Answers · Mass, weight and density

Mass, weight and density — return questions key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. DR1 · Return

Model answer. (a) The quantity of matter in an object; kilogram (kg). (b) The gravitational force on an object that has mass; newton (N). (c) W = m × g = 0.10 kg × 9.8 N/kg = 0.98 N. (d) The Moon’s weaker field pulls both pans less, by the same factor, so the beam is still level when the masses are equal. (e) 9.8 m/s². The acceleration of free fall and the gravitational field strength are the same quantity: g = 9.8 N/kg = 9.8 m/s².

A full answer includes

(a) Mass is the amount of matter in an object, in kilograms.
(b) Weight is the gravitational force on an object, in newtons.
(c) W = 0.10 kg × 9.8 N/kg = 0.98 N.
(d) Both pans are in the same field, so both weights change by the same factor and equal weights still mean equal masses.
(e) 9.8 m/s²: the acceleration of free fall is equal to the gravitational field strength, g = 9.8 N/kg.

Also accept

(a) matter, kg; (b) gravitational force, N; (c) 0.98 N; (d) same field on both pans; (e) 9.8 m/s², the same as g.

Watch for

“Weight is measured in kilograms.” — Weight is a force, in newtons. Kilograms measure mass.
“On the Moon the balance tips because things are lighter.” — Both sides are lighter by the same factor, so the beam stays level.

2. DR2 · Return

Model answer. (a) Mass per unit volume: ρ = m / V. (b) Put water in a measuring cylinder and read the level; lower the stone on a thread until it is completely under water; read the new level; the stone’s volume is the difference. (c) ρ = 25.0 g ÷ 20 cm³ = 1.25 g/cm³. (d) Put the empty cylinder on the balance and press zero (tare) before pouring, or subtract the empty cylinder’s mass from the full reading. (e) Measure the length, width and height with a rule, eye level with each mark, and multiply: V = length × width × height.

A full answer includes

(a) Density is mass per unit volume: ρ = m / V.
(b) Read the level of water in a measuring cylinder, lower the stone in until it is under water, read again; the volume is the rise.
(c) 25.0 g ÷ 20 cm³ = 1.25 g/cm³ (1.3 g/cm³).
(d) Zero (tare) the balance with the empty cylinder on it, or weigh it empty and full and subtract.
(e) Measure its length, width and height with a rule and multiply them: V = l × w × h.

Also accept

(a) ρ = m / V; (b) rise in level; (c) 1.25 g/cm³; (d) tare or subtract; (e) length × width × height.

Watch for

“The volume of the stone is the level after it goes in.” — The level after includes the water already there. The stone is the rise.
“Density = volume ÷ mass.” — Density is mass per unit volume: mass ÷ volume.

3. DR3 · Return

Model answer. (a) ρ = 40 g ÷ 50 cm³ = 0.80 g/cm³, less than water’s 1.00 g/cm³, so it floats. (b) X (0.70 g/cm³) is on top of Y (1.20 g/cm³). (c) For example, a 600 g pine block floats while a 31 g stone sinks: the block is heavier but less dense than water (0.60 g/cm³), the stone is lighter but denser (2.6 g/cm³).

A full answer includes

(a) 40 g ÷ 50 cm³ = 0.80 g/cm³: less than 1.00, so it floats.
(b) X, the less dense liquid, is on top.
(c) A heavy object that floats (a big log, a ship), explained by density. A light object that sinks does not show that heavy things can float.

Also accept

(a) 0.80 g/cm³, floats; (b) X; (c) heavy log floats, light stone sinks.

Watch for

“The block sinks because 40 g is more than 1.00.” — Compare density with density: 0.80 g/cm³ with 1.00 g/cm³.
“Y is on top because it is denser.” — A denser liquid sinks below a less dense one.