Explanation:
Draw a free body diagram. There are three forces on the block:
Weight force mg pulling down,
Buoyancy force B pushing up,
Tension force T pushing up.
Sum of the forces in the y direction:
∑F = ma
B + T − mg = 0
T = mg − B
Buoyancy is the weight of the displaced fluid:
T = mg − ρVg
The block is fully submerged, so the volume of displaced fluid equals the volume of the block. The volume of the block is its mass divided by its density.
T = mg − ρ (m/ρₓ) g
T = mg (1 − ρ/ρₓ)
Plug in values and solve.
T = (0.5 kg) (10 m/s²) (1 − (1000 kg/m³) / (8000 kg/m³))
T = (5 N) (1 − ⅛)
T = 4.375 N
