Question

A piece of wood that floats on water has a mass of 0.0175 kg. A lead sinker is tied to the wood, and the apparent mass with the wood in air and the lead sinker submerged in water is 0.0765 kg. The apparent mass with both the wood and the sinker both submerged in water is 0.0452 kg. What is the SG of the wood

Answer 1

Answer:

The specific gravity of the wood is 1.56

Explanation:

Given;

mass of the wood in water, $M_w_{H_2O}$ = 0.0175 kg

apparent mass of the wood and lead sinker submerged in water, $M_w_{(air)} + M_s_{H_2O}$ = 0.0765 kg

apparent mass with both the wood and the sinker both submerged in water, $M_w_{H_2O} + M_s_{H_2O} = 0.0452 \ kg$

Mass of the lead sinker alone submerged in water;

$M_w_{H_2O} + M_s_{H_2O} = 0.0452 \ kg\\\\0.0175 \ kg + M_s_{H_2O} = 0.0452 \ kg\\\\M_s_{H_2O} = 0.0452 \ kg - 0.0175 \ kg\\\\M_s_{H_2O} = 0.0277 \ kg$

Mass of the wood in the air;

$M_w_{(air)} + M_s_{H_2O} = 0.0765 \ kg\\\\M_w_{(air)} + 0.0277 \ kg = 0.0765 \ kg\\\\M_w_{(air)} = 0.0765 \ kg - 0.0277 \ kg\\\\M_w_{(air)} = 0.0488 \ kg$

Mass of water is calculated as follows;

$M_w_{(air)} - M_w_{H_2O} = M_{H_2O}\\\\0.0488 \ kg - 0.0175 \ kg = M_{H_2O}\\\\0.0313 \ kg = M_{H_2O}$

The specific gravity of the wood is calculated as follows;

$Specific \ gravity\ (S.G) \ of \ wood = \frac{mass \ of \ wood\ in \ air }{mass \ of \ water} \\\\Specific \ gravity\ (S.G) \ of \ wood = \frac{0.0488}{0.0313} \\\\Specific \ gravity\ (S.G) \ of \ wood = 1.559 = 1.56$

Therefore, the specific gravity of the wood is 1.56