer: both feel the same upthrust, because volume, not weight, decides F_b.

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Frequently asked

What is Archimedes' principle in one line?

When a body is fully or partly dipped in a fluid, the fluid pushes it up with a force equal to the weight of the fluid it displaces.

What is the formula for buoyant force?

F_buoyant = rho_fluid x V_displaced x g, where rho_fluid is the fluid density, V_displaced is the submerged volume, and g is the acceleration due to gravity.

What is apparent weight?

Apparent weight is what a spring balance reads when the object hangs in a fluid. Apparent weight = real weight minus buoyant force = W minus rho_fluid x V x g.

Why does the buoyant force act upward?

Pressure in a fluid increases with depth. The bottom face of the object is deeper, so it feels more pressure than the top face. This extra upward push at the bottom is the net buoyant force, and it always acts upward.

What is the condition for a body to float?

A body floats when its weight equals the buoyant force at the surface, which means rho_object x V_object = rho_fluid x V_submerged. In short, its average density must be less than or equal to the fluid density.

Does buoyant force change with depth for a fully submerged object?

No. Once the object is fully submerged, its displaced volume stays the same, so F_b stays the same at any depth (assuming the fluid density does not change). It does not keep increasing as you push it deeper.