A block of metal has a mass of 0.5Kg and density of 8000kg/m3. if it is suspended from a string and completely immerged in water (gw=1000kg/m3). the tension in the string (the answer is 4.375N what are the steps)

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