An object is put one by one in three liquids having different densities. The object floats with 1/9, 2/11 and 3/7 parts of their volumes outside the liquid surface in liquids d1, d2 and d3 respectively. Which of the following statement is correct? a. d1 > d2 < d3b.d1 < d2 < d3c.d1 > d2 > d3d. d1 < d2 > d3Clear my choice
Question
An object is put one by one in three liquids having different densities. The object floats with 1/9, 2/11 and 3/7 parts of their volumes outside the liquid surface in liquids d1, d2 and d3 respectively. Which of the following statement is correct? a. d1 > d2 < d3b.d1 < d2 < d3c.d1 > d2 > d3d. d1 < d2 > d3Clear my choice
Solution
The principle of flotation states that when an object is partially or wholly immersed in a fluid, it displaces its own weight of the fluid. The fraction of the volume of the object that is submerged when the object is floating is equal to the ratio of the density of the object to the density of the fluid.
Let's denote the density of the object as d0.
In the first liquid (d1), 1/9 of the object's volume is outside the liquid, which means 8/9 of the object's volume is submerged. So, we have the equation: d0/d1 = 8/9.
In the second liquid (d2), 2/11 of the object's volume is outside the liquid, which means 9/11 of the object's volume is submerged. So, we have the equation: d0/d2 = 9/11.
In the third liquid (d3), 3/7 of the object's volume is outside the liquid, which means 4/7 of the object's volume is submerged. So, we have the equation: d0/d3 = 4/7.
From these equations, we can see that d1 < d2 < d3.
So, the correct answer is b. d1 < d2 < d3.
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