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A block with volume 1.8 m^3 is half submerged when placed in water. When the same block...

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carolinesmiths | Student, Kindergarten | (Level 1) Salutatorian

Posted August 28, 2013 at 2:43 PM via web

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A block with volume 1.8 m^3 is half submerged when placed in water. When the same block of wood is placed in an unknown liquid it is 75% submerged. Taking the standard density of water, what is the density of the unknown liquid.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 28, 2013 at 2:48 PM (Answer #1)

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A block of wood with volume 1.8 m^3 when placed in water is half submerged. When an object is placed in a liquid, the weight of volume of water displaced is equal to the weight of the body. Here, as 0.9 m^3 of water is displaced and the standard density of water is 1000 kg/m^3, the mass of the block of wood is 0.9*1000 = 900 kg.

When the same block of wood is placed in an unknown liquid 75% of the volume is submerged. This volume of liquid displaced is equal to 0.75*1.8 = 1.35 m^3. The mass of this volume is equal to 900 kg.

The density of the unknown liquid is 900/1.35 = 666.67 kg/m^3

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