To find the volume of the block, we can calculate the volume of water displaced and the volume of oil displaced when the block is immersed in the respective liquids. The volume of the block can be obtained by subtracting the volume of water displaced from the volume of oil displaced.
To find the volume of the block, we can use the concept of buoyancy and Archimedes' principle. Here are the steps to calculate the volume of the block:
1. We know that when the block is in air, the scale reads 37.4 N. This is the weight of the block in air, which is equal to the gravitational force acting on the block.
2. When the block is immersed in water, the scale reads 31.8 N. This reading represents the apparent weight of the block in water, which is less than its weight in air. The difference in weight between the block in air and the block in water is equal to the buoyant force acting on the block.
3. Similarly, when the block is immersed in oil, the scale reads 32.7 N. This reading represents the apparent weight of the block in oil.
4. We can calculate the buoyant force acting on the block in water using Archimedes' principle. The buoyant force is equal to the weight of the water displaced by the block. Since the density of water is 1000 kg/m³, we can calculate the volume of water displaced by the block using the equation:
Buoyant Force = Weight of Water Displaced
Density of Water * Volume of Water Displaced * Gravitational Acceleration = Weight of Water Displaced
Solving for Volume of Water Displaced, we have:
Volume of Water Displaced = (Weight of Water Displaced) / (Density of Water * Gravitational Acceleration)
5. Similarly, we can calculate the volume of oil displaced by the block using the same equation, but substituting the density of oil instead of the density of water.
6. Now, to find the volume of the block, we can subtract the volume of water displaced from the volume of oil displaced. This is because the block occupies the same volume as the combined volume of water and oil displaced when it is immersed in the liquids.
7. Therefore, Volume of Block = Volume of Oil Displaced - Volume of Water Displaced
By following these steps, we can find the volume of the block.