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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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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