The iron nail sinks in water because the downward force due to gravitational attraction on the nail is greater than the upthrust of water on the nail.
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The magnitude of the buoyant force depends on the density of the fluid.
Yes, all objects experience a force of buoyancy when they are immersed in a fluid.
The upward force exerted by the water on the bottle is called upthrust or buoyant force.
The balance can be achieved by applying an external downward force equal to the difference between the upward force and the weight of the bottle.