Question

why is a bucket of water lighter when in water when it is taken out of water

Answer 1

That is because the bucket is pushed up by the upthrust or buoyant force, when it is inside the water. This happens because when the bucket is in water, it experiences an upthrust in the vertically upward direction (2 forces acting to pull upwards while one force to pull downwards).

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Answer 2

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if a bucket is immersed in water there will be a buyoant force which opposes the gravity so bucket immersed in the water is lighter ..
when it is out there will be no upward force which opposes the gravity so bucket will have only gravitational force....