Final answer:
The density of the stone is 2 g/ml. The density of the metal bar is 16 g/ml. The mass of the wooden block is 1780 g. The relative density of liquid L is 0.79. The total mass of the vessel when filled with equal volumes of water and liquid L is 286 g.
Step-by-step explanation:
In order to calculate the density of an object, you need to know its mass and its volume. In the first question, the stone has a mass of 200 grams and displaces 100 ml of water, so its density can be calculated by dividing mass by volume: 200 g / 100 ml = 2 g/ml.
In the second question, the metal bar initially displaces 89 ml of water and then displaces 86 ml of water when submerged. The difference in volume is the volume of the metal bar: 89 ml - 86 ml = 3 ml. The density can be calculated by dividing mass by volume: 48 g / 3 ml = 16 g/ml.
In the third question, the density of the wooden block is given as 8.9 g/cm³. To calculate the mass of the block, we can multiply the density by its volume: 10 cm * 4 cm * 5 cm * 8.9 g/cm³ = 1780 g.
In the fourth question, the relative density of liquid L can be determined by dividing the mass of the liquid by the mass of an equal volume of water (since water has a relative density of 1): (110 g - 50 g) / (126 g - 50 g) = 60 g / 76 g ≈ 0.79.
To calculate the total mass of the vessel when filled with equal volumes of water and liquid L, we can add the mass of the vessel to the mass of the liquid and the mass of the water: 50 g + 110 g + 126 g = 286 g.