In an experiment, a rectangular block with height h is allowed to float in two separate liquids. in the first liquid, which is water, it floats fully submerged. in the second liquid it floats with height h/7 above the liquid surface. what is the relative density (the density relative to that of water) of the second liquid?

The relative density of the second liquid is 7.

Explanation:

From archimede's principle we know that the force that a liquid exerts on a object equals to the weight of the liquid that the object displaces.

Let us assume that the volume of the object is 'V'

Thus for the liquid in which the block is completely submerged

The buoyant force should be equal to weight of liquid

Mathematically

Thus for the liquid in which the block is 1/7 submerged

The buoyant force should be equal to weight of liquid

Mathematically

Comparing equation 'i' and 'ii' we see that

Since the first liquid is water thus

Thus the relative density of the second liquid is 7.