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Question

Why a bucket of water weighs lighter inside the well than when it is outside the water

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Solution

Water is a fluid. It applies an upward force or buoyant force on any solid immeresed in it . When a bucket is immeresed in water it experiences an upthrust which acts against the weight of the bucket. Therefore the weight of the bucket seems less when it is inside water. As the bucket is lifted outside the water there is no upthrust and the bucket seems to be heavier than when it was inside the water

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