48 questions. Try each one, then open the answer to check yourself and read the explanation.
Which of the following represents the correct precision if the length of a piece of wire is measured with a metre rule?
Answer: A (35 mm)
A metre rule's smallest division is 1 mm, so it can only measure to the nearest millimetre: 35 mm. Writing 35.0 mm or 35.00 mm would claim a precision the rule does not have.
Figure 1 is a graph of force against extension for a spiral spring. The force constant of the spring is given by the
Answer: A (slope of the linear portion of the graph)
Hooke's law F = ke holds on the straight part of the graph, so k = F/e is its slope.
A heavy object is suspended from a string and lowered into water so that it is completely submerged. The object appears lighter because
Answer: C (it experiences an upthrust)
The water pushes up on the object with an upthrust equal to the weight of water displaced, so less tension is needed to hold it.
Which of the following is a derived unit?
Answer: D (Newton)
The newton is made from base units: 1 N = 1 kg m s−2. The others are base units.
Two objects, one having three times the mass of the other, are dropped at the same time from a tall building. When they are above the ground, the two objects will have the same
Answer: D (acceleration)
All bodies falling freely have the same acceleration g, whatever their mass. Momentum and energies depend on mass.
Which of the following is in a neutral equilibrium?
Answer: B (A cone resting on its slant edge)
A cone lying on its side can roll to any new position and stays there; its centre of gravity neither rises nor falls, so it is in neutral equilibrium.
A ball is thrown vertically into the air with an initial velocity u. What is the greatest height reached?
Answer: D (u2/2g.)
At the top v = 0, so 0 = u² − 2gh, giving h = u²/2g.
Which of the following assumptions is made in a simple pendulum experiment? The
Answer: A (suspending string is inextensible)
The simple pendulum theory assumes a light, inextensible string, a point-like bob and small swings.
A uniform metre rule QR is balanced on a knife edge which is 55 cm from R. When a mass of 10 g is hung at P as shown in Fig. 2, the mass of the metre rule is
Answer: C (70 g)
From R, P is at 90 cm, the pivot at 55 cm and the rule's centre of gravity at 50 cm. Moments: 10 × 35 = m × 5, so m = 70 g.
In Fig. 3, the three forces F1, F2, F3 acting at O are in equilibrium. If the magnitude of F1 is 10.0 N and the magnitude of F2 is 5.0 N, find the magnitude of F3.
Answer: C (13.2 N)
F3 balances the resultant of F1 and F2, which are 60° apart: R² = 10² + 5² + 2 × 10 × 5 × cos 60° = 175, so R ≈ 13.2 N.
When a box of mass 45 kg is given an initial speed of 5 m s−1, it slides along a horizontal floor a distance of 3 m before coming to rest. What is the coefficient of the kinetic friction between the box and the floor? (g = 10 m s−2)
Answer: B (5/12)
Deceleration a = u²/2s = 25/6 m s−2. Friction μmg = ma, so μ = a/g = (25/6)/10 = 5/12.
Figure 4 represents a block-and-tackle pulley system on which an effort of W Newtons supports a load of 120.0 N. If the efficiency of the machine is 40%, then the value of W is
Answer: C (50.0 N)
The system has six supporting strands, so VR = 6. MA = 0.4 × 6 = 2.4, and W = 120 ÷ 2.4 = 50 N.
A constant force of magnitude F acts on an object of mass 0.04 kg initially at rest at a point O. If the speed of the object when it has moved 50 m from O is 500 m s−1, what is the value of F?
Answer: B (100.0 N)
a = v²/2s = 500²/100 = 2500 m s−2. F = ma = 0.04 × 2500 = 100 N.
A rectangular tank contains water to a depth of 2 m. If the base is 4 m × 3 m, calculate the force on the base (Density of water = 103 kg m−3, g = 10 m s−2)
Answer: A (2.4 × 105 N)
Pressure = hρg = 2 × 1000 × 10 = 2 × 104 Pa. Force = pressure × area = 2 × 104 × 12 = 2.4 × 105 N.
A 1000 kg elevator is descending vertically with an acceleration of 1.0 m s−2. If the acceleration due to gravity is 10.0 m s−2, the tension in the suspending cable is
Answer: C (9000.0 N)
Accelerating downwards, mg − T = ma, so T = m(g − a) = 1000 × 9 = 9000 N.
