A Level Physics 1.1 Physical Quantities MCQs – 30 Practice Questions with Answers (Cambridge 9702)

Answer: B – Electric current is one of the seven SI base quantities, measured in amperes. Energy (joule), force (newton) and pressure (pascal) are all derived quantities built from base units.

Answer: D – There are 7 SI base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. Every other quantity in physics is derived from these.

Answer: B – Pressure (force per unit area) and energy are both derived. Mass, time, current, length and temperature are all base quantities, so every other pair contains at least one base quantity.

Answer: C – Amount of substance is measured in moles (symbol mol). The kilogram is the base unit of mass, not of amount of substance.

Answer: C – A physical quantity = numerical magnitude × unit. Saying a mass is “5” means nothing until the unit is given: 5 kg and 5 g are very different quantities.

Answer: B – Energy = force × distance. Force has units kg m s⁻², so energy = kg m s⁻² × m = kg m² s⁻². Option (A) is the newton, the unit of force.

Answer: A – Refractive index is a ratio of two speeds, so the units cancel and it has no unit. Frequency is measured in hertz (s⁻¹), charge in coulombs, and luminous intensity is a base quantity measured in candelas.

Answer: C – The candela is the base unit of luminous intensity. The newton, joule and volt are all derived units.

Answer: A – Length, mass and time are all base quantities. Force, energy and power are derived, so each of the other sets contains at least one derived quantity.

Answer: A – Charge = current × time (Q = It), so 1 coulomb = 1 ampere × 1 second = A s. Option (B), A s⁻¹, would be current divided by time, which is wrong.

Answer: B – v² and u² have units (m s⁻¹)² = m² s⁻², and 2as has units m s⁻² × m = m² s⁻². All three terms match, and the number 2 is dimensionless.

Answer: C – In (C), vt has units m s⁻¹ × s = m, but ½at has units m s⁻² × s = m s⁻¹, which cannot be added to a length. The correct term is ½at². In (B), Fv = kg m s⁻² × m s⁻¹ = kg m² s⁻³, the unit of power, so it is homogeneous.

Answer: A – Rearranging, G = Fr² / (m₁m₂). Units: (kg m s⁻²)(m²) / (kg²) = kg⁻¹ m³ s⁻². Notice one power of kg cancels, leaving kg⁻¹.

Answer: B – l / g has units m / (m s⁻²) = s², so √(l / g) has unit s, as it must for a period. The factor 2π is a pure number with no unit.

Answer: D – ρgh has units kg m⁻³ × m s⁻² × m = kg m⁻¹ s⁻², which is exactly the unit of pressure (force per unit area: kg m s⁻² / m²).

Answer: C – Homogeneity is necessary but not sufficient. It checks units only, so it cannot detect wrong dimensionless constants: s = ut + 2at² is perfectly homogeneous, but it is wrong (the constant should be ½). A homogeneous equation may be correct – it is not guaranteed to be.

Answer: A – k = F / x, so its units are N m⁻¹ = (kg m s⁻²) / m = kg s⁻². Option (D) is the unit of pressure, a common trap.

Answer: C – h = E / f, so its units are (kg m² s⁻²) / (s⁻¹) = kg m² s⁻¹ (equivalently, joule seconds). Option (A) is just the unit of energy itself.

Answer: B – ρgh² has units kg m⁻³ × m s⁻² × m² = kg s⁻². Pressure has units kg m⁻¹ s⁻². The units differ by a factor of metres, so the equation cannot be correct – and changing the size of the unit (option D) can never fix homogeneity.

Answer: A – b = F / v², so its units are (kg m s⁻²) / (m² s⁻²) = kg m⁻¹. The s⁻² cancels completely, which is why options (C) and (D) are wrong.

Answer: D – A typical adult has a mass of about 70 kg (order of magnitude 10² kg). 7 kg is a small baby, and 700 kg is closer to the mass of a horse or a small car.

Answer: B – Atmospheric pressure is about 1.0 × 10⁵ Pa (roughly 100 kPa). This is a standard value worth memorising for estimation questions.

Answer: D – Atoms are about 10⁻¹⁰ m across. 10⁻¹⁵ m is the scale of the nucleus, which is about 10 000 times smaller than the atom.

Answer: A – A brisk walk covers about 1.5 m each second. 15 m s⁻¹ is faster than a world-class sprinter, and 0.15 m s⁻¹ would take nearly two hours to walk a kilometre.

Answer: D – A kettle is one of the most powerful appliances in the home, rated at about 2000 W (2 kW). 200 W is closer to a television or a few light bulbs.

Answer: D – A mug holds roughly 300 cm³ (about a third of a litre). 30 cm³ is only a couple of tablespoons, and 3000 cm³ is a large jug.

Answer: A – E_k = ½mv² = ½ × 70 × 3² = 315 J, which is of the order of 10² J, i.e. about 3 × 10² J.

Answer: C – Visible light has wavelengths of roughly 400-700 nm; a mid-range value of 5 × 10⁻⁷ m (500 nm) is the sensible estimate.

Answer: B – A family car has a mass of about 1000 kg (one tonne). 10⁴ kg is a loaded truck, and 10² kg is only about the mass of two adults.

Answer: D – E = mcΔΘ = 1.5 × 4200 × (100 − 20) = 1.5 × 4200 × 80 ≈ 5.0 × 10⁵ J. This matches a 2000 W kettle taking about four minutes to boil.