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Q.

Which of the following statements is correct about floatation?

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a

Weight of the liquid displaced = weight of the floating body

b

Weight of the liquid > weight of the floating body

c

Weight of the liquid displaced < weight of the floating body

d

Weight of the liquid displaced  weight of the floating body

answer is A.

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Detailed Solution

According to the principle of floatation, when a body is partially or partly immersed in fluid then the weight of the displaced fluid is equal to the weight of the floating body.

Let's look at one example to understand:
When a cube of ice is immersed in water, its 9/10th part is floating inside the water.
That means if ice of 1m3 is immersed in water, 0.9m3 will be inside the water.
 Volume of ice= 1m3
Therefore,
 Volume of the submerged part of ice= 0.9m3
According to the principle of displacement, the volume of ice submerged inside the water will displace water equal to the volume of the ice.
Therefore, 
The volume of displaced water= 0.9m3

Mass= volume X density 
Density of ice= 900kg/m3  
Density of water= 1000kg/m3  
Weight of ice= volume of ice X density of ice 
Weight of ice= 1 x 900= 900kg 
Weight of displaced water= volume of displaced water X density of water 
Weight of displaced water= 0.9 X 1000 = 900kg  
Weight of ice= weight of displaced water
 

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