Answer: 0.85 N
Explanation: We can solve this problem using the principles of buoyancy and Newton's laws.
First, we need to find the buoyant force acting on the metallic alloy block. The buoyant force is equal to the weight of the water displaced by the block, which can be calculated using the block's volume and the density of water:
V = m_block / ρ_block = 3.4 kg / 3700 kg/m³ = 0.0009189 m³
F_buoyant = ρ_water x g x V = 1000 kg/m³ x 9.8 m/s² x 0.0009189 m³ = 8.96 N
So the buoyant force acting on the metallic alloy block is 8.96 N.
Next, we can calculate the tension force in the spring scale attached to the block. Since the block is in static equilibrium, the tension force must be equal in magnitude and opposite in direction to the weight of the block plus the buoyant force:
Tension force = weight of block + buoyant force
Tension force = m_block x g + F_buoyant
Tension force = 3.4 kg x 9.8 m/s² + 8.96 N = 42.04 N
So the hanging scale reads 42.04 N.
Finally, we can find the reading of the lower scale. The lower scale measures the weight of the beaker and the water in it, minus the buoyant force acting on the beaker. The weight of the beaker and the water is:
weight of beaker + weight of water = m_beaker x g + m_water x g
weight of beaker + weight of water = 1.3 kg x 9.8 m/s² + 2.5 kg x 9.8 m/s² = 35.35 N
The buoyant force acting on the beaker can be calculated using the volume of water displaced by the beaker:
V = m_water / ρ_water = 2.5 kg / 1000 kg/m³ = 0.0025 m³
F_buoyant = ρ_water x g x V = 1000 kg/m³ x 9.8 m/s² x 0.0025 m³ = 24.5 N
So the reading of the lower scale is:
Reading of lower scale = weight of beaker + weight of water - buoyant force
Reading of lower scale = 35.35 N - 24.5 N = 10.85 N
Therefore, the lower scale reads 10.85 N.