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In our textbook it is said that if buoyant force is W and weight of an object is w then

  1. object will float when W > w

  2. object will be submerged and it wont float(it will sink) when W < w

  3. object will float but it will be totally submerged when W = w.

Is it a misconception (point no.3)?

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    $\begingroup$ Why do you think point 3 is a misconception? At the moment this isnt a particularly well written question so you may want to include what you struggle with conceptually with point 3. $\endgroup$ – Sean Nov 8 '14 at 13:25
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    $\begingroup$ I think "float" in point three means "goes neither up nor down". Forces are balanced, and it just sits there. Normally "float" means "stay on top of the water, partially submerged". That's what it means in part 1. The use of that word in part 3 is inconsistent with that usage in part 1. Definite cause for confusion. $\endgroup$ – garyp Nov 8 '14 at 14:22
  • $\begingroup$ obviously here "float" does not mean it will be on the fluid surface rather it define the equilibrium state of two forces acting on the object. $\endgroup$ – Rajesh Sardar Nov 8 '14 at 15:23
  • $\begingroup$ possible duplicate of Floating objects and fluid statics $\endgroup$ – Brandon Enright Dec 8 '14 at 16:22
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You are right in being confused because as garyp commented float is used with two senses in this write up.

In 3. wherever you put the mass it will stay there moving neither up nor down. Hover is a better word except it is usually used for air flight. It is simple to visualize because think of it as being water . If you outlined the equivalent volume anywhere, down, in the still water, nothing moves. You could replace it with the w anyplace in the water.

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    $\begingroup$ The situation in 3. is commonly referred to as neutrally buoyant $\endgroup$ – Michiel Nov 9 '14 at 7:00
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In point 3. it is said that if W= w then the object will float but will be totally submerged.That means the object will be floating being totally into the fluid, i.e. the net force acting on the object will be zero. And hence 3rd statement is also true.

When W=w then weight of the object=buoyant force acting on the object.

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