To keep the bottle completely immersed, the upward force on the bottle due to water must be balanced by an externally applied downward force.
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We have learned that the weight of an object is the force due to the gravitational attraction of the Earth.
When the upward force exerted by the water is greater than the bottle’s weight, the bottle rises up when released.
The water exerts an upward force on the bottle.
The bottle is pulled downwards because of the gravitational force acting on it.