If an object is floating in a fluid, its weight *W*_{o} must be exactly balanced by upthrust *U*. Since upthrust is equal to the weight of the displaced fluid *W*_{f},

This is called the law of floatation. Obviously, this law applies only when an object is floating. It does not apply when an object is sunk. It also does not apply when forces other than *W*_{o} and *U* are involved. (e.g. an object is tied to a string and lowered into the fluid)

We can write *W*_{o} and *W*_{f} as and respectively, where *V*_{o} is the total volume of the object, and *V*_{f} is the volume of the displaced fluid.

Object is less dense than fluid

If , then the object will float with of its volume submerged.

Object is denser than fluid

If , then the object will sink. This is because even when the object is already fully submerged, the volume of fluid it can displace is only *V*_{o}. The upthrust it can achieve is only , which is obviously smaller than , which is the weight of the object *W*.

Object has the same density as the fluid

If , then object can hover at equilibrium **at any depth** in the fluid. As long as the object is fully submerged, the weight of the displaced fluid is exactly equal to the weight of the object.

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**Illustrations**

How High do they Float

**Concept Test**

0606

**Demonstrations**

Sink the Boat

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