Final answer:
To find the apparent weight of the steel block in water, buoyancy must be considered. The steel block's true weight is calculated based on its density and volume, and then the buoyant force due to the water it displaces is subtracted from this true weight. The calculated apparent weight does not match any of the options given, suggesting a possible mistake in the question. Option D is the nearest correct answer.
Step-by-step explanation:
The question asks to calculate the apparent weight of a steel block when it is weighed in water, given that steel has a relative density of 7. This problem can be solved using the concept of buoyancy, which is a result of the fluid displacement caused by a submerged object. The relative density of steel refers to its density compared to the density of water. Since steel's relative density is 7, this means that the density of steel is 7 times that of water. To find the apparent weight, we need to consider the buoyant force that water exerts on the submerged steel block.
Firstly, the volume of the steel block can be calculated as 5 cm × 5 cm × 5 cm = 125 cm³. The weight of the volume of water displaced by the steel block gives us the buoyant force, using the relationship that 1 cm³ of water has a mass of 1 g. Hence, the steel block displaces 125 g of water. Converting this mass into Newtons (since weight is a force and should be expressed in Newtons), we multiply the mass of the displaced water by the acceleration due to gravity (9.8 m/s²), which gives us a buoyant force of 1.225 N (125 × 9.8 × 10⁻³).
To find the apparent weight of the steel block, we subtract this buoyant force from the true weight of the steel block in air. The mass of the steel block is 125 cm³ × 7 g/cm³ (since the relative density of steel is 7), which equals 875 g or 0.875 kg. The true weight is then 0.875 kg × 9.8 m/s² = 8.575 N. Subtracting the buoyant force, the apparent weight in water is 8.575 N - 1.225 N = 7.35 N, which is not listed in the options provided. It seems that there might be a mistake in the original question, as none of the provided options match the calculated result based on the given relative density and volume of the steel block.