Answer :
The sinker will weigh approximately 2.8676 oz in alcohol.
To find the weight of the sinker in alcohol, we need to calculate the buoyant force and subtract it from the weight of the sinker.
Weight of the sinker in water = 3 oz
Density of alcohol = 0.81 g/cm^3
First, let's convert the density of alcohol to ounces per cubic inch to match the units of weight:
Density of alcohol = 0.81 g/cm^3
= (0.81 g/cm^3) × (0.03527396 oz/g) × (1 cm^3 / 0.06102374 in^3)
≈ 0.046708 oz/in^3
The buoyant force is equal to the weight of the liquid displaced by the sinker. The volume of liquid displaced is the difference in volume between the sinker in water and the sinker in alcohol.
To find the weight of the sinker in alcohol, we need to calculate the volume of the sinker in water and the volume of the sinker in alcohol:
Volume of sinker in water = Weight of sinker in water / Density of water
= 3 oz / 1 oz/in^3
= 3 in^3
Volume of sinker in alcohol = Volume of sinker in water - Volume of liquid displaced
= 3 in^3 - 3 in^3 × (Density of alcohol / Density of water)
= 3 in^3 - 3 in^3 × (0.046708 oz/in^3 / 1 oz/in^3)
= 3 in^3 - 3 in^3 × 0.046708
= 3 in^3 - 0.140124 in^3
≈ 2.859876 in^3
Finally, we can calculate the weight of the sinker in alcohol by subtracting the buoyant force from the weight of the sinker:
Weight of the sinker in alcohol = Weight of the sinker in water - Buoyant force
= 3 oz - (Volume of sinker in alcohol × Density of alcohol)
= 3 oz - (2.859876 in^3 × 0.046708 oz/in^3)
≈ 2.867576 oz
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