These ten questions are original and invented for practice, not taken from any exam paper. They cover weight, density, unit conversion, volume, floating and sense-checking, in roughly increasing difficulty. Use g = 10 N/kg and water = 1000 kg/m³ (1.0 g/cm³) unless told otherwise.
Write your working on paper, with a unit on every line, before opening the answer. Keep a mistake log of anything you miss. The parent topic is mass, weight and density.
Questions
1. A bag of sugar has a mass of 2.0 kg. (a) Find its weight. (b) Another object weighs 35 N. Find its mass.
Show answer
(a) W = mg = 2.0 × 10 = 20 N.
(b) m = W ÷ g = 35 ÷ 10 = 3.5 kg.
2. An astronaut’s suit and equipment have a mass of 12 kg. On the Moon, g = 1.6 N/kg. Find the weight on Earth and on the Moon, and state the mass on the Moon.
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Earth: 12 × 10 = 120 N. Moon: 12 × 1.6 = 19.2 N. The mass on the Moon is still 12 kg, because mass does not depend on gravity.
3. (a) Convert 11.3 g/cm³ to kg/m³. (b) Convert 1250 kg/m³ to g/cm³.
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(a) 11.3 × 1000 = 11 300 kg/m³.
(b) 1250 ÷ 1000 = 1.25 g/cm³.
4. A rectangular block measures 4.0 cm by 5.0 cm by 6.0 cm and has a mass of 240 g. Find its density in g/cm³ and in kg/m³.
Show answer
Volume = 4.0 × 5.0 × 6.0 = 120 cm³. Density = 240 ÷ 120 = 2.0 g/cm³. In kg/m³: 2.0 × 1000 = 2000 kg/m³.
5. A stone of mass 62.4 g is lowered into a measuring cylinder. The water level rises from 50 cm³ to 74 cm³. Find the density of the stone in g/cm³.
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Volume of stone = 74 − 50 = 24 cm³. Density = 62.4 ÷ 24 = 2.6 g/cm³. Check: 24 × 2.6 = 62.4.
6. An iron plate has a mass of 3.9 kg. The density of iron is 7800 kg/m³. Find its volume in m³ and in cm³.
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V = m/ρ = 3.9 ÷ 7800 = 0.000 5 m³ = 5.0 × 10⁻⁴ m³. In cm³: 0.000 5 × 1 000 000 = 500 cm³. Check: 7800 × 0.000 5 = 3.9.
7. A liquid has density 1.2 g/cm³. What is the mass of 250 cm³ of it, in g and in kg?
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m = ρV = 1.2 × 250 = 300 g = 0.30 kg.
8. A plastic object has density 0.85 g/cm³. Will it float in water? Will it float in a liquid of density 0.80 g/cm³? Explain each.
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In water (1.0 g/cm³): 0.85 is less than 1.0, so it floats. In the liquid of 0.80 g/cm³: 0.85 is greater than 0.80, so the object is denser than the liquid and sinks.
9. A boat floats at rest with a weight of 5000 N. (a) State the upthrust on it. (b) Find the mass and the volume of water it displaces.
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(a) Forces are balanced at rest, so upthrust = 5000 N.
(b) The displaced water weighs 5000 N, so its mass = 5000 ÷ 10 = 500 kg. Volume = 500 ÷ 1000 = 0.5 m³.
10. A student finds a 2.0 kg steel bar with volume 250 cm³ and writes its density as 8 kg/m³. Decide whether this is reasonable and find the correct value in kg/m³.
Show answer
Steel is about 7800 kg/m³, so 8 kg/m³ is unreasonable. Mass = 2000 g, so density = 2000 ÷ 250 = 8 g/cm³. Convert: 8 × 1000 = 8000 kg/m³. The student left the answer in g/cm³ but wrote the wrong unit. The bounds and rounding explainer helps you judge how many figures to quote.
If you got these wrong
| What went wrong | Questions | Go to |
|---|---|---|
| Wrote weight in kg, or mass in N, or said mass changes with gravity | 1, 2 | Separate mass from gravitational force |
| Answer wrong by a factor of 1000, or wrong density unit | 3, 4, 10 | Convert density units |
| Flipped the formula or mixed g with m³ | 5, 6, 7 | Calculate an unknown volume from mass and density |
| Floating explained with “heavy” or “light”, or unequal forces at rest | 8, 9 | Explain floating using an appropriate force model |
| Did not notice an impossible value | 10 | Identify an unreasonable material-density answer |
Redo a missed question a few days later with different numbers. If the same error returns, the cause is usually a habit, not a fact.
For a teacher to watch that habit live, see online one-to-one Physics tuition.