A ball attached to one end of a string moves anti-clockwise around a circle whose centre is O. If the string suddenly breaks when the ball is at the point P along which of the following paths will it move?
Answer: B (B)
When the string breaks there is no centripetal force, so the ball flies off along the tangent in the direction it was moving; going anticlockwise at P, that is straight up the page, as in B.
The mode of heat transfer which does not require a material medium is
Answer: B (radiation)
Radiation travels as electromagnetic waves and can cross a vacuum.
The expansion of solids can be considered a disadvantage in the
Answer: A (balance wheel of a watch)
When a watch's balance wheel expands in heat its timing changes, which is a nuisance. Fitting tyres on wheels, fire alarms and thermostats all make use of expansion.
In an experiment in which molten naphthalene is allowed to cool, the cooling curve in Fig. 5 was obtained. The temperature 80°C is known as the
Answer: C (melting point)
The flat part of the cooling curve at 80°C is where the liquid solidifies at constant temperature; this is the melting (freezing) point.
The specific latent heat of fusion of lead is the amount of heat required to
Answer: C (change the state of a unit mass of lead at its melting point)
Specific latent heat of fusion is the heat needed to change unit mass from solid to liquid at the melting point, with no temperature change.
Which of the following is common to evaporation and boiling? They
Answer: C (involve change of state)
Both turn liquid into vapour, so both are changes of state. Evaporation happens at any temperature at the surface; boiling happens throughout at one temperature.
Mercury is suitable as a barometric fluid because it
Answer: C (is several times denser than water)
Mercury's high density means atmospheric pressure supports only about 76 cm of it, a convenient length; water would need over 10 m.
Which of the following properties makes metals ideal for cooking utensils?
Answer: B (Good conduction of heat)
Metals conduct heat well, carrying heat quickly from the flame to the food.
A gas occupies a volume of 300 cm3 at a temperature of 27°C. What is its volume at 54°C, when the pressure is constant?
Answer: C (327 cm3)
Charles' law with kelvin temperatures: V2 = 300 × 327/300 = 327 cm3.
When two objects P and Q are supplied with the same quantity of heat, the temperature change in P is observed to be twice that of Q. The mass of P is half that of Q. The ratio of the specific heat capacity of P to Q is
Answer: C (1 : 1)
Q = mcθ is the same for both: cP × (½m) × 2θ = cQ × m × θ, so cP = cQ and the ratio is 1 : 1.
In Fig. 6, a ray of light in air strikes a glass plate at an angle of incidence of 60°. The reflected ray is observed to be perpendicular to the refracted ray. What is the refractive index of the glass?
Answer: A (1.73)
Reflected ray is at 60° to the normal; for it to be at 90° to the refracted ray, the angle of refraction is 180° − 60° − 90° = 30°. n = sin 60°/sin 30° ≈ 1.73.
A lens of focal length 12.0 cm forms an upright image three times the size of a real object. The distance between the object and the image is
Answer: B (16.0 cm)
An upright, magnified image from a converging lens is virtual and on the same side as the object, with v = −3u. 1/u − 1/(3u) = 1/12 gives u = 8 cm and the image 24 cm from the lens, so they are 24 − 8 = 16 cm apart.
In which of the following arrangements is the wavelength in an increasing order?
Answer: B (Gamma rays, x-rays, infra-red ray, radiowaves)
From shortest to longest wavelength: gamma rays, X-rays, (ultraviolet, visible,) infra-red, radio waves.
If the refractive index of glass is 1.5, what is the critical angle at the air-glass interface?
Answer: B (sin−1 ⅔)
sin C = 1/n = 1/1.5 = 2/3, so C = sin−1(2/3).
A dentist obtains a linear magnification of 4 of a hole in a tooth by placing a concave mirror at a distance of 2.0 cm from the tooth. The radius of curvature of the mirror is
Answer: A (5.3 cm)
The dentist sees an upright, virtual image, so v = −8 cm when u = 2 cm. 1/f = 1/2 − 1/8 = 3/8, f ≈ 2.67 cm and r = 2f ≈ 5.3 cm.
