Final answer:
To determine the specific gravity of the block, we calculated the buoyant force, volume, and density of the block. We found the density to be 7.32 kg/L and divided it by the density of water to get the specific gravity, which is 7.32. This value does not match exactly with the options provided.
Step-by-step explanation:
The student wants to find the specific gravity of a block of an unknown material, which requires the use of the concepts of buoyant force and mass. We know the mass of the block in air (6.0 kg) and the apparent mass in water (50.8 N), which allows us to calculate the buoyant force.
First, convert the weight in Newton to mass in water by dividing by the acceleration due to gravity (9.8 m/s²):
Mass in water = Force in water / g = 50.8 N / 9.8 m/s² = 5.18 kg
Next, calculate the buoyant force that is equal to the loss of mass when submerged:
Buoyant force = Mass in air - Mass in water = 6.0 kg - 5.18 kg = 0.82 kg
Convert the buoyant force to Newtons (N), as it is equal to the weight of the water displaced (in N). Then we can get the volume of the block since the density of water is 1.0 kg/L:
Weight of water displaced = Buoyant force (kg) × g (9.8 m/s²) = 0.82 kg × 9.8 m/s² = 8.036 N
Volume of the block = Mass of water displaced / density of water = 0.82 kg / 1.0 kg/L = 0.82 L
Then calculate the density of the block:
Density of block = Mass of block in air / Volume of block = 6 kg / 0.82 L = 7.32 kg/L
To find the specific gravity, divide the density of the block by the density of water (which is 1.0 kg/L):
Specific gravity of the block = Density of block / Density of water = 7.32 kg/L / 1.0 kg/L = 7.32
Looking at the answer options, none exactly match our calculation. Therefore, the question might need clarification or there might be a typo in the options. However, conceptually, if we were to choose the closest given option, it would be option (d) 5.0, acknowledging it doesn't match our precise calculation.