(II) A 0.43-kg piece of wood floats in water but is found to sink in alcohol (SG =0.79), in which it has an apparent mass of 0.047 kg. What is the SG of the wood?

Solution 32P:

When a piece of wood placed in the water its float whereas placed in the alcohol it sink, as the amount of alcohol displaced does not exert sufficient amount to buoyant force on the wood. We have to determine the specific gravity of the wood.

Step 1 of 3</p>

Concept:

The mass of the alcohol displaced is the volume of the wood times the density of the alcohol. Mathematically,

..(1)

Specific gravity of the substance is defined as the ratio of density of the substance to density of water . Mathematically.

…(2)

Density of the body is defined as the ratio of mass of the body to its volume. Mathematically,

…(3)

Step 2 of 3</p>

Mass of wood in air

SG of alcohol

Density of alcohol

Apparent mass in alcohol

Using relation (1), mass of alcohol displaced

…[From (3)]

…[From (2)]

…(4)[From (2)]

Step 4 of 4</p>

The difference in the actual mass and the apparent mass of the wood is the mass of the alcohol displaced by the wood. Therefore,

…(5)

From equations (4) and (5), we get,

Thus, the specific gravity of the wood is .