What is the effect of the increase in the size of the hole of a pin-hole camera on the image? It
Answer: A (gives a blurred image)
A bigger hole lets light from each point of the object form a patch rather than a point, so the overlapping patches blur the image (though it is brighter).
A pencil is placed vertically between a concave mirror and its focal point. The image of the pencil in the mirror will be
Answer: D (virtual, erect and enlarged.)
An object inside the focal length of a concave mirror gives a virtual, upright, magnified image (as in a shaving mirror).
A wave of frequency 10 Hz forms a stationary wave pattern in a medium where the velocity is 20 cm s−1. The distance between adjacent nodes is
Answer: A (1.0 cm)
λ = v/f = 20/10 = 2 cm. Adjacent nodes are λ/2 = 1 cm apart.
In Fig. 7, a resonance tube experiment is performed using one tuning fork. As the water level is lowered the first resonance is obtained when the length of the air column l = λ/4. The second resonance is obtained when l equals
Answer: B (3λ/4)
A tube closed at one end resonates at λ/4, 3λ/4, 5λ/4…, so the second resonance is at 3λ/4.
Which of the following is true of the loudness of sound? It
Answer: A (depends on the square of the amplitude of the vibrating body)
Loudness depends on intensity, and intensity is proportional to the square of the amplitude.
A man clapping his hands at regular intervals observes that the echo of a clap coincides with the next clap. If the reflecting cliff is 160 m away and the speed of sound is 320 m s−1, what is the frequency of the clapping?
Answer: A (1 Hz)
The echo travels 320 m there and back in 320/320 = 1 s, so the claps are 1 s apart: 1 Hz.
The vibration of an air column produces the sound in the
Answer: C (flute)
A flute is a wind instrument: its note comes from the vibrating air column inside it. Pianos and guitars use strings, and a bell vibrates itself.
If Fig. 8, E is an accumulator with negligible internal resistance. If the emf is 9.0 V, then the total current is
Answer: C (1.0 A)
The 5 Ω and 20 Ω in parallel give 4 Ω; with the other 5 Ω in series the total is 9 Ω. I = 9/9 = 1.0 A.
In Fig. 9, the value of R is
Answer: D (6 Ω)
Total resistance = 12/2 = 6 Ω. So R in parallel with 6 Ω must be 3 Ω, which needs R = 6 Ω.
Which of the following is NOT a part of a d.c. electric motor?
Answer: D (Transformer.)
A d.c. motor has a field magnet, an armature coil and a commutator. A transformer is a separate device that works only with a.c.
Which of the following is stored by a dry Leclanche cell?
Answer: D (Chemical energy.)
A cell stores chemical energy and turns it into electrical energy when current is drawn.
Which of the following arrangements will produce an equivalent resistance of 1.5 Ω from three 1 Ω resistors?
Answer: D (D)
Two 1 Ω resistors in parallel give 0.5 Ω; adding the third in series gives 1.5 Ω, which is arrangement D.
Which of the following is true of magnetism?
Answer: A (Iron filings cling mainly round the ends of a bar magnet)
The magnetic force is strongest at the poles, near the ends of a bar magnet, so iron filings gather there. A suspended magnet points along the magnetic (not geographic) meridian.
The angle between the magnetic meridian and the geographic meridian at a locality on the earth is the
Answer: D (angle of declination of the locality.)
The angle between magnetic north and true north at a place is the declination.
The sign of the charge on a charged glass rod may be determined with
Answer: A (a charged electroscope)
Bring the rod near an electroscope of known charge: if the leaves open further the charges are alike; an uncharged electroscope only shows that there is a charge.
If the inclination at Ibadan is 7°S, this means that
Answer: B (the earth's resultant magnetic intensity at Ibadan makes angle 7° with the horizontal direction)
Inclination (dip) is the angle the earth's total field makes with the horizontal; 7°S means the south-seeking end dips.
The wavelength of ultraviolet radiation is 400 nm. If the speed of light in air is 3 × 108 m s−1, then the frequency of the ultraviolet radiation is
Answer: D (7.5 × 1014 Hz)
f = c/λ = 3 × 108 ÷ (400 × 10−9) = 7.5 × 1014 Hz.
Which of the following is most strongly deflected by a magnetic field?
Answer: C (β-particles)
γ-rays and X-rays carry no charge. β-particles are light and charged, so they are bent far more than the heavy α-particles.