Physics › Practise › Questions › Mass and weight
Questions on mass and weight
Mass is a scalar measure of inertia, in kilograms, while weight is the gravitational force on that mass, W = mg, measured in newtons. Move an object to a place where g differs and its mass is unchanged while its weight is not. A beam balance compares masses and reads the same anywhere; a newton meter measures force.
18 original questions · 53 marks · the mass and weight notes · Mechanics
To print: the questions (PDF, 58 KB) · the worked answers (PDF, 74 KB)
Every question here is written for this library rather than taken from a past paper. Write your answer out before opening a mark scheme: the schemes award marks point by point, and the marks are easier to see when you have something of your own to compare against.
Distinguish between the mass and the weight of an object, including the unit of each.
Mark scheme
Mass is a measure of an object's inertia (accept: the amount of matter in it), a scalar measured in kilograms (1). Weight is the gravitational force on it, a vector measured in newtons (1).Calculate the weight of a 5.0 kg object on Earth, where g = 9.81 m s−2.
Mark scheme
W = mg = 5.0 × 9.81 (1)
W = 49.1 N (1)State what a chemical balance and a newton meter (spring balance) each measure.
Mark scheme
A balance compares mass, in kg (1); a newton meter measures force, so it reads weight, in N (1).The gravitational field strength g may be quoted as 9.81 N kg−1 or as 9.81 m s−2. Show that these two units are equivalent.
Mark scheme
1 N = 1 kg m s−2 (from F = ma) (1), so N kg−1 = kg m s−2/kg = m s−2 (1).A parcel has a weight of 34.3 N on Earth, where g = 9.81 N kg−1. Calculate its mass.
Mark scheme
m = W/g = 34.3/9.81 (1) = 3.5 kg (1).State the direction in which an object's weight acts.
Mark scheme
Vertically downwards, towards the centre of the Earth (1).The same 5.0 kg object is taken to the Moon, where g = 1.62 N kg−1. State its mass there and calculate its weight.
Mark scheme
Mass is unchanged at 5.0 kg (1)
Weight = mg = 5.0 × 1.62 (1)
Weight = 8.1 N (1)An astronaut has a mass of 80 kg. Calculate their weight (a) on Earth (g = 9.81 m s−2) and (b) on Mars (g = 3.70 m s−2).
Mark scheme
(a) W = 80 × 9.81 (1)
W = 785 N (1)
(b) W = 80 × 3.70 (1)
W = 296 N (1)A person of mass 60 kg stands on a set of scales in a lift. Taking g = 9.81 m s−2, calculate the reading (the normal force) when the lift accelerates downwards at 3.0 m s−2, and state how the reading compares with the person's weight.
Mark scheme
mg − N = ma (1)
N = m(g − a) = 60 × (9.81 − 3.0) (1)
N = 409 N (1)
This is less than their true weight of 589 N, so they feel lighter (1)The value of g varies slightly over the Earth's surface: it is 9.78 N kg−1 at the equator and 9.83 N kg−1 at the poles. A scientist of mass 70.0 kg travels from the equator to the South Pole. State what happens to her mass, and calculate the change in her weight.
Mark scheme
Her mass is unchanged at 70.0 kg; mass does not depend on location (1). ΔW = mΔg = 70.0 × (9.83 − 9.78) (1) = 3.5 N increase (1).An airline limits cabin baggage to a mass of 7.0 kg. A passenger's bag has a mass of 1.9 kg and contains a laptop of mass 1.6 kg, a camera of mass 850 g and books of mass 2.3 kg. Deduce whether the baggage is within the limit, and calculate its total weight. g = 9.81 N kg−1.
Mark scheme
Total mass = 1.9 + 1.6 + 0.850 + 2.3 = 6.65 kg (850 g converted to 0.850 kg) (1). 6.65 kg is less than 7.0 kg, so the baggage is within the limit (1). W = mg = 6.65 × 9.81 = 65 N (1).A stone hangs from a newton meter on Earth, where g = 9.81 N kg−1; the meter reads 12.0 N. The same stone and meter are taken to Europa, where g = 1.31 N kg−1. Calculate the reading on Europa.
Mark scheme
m = W/g = 12.0/9.81 = 1.22 kg, the same on Europa (1). Reading = mgEuropa = 1.22 × 1.31 (1) = 1.6 N (1).A planet has mass 6.0 × 1024 kg and radius 6.4 × 106 m. Using g = GM/r2 with G = 6.67 × 10−11 N m2 kg−2, calculate the gravitational field strength at its surface.
Mark scheme
g = GM/r2 (1)
GM = 6.67 × 10−11 × 6.0 × 1024 (1)
g = GM / (6.4 × 106)2 (1)
g = 9.77 N kg−1 (1)In the absence of air resistance, a hammer and a feather dropped together on the Moon land at the same time. Explain why, referring to mass and weight.
Mark scheme
Acceleration = weight/mass = mg/m = g, independent of mass (1). Both objects fall with the same acceleration g (1), so with no air resistance they land together, even though the hammer has far more mass and weight (1).A student says 'the object weighs 5 kg'. Explain what is wrong with this statement and give the correct way to express it.
Mark scheme
Kilograms measure mass, not weight (1). The object has a mass of 5 kg; its weight is a force of about 49 N on Earth, from W = mg (1). Weight should be quoted in newtons (1).A probe lands on the surface of a planet and hangs a 6.00 kg calibration mass from a newton meter, which reads 53.2 N. Use the data below to deduce which planet the probe has landed on.
Surface gravitational field strength in N kg−1: Mercury 3.70; Mars 3.71; Venus 8.87; Earth 9.81.Mark scheme
g = W/m = 53.2/6.00 (1) = 8.87 N kg−1 (1). This matches Venus; it is far too large for Mercury or Mars and too small for Earth (1).A student stands on a set of bathroom scales on the floor of a drop-tower ride. During the ride the cabin falls freely. Explain why the scales read zero during the fall, and state whether the student's weight has changed.
Mark scheme
The scales read the normal contact force between the student and the scales, not the weight itself (1). In free fall the student, scales and cabin all accelerate downwards at g (1), so no contact force is needed between the student and the scales and the reading falls to zero (1). The weight is unchanged at mg; gravity still acts throughout the fall (1).A geologist checks a rock sample of mass 3.0 kg with two instruments: a beam balance and a newton meter. Both instruments are then taken to the Moon, where g = 1.62 N kg−1 (on Earth g = 9.81 N kg−1). Describe and explain the reading each instrument gives on the Moon.
Mark scheme
A beam balance compares the sample with standard masses (1). Gravity acts equally on both sides of the balance, so its effect cancels and the balance still indicates 3.0 kg on the Moon (1). A newton meter measures the gravitational force on the sample directly, through the extension of its spring (1). On Earth it reads W = 3.0 × 9.81 = 29.4 N, but on the Moon it reads 3.0 × 1.62 = 4.9 N, about one sixth as much (1). The mass is unchanged by the move; only the weight depends on g, and the two instruments measure different quantities (1).
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
Practise mass and weight one question at a time
The player marks nothing for you. It shows one question, waits, then shows the scheme so you can mark yourself, and brings a question back sooner when it went badly.