prove that loss in the weight of a body in a liquid is equal to weight of liquid displaced
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So, when a solid is fully immersed in a liquid, it loses weight which is equal to the weight of the liquid it displaces. ... The loss in weight of the body = Weight of water displaced by the body = Buoyant Force or up-thrust exerted by water on the body.
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according to Archimedes principle the weight of water displaced is equal to the weight of the immersed part . for a solid floating in a liquid it's weight acting vertically downward at its centre of gravity is equal to the weight of the liquid displaced by the immersed part of the solid acting vertically upward at its centre of buoyancy .In the floating condition the apparent density of the solid is zero and the body is said to be weightless.
Hope this helps.
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