Measurement anchors the whole UTME Physics syllabus. The International System of Units (SI) has exactly seven base units: the metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance) and candela (luminous intensity); every other unit is derived from these. In mechanics the fundamental quantities are length, mass and time (m, kg, s), while speed, force and energy are derived quantities. The vernier callipers read to 0.01 cm (0.1 mm) and the micrometer screw gauge to 0.01 mm — the micrometer is the more precise instrument, used for very small lengths such as the diameter of a wire.
A scalar has magnitude only (distance, speed, mass, time, energy); a vector has both magnitude and direction (displacement, velocity, acceleration, force, momentum). For uniformly accelerated motion, apply v = u + at, s = ut + ½at² and v² = u² + 2as. A freely falling body accelerates at about 9.8 m s⁻² regardless of its mass (air resistance neglected); UTME papers normally state g = 10 m s⁻². For a projectile launched at speed u and angle θ over level ground: range R = u² sin 2θ / g (maximum at θ = 45°), time of flight T = 2u sin θ / g, and maximum height H = u² sin²θ / 2g.
Key formulae to memorise:
The syllabus also covers the gravitational field, simple harmonic motion (restoring force proportional to displacement, as in a Hooke's-law spring) and fluids, where Archimedes' principle gives the upthrust on an immersed body as the weight of fluid displaced.
Exam tip: check units first — distractors often give μ a unit (it has none), swap scalar and vector quantities, or use 9.8 instead of the stated g = 10 m s⁻².
1. How many base units are defined in the International System of Units (SI)?
The SI has exactly seven base units: metre, kilogram, second, ampere, kelvin, mole and candela, from which all other units are derived. (BIPM, SI Brochure (9th ed., 2019); JAMB UTME Physics Syllabus, Topic 1)
2. Which of the following is a base SI unit rather than a derived unit?
The kilogram is one of the seven SI base units, while the newton, joule and watt are derived units formed from combinations of base units. (BIPM, SI Brochure (9th ed., 2019))
3. The SI base unit of electric current is the:
The ampere is the SI base unit for electric current; the volt, ohm and coulomb are all derived units. (BIPM, SI Brochure (9th ed., 2019); JAMB UTME Physics Syllabus, Topic 1)
4. The three fundamental quantities used in mechanics, from which quantities like speed and force are derived, are:
Length (m), mass (kg) and time (s) are the fundamental quantities in mechanics; all other mechanical quantities are derived from combinations of these. (JAMB UTME Physics Syllabus, Topic 1: Measurements and Units)
5. Which of the following is a scalar quantity?
Energy has magnitude only and no direction, making it a scalar quantity, unlike velocity, displacement and force, which are vectors. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors)
6. A student needs to measure the diameter of a thin copper wire as accurately as possible. Which instrument should be used?
The micrometer screw gauge has a least count of 0.01 mm, making it more precise than the vernier callipers (0.01 cm) for measuring very small lengths such as wire diameter. (JAMB UTME Physics Syllabus, Topic 1 (use of vernier callipers and micrometer screw gauge))
7. What is the least count (reading accuracy) of the vernier callipers?
The vernier callipers has a least count of 0.01 cm (0.1 mm), while the micrometer screw gauge is more precise at 0.01 mm. (JAMB UTME Physics Syllabus, Topic 1; Anyakoha, New School Physics for Senior Secondary Schools)
8. By definition, a force of one newton is the force that gives a mass of 1 kg an acceleration of:
From Newton's second law, F = ma, so one newton is defined as the force needed to give a 1 kg mass an acceleration of 1 m s⁻². (JAMB UTME Physics Syllabus, Topic 3: Motion (Newton's laws of motion))
9. Which of the following is a vector quantity?
Momentum has both magnitude and direction, so it is a vector quantity, unlike mass, time and energy, which are scalars. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors)
10. What is the unit of the coefficient of friction, μ?
The coefficient of friction is the ratio of limiting frictional force to normal reaction (μ = F/R); since both are forces, μ has no unit. (JAMB UTME Physics Syllabus, Topic 7: Friction)
11. Density is defined as mass per unit volume. What are the dimensions of density in terms of mass (M), length (L) and time (T)?
Since density = mass/volume and volume has dimension L³, the dimension of density is mass divided by length cubed, giving ML⁻³. (JAMB UTME Physics Syllabus, Topic 1: Measurements and Units (fundamental and derived quantities))
12. Which of the following correctly pairs an SI base unit with the physical quantity it measures?
The candela is the SI base unit of luminous intensity; kelvin measures temperature, mole measures amount of substance, and ampere measures electric current. (BIPM, SI Brochure (9th ed., 2019); JAMB UTME Physics Syllabus, Topic 1)
13. The moment of a force about a point is defined as the product of the force and the:
The moment of a force about a point equals the force multiplied by the perpendicular distance from the point to the force's line of action. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (moment of a force))
14. What is the SI unit of the moment of a force?
Since moment = force × perpendicular distance, its unit is the newton-metre (N m). Although dimensionally equal to the joule, the joule is reserved for work and energy. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces)
15. According to the principle of moments, a rigid body acted on by several coplanar forces is in rotational equilibrium when:
The principle of moments states that for a body in rotational equilibrium, the sum of clockwise moments about a point equals the sum of anticlockwise moments about the same point. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (principle of moments))
16. For a rigid body acted on by coplanar forces to be in complete (static) equilibrium, which conditions must be satisfied?
