Physical Quantities and Measurement

13600 kg m⁻³ and relative density = 13.6

Step 1: Conversion: 1 g cm⁻³ = 1000 kg m⁻³, so 13.6 g cm⁻³ = 13600 kg m⁻³. Step 2: Relative density = Density of substance / Density of water = 13600 / 1000 = 13.6. Step 3: Relative density is dimensionless and equals the numerical value of density in g cm⁻³. Option 2 wrongly divides instead of multiplying by 1000. Option 3 confuses the SI value with relative density. Option 4 multiplies by 10 instead of 1000.

2 g cm⁻³

Step 1: Volume = length × breadth × height = 40 × 20 × 5 = 4000 cm³. Step 2: Mass = 8 kg = 8000 g (convert to grams). Step 3: Density = M/V = 8000 / 4000 = 2 g cm⁻³. Option 0.5 arises from not converting kg to g. Option 20 comes from using 400 cm³ as volume (missing one dimension). Option 4 results from using 2000 g instead of 8000 g.

It floats with approximately 59.5% of its volume inside glycerine

Step 1: Density of wood (0.75 g cm⁻³) < Density of glycerine (1.26 g cm⁻³), so the block floats. Step 2: Fraction submerged = ρ_wood / ρ_glycerine = 0.75 / 1.26 = 0.595 ≈ 59.5%. Step 3: So approximately 59.5% of the block is inside glycerine and 40.5% is outside. Option 2 is wrong because the wood's density is less than glycerine's. Option 3 confuses density of wood (0.75) as a direct percentage. Option 4 has no physical basis here.

117.6 m³

Step 1: Fraction submerged = ρ_ice / ρ_sea water = 0.9 / 1.02 = 0.8824. Step 2: Volume submerged = 0.8824 × 1000 = 882.4 m³. Step 3: Volume above surface = 1000 – 882.4 = 117.6 m³. Option 882.4 m³ is the submerged part, not the visible part. Option 100 m³ uses ratio 0.9:1 (using fresh water density). Option 900 m³ uses incorrect fraction.