My question is that when we place a body in water it exerts a buoyant force but it exerts an equal force in downward direction then why its buoyant force is greater and the object floats?
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6The same in all directions does not mean the same in every location. – John Alexiou Feb 10 '23 at 14:14
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Take a look at the diagram in this answer https://physics.stackexchange.com/a/597482/93729 (shamelessly self promoting) – AccidentalTaylorExpansion Feb 11 '23 at 10:20
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I guess it is the time of year when they start teaching the Fluids section in physics 101... – hft Feb 11 '23 at 17:47
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https://en.wikipedia.org/wiki/Buoyancy – hft Feb 11 '23 at 17:51
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The force is equal in all directions, but it also depends on the depth. An object of finite size, submerged in a liquid, has its bottom and upper parts at different depths, and the force at the bottom is bigger than that at the top. An object floating on the surface even doesn't have its upper part in the liquid.

Roger V.
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Even more simply, when it is on the surface there is no fluid on the top of the object, so all the vertical force is upward if the object is a box. – Ross Millikan Feb 11 '23 at 03:47
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@RossMillikan what is the difference in between air pressure and water pressure at the surface of a lake? Right where the air and water touch. – JohnFilleau Feb 11 '23 at 19:35