Complete equilibrium of a rigid body under coplanar forces requires both zero resultant force (translational equilibrium) and zero resultant moment (rotational equilibrium). (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (conditions for equilibrium of a rigid body))
17. Two equal and opposite parallel forces whose lines of action do not coincide form a:
A couple consists of two equal, opposite and parallel forces whose lines of action are different, producing a turning effect but no resultant force. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (moments and couples))
18. A uniform metre rule is pivoted at its 50 cm mark. A weight of 2 N is hung at the 20 cm mark. At what mark should a weight of 4 N be hung on the other side to balance the rule?
The 2 N weight is 30 cm from the pivot, giving a moment of 60 N cm; to balance this, the 4 N weight must be 15 cm from the pivot (4 × 15 = 60), i.e. at the 65 cm mark. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (principle of moments))
19. A uniform plank 5 m long is pivoted at its midpoint. A boy weighing 300 N sits 2 m from the pivot on one side. How far from the pivot must a girl weighing 240 N sit on the other side for the plank to balance?
By the principle of moments, 300 N × 2 m = 240 N × d, so d = 600/240 = 2.5 m from the pivot. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (principle of moments))
20. A body is said to be in stable equilibrium if, when it is slightly displaced and released, it:
A body in stable equilibrium returns to its original position after a small displacement, because the resulting moment restores it. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (types of equilibrium and stability))
21. A loaded truck with its cargo packed low is generally more stable than an empty one of the same shape mainly because loading it:
When the load is packed low, the centre of gravity is lowered relative to the base, which increases stability because a larger moment is then required to topple the body. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (centre of gravity and stability))
22. A block of weight 50 N rests on a rough horizontal surface. If the coefficient of limiting friction between the block and the surface is 0.4, what is the maximum horizontal force that can be applied without the block beginning to slide?
The limiting frictional force is F = μR = 0.4 × 50 N = 20 N, which is the maximum force the block can withstand while remaining in equilibrium. (JAMB UTME Physics Syllabus, Topic 7: Friction (coefficient of limiting friction); Topic 5: Equilibrium of Forces)
23. A point is kept in equilibrium by three coplanar forces. Two of the forces, 3 N and 4 N, act at right angles to each other. What is the magnitude of the third force (the equilibrant)?
The resultant of the 3 N and 4 N forces acting at right angles is √(3² + 4²) = 5 N; the equilibrant that balances the point must be equal in magnitude (5 N) but opposite in direction. (JAMB UTME Physics Syllabus, Topic 5: Equilibrium of Forces (triangle/parallelogram of forces))
24. A body is suspended in equilibrium from a spring of force constant 200 N m⁻¹, producing an extension of 5 cm. What is the weight of the body?
By Hooke's law, F = ke = 200 N m⁻¹ × 0.05 m = 10 N, which equals the weight of the body since it hangs in equilibrium. (JAMB UTME Physics Syllabus, Topic 9: Elasticity (Hooke's law); Topic 5: Equilibrium of Forces)
25. Which of the following best defines a scalar quantity?
A scalar quantity is completely described by its size (magnitude) alone, with no associated direction, unlike a vector quantity. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (definition and examples of scalar and vector quantities))
26. A vector quantity is one that has:
A vector quantity requires both a magnitude and a direction to be fully specified, for example force or velocity. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (definition and examples of scalar and vector quantities))
27. A student walks 4 m due east and then 3 m due north. What is the magnitude of his total displacement from the starting point?
Since the two legs of the walk are at right angles, the resultant displacement is found by Pythagoras' theorem: √(4² + 3²) = √25 = 5 m. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (composition/resolution of vectors))
28. Two forces of 3 N and 4 N act on a body at right angles to each other. What is the magnitude of their resultant?
For perpendicular vectors the resultant is R = √(3² + 4²) = √25 = 5 N, obtained using Pythagoras' theorem. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (parallelogram law and resultant of vectors))
29. Two forces, each of magnitude 10 N, act at a point and are inclined to each other at 60°. What is the magnitude of their resultant?
Using the parallelogram law, R = √(F1² + F2² + 2F1F2cosθ) = √(100 + 100 + 100) = √300 ≈ 17.3 N. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (parallelogram law of vector addition))
30. The equilibrant of two forces acting on a body is a single force that:
The equilibrant balances the combined effect of the forces, so it must be equal in size but opposite in direction to their resultant, keeping the body in equilibrium. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (resultant and equilibrant of vectors))
31. Which pair below correctly classifies the quantities as scalar and vector respectively?
Speed is the magnitude only of the rate of motion and is a scalar, while velocity also specifies direction and is a vector. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (definition and examples of scalar and vector quantities))
32. A force of 20 N acts at an angle of 30° to the horizontal. What is the horizontal component of the force? (cos 30° = 0.87)
The horizontal component of a force F acting at angle θ to the horizontal is Fcosθ = 20 × cos30° ≈ 17.3 N. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (resolution of vectors into components))
33. Which of the following is NOT a vector quantity?
Time has magnitude only and no direction, so it is a scalar quantity, unlike acceleration, weight and impulse which are all vectors. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (definition and examples of scalar and vector quantities))
34. Two forces of magnitude 6 N and 8 N act on a body. Which of the following CANNOT be the magnitude of their resultant, whatever the angle between them?
The resultant of two forces can only range between the difference (8 − 6 = 2 N) and the sum (8 + 6 = 14 N) of their magnitudes, so 20 N is impossible. (JAMB UTME Physics Syllabus, Topic 2: Scalars and Vectors (maximum and minimum resultant of two vectors))
35. The mechanical advantage (MA) of a simple machine is defined as:
Mechanical advantage compares the load a machine can move to the effort applied to move it, so MA = load/effort. (JAMB UTME Physics Syllabus, Topic 8: Simple Machines (mechanical advantage, velocity ratio and efficiency))