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Question

An object is put one by one in three liquids having different densities. The object floats with 1/9, 2/11, 3/7 parts of its volume outside the liquid surface in liquids of densities d1,d2 and d3 respectively. Which of the following statements is correct?

A
d1>d2>d3
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B
d1>d2<d3
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C
d1<d2>d3
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D
d1<d2<d3
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Solution

The correct option is D d1<d2<d3
Buoyant Force is when a rigid object is submerged in a fluid (completely or partially), there exits an upward force on the object that is equal to the weight of the fluid that is displaced by the object.
In this case, there are 3 liquids with varying densities.
19=0.11,211=0.18and37=0.43. These are the volume outside of liquids of densities d1,d2 and de respectively. This means that the buoyant force is maximum for d3 and minimum for d1. As the buoyant force is proportional to density, the densities of the liquids are in the order d1<d2<d3.

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