Question

An object is put one by one in three liquids having different densities. the object floats with 1/9, 1/11 and 1/7 parts of their volumes outside the liquid surface in liquids of densities d1, d2 and d3 respectively. which of the following statement is correct?

a. d₁ > d₂ > d₃
b. d₁ > d₂ < d₃
c. d₁ < d₂ > d₃
d. d₁ < d₂ < d₃

Answer 1

Based on Archimedes' Principle, the order of densities for the liquids based on how much of the object's volume is submerged is d1 < d2 < d3. Option number d is correct.

Step-by-step explanation:

When an object is placed in different liquids of varying densities, the fraction of the object submerged can tell us about the relative densities of those liquids. According to Archimedes' Principle, the fraction of an object's volume that is submerged is equal to the density of the object divided by the density of the fluid. Since only 1/9, 1/11 and 1/7 parts of the object's volumes are outside the liquids of densities d1, d2, and d3 respectively, it means 8/9, 10/11 and 6/7 parts are submerged.

For the object to have a consistent density while being floated in different liquids, the liquid that submerges the object the most (smallest fraction outside) will be the densest. Thus, the correct order of densities would be d1 < d2 < d3 since 8/9 (d1) < 10/11 (d2) < 6/7 (d3). Option d. d1 < d2 < d3 is therefore the correct answer.