#### 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 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

Ans. D

Sol.

If an object is floating in liquid, that means the force of buoyancy is equal to the object's weight.

Fb=mg

Weight of the object in all three liquids will be the same; hence the force of buoyancy by all three liquids will be same.

Force of buoyancy in any liquid is equal to weight of displaced fluid.

Fb=dVg

Therefore, the weight of displaced fluid will be same in all three cases.

Weight of displaced fluid will be proportional to mass of displaced fluid.

Therefore, mass of displaced liquid will be same in all three cases.

We know that mass is equal to the product of density and volume of displaced liquid.

Therefore, density will be inversely proportional to displaced liquid volume.

In the first case, displaced volume is most, hence density will be least.

In the third case, displaced volume is least, hence density will be most.

So, the correct option for this question is option D.