A block of mass 5 kg has density 600 kg/m^3 and is submerged in water (density 1000 kg/m^3). What fraction of its volume is submerged?

A block of mass 5 kg has density 600 kg/m^3 and is submerged in water (density 1000 kg/m^3). What fraction of its volume is submerged?

• A. 0.30 (30%)
• B. 0.50 (50%)
• C. 0.60 (60%)
• D. 0.75 (75%)

Answer: (C)

When an object floats, the buoyant force from the displaced water exactly balances the object's weight. The buoyant force is set by the volume of the object that is submerged, multiplied by the water’s density and gravity. Setting buoyancy equal to weight gives ρ_water × V_submerged × g = m × g. Since m = ρ_block × V_block, the fraction submerged is V_submerged / V_block = ρ_block / ρ_water. Plugging in ρ_block = 600 kg/m^3 and ρ_water = 1000 kg/m^3 gives 600/1000 = 0.6, i.e., 60% of the block’s volume is submerged. For context, the block’s total volume is V_block = m/ρ_block = 5/600 ≈ 0.00833 m^3, so V_submerged ≈ 0.005 m^3, which is 60% of the total volume. If the block were denser than water, it would sink; if less dense, the submerged fraction would be less than 1 and equal to the density ratio.

When an object floats, the buoyant force from the displaced water exactly balances the object's weight. The buoyant force is set by the volume of the object that is submerged, multiplied by the water’s density and gravity. Setting buoyancy equal to weight gives ρ_water × V_submerged × g = m × g.

Since m = ρ_block × V_block, the fraction submerged is

V_submerged / V_block = ρ_block / ρ_water.

Plugging in ρ_block = 600 kg/m^3 and ρ_water = 1000 kg/m^3 gives 600/1000 = 0.6, i.e., 60% of the block’s volume is submerged.

For context, the block’s total volume is V_block = m/ρ_block = 5/600 ≈ 0.00833 m^3, so V_submerged ≈ 0.005 m^3, which is 60% of the total volume. If the block were denser than water, it would sink; if less dense, the submerged fraction would be less than 1 and equal to the density ratio.