A large container of water is placed on a set of scales which initially read 0.500 kg. The container has a overflow spout that can be used to collect any overflow into a second container.The second container is also on a set of scales and is initially empty. The second set of scales initially read 0.065 kg.A small ball is lowered into the large container, displacing water down the overflow spout and into the second container.The readings on both scales are now 0.585 kg and 0.100 kg respectively.What is the density of the ball? (to 2 s.f and in kg m−3)(ρwater = 1000 kg m−3)
Question
A large container of water is placed on a set of scales which initially read 0.500 kg. The container has a overflow spout that can be used to collect any overflow into a second container.The second container is also on a set of scales and is initially empty. The second set of scales initially read 0.065 kg.A small ball is lowered into the large container, displacing water down the overflow spout and into the second container.The readings on both scales are now 0.585 kg and 0.100 kg respectively.What is the density of the ball? (to 2 s.f and in kg m−3)(ρwater = 1000 kg m−3)
Solution
To find the density of the ball, we need to first find the volume of the water displaced, which is equal to the volume of the ball. We can then use the formula for density, which is mass divided by volume.
Step 1: Find the mass of the water displaced The mass of the water displaced is equal to the final reading on the second set of scales minus the initial reading. So, 0.100 kg - 0.065 kg = 0.035 kg.
Step 2: Find the volume of the water displaced The density of water is given as 1000 kg/m^3. We can use the formula for density (density = mass/volume) to find the volume. Rearranging the formula gives us volume = mass/density. So, 0.035 kg / 1000 kg/m^3 = 0.000035 m^3.
Step 3: Find the mass of the ball The mass of the ball is equal to the final reading on the first set of scales minus the initial reading. So, 0.585 kg - 0.500 kg = 0.085 kg.
Step 4: Find the density of the ball Now we can use the formula for density again, this time with the mass and volume of the ball. So, density = mass/volume = 0.085 kg / 0.000035 m^3 = 2428.57 kg/m^3.
Rounding to 2 significant figures gives a final answer of 2400 kg/m^3.
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