50 questions. Try each one, then open the answer to check yourself and read the explanation.
In the diagram above, which of the simple pendula will resonate with P when set into oscillation?
Answer: A (T)
A pendulum resonates with another of the same natural frequency, which means the same length. Only T has the same length as P.
The height at which the atmosphere ceases to exist is about 80 km. If the atmospheric pressure on the ground level is 760 mmHg, the pressure at a height of 20 km above the ground level is
Answer: B (570 mmHg)
Taking the pressure to fall evenly from 760 mmHg at 0 km to 0 at 80 km, 20 km is a quarter of the way up, so the pressure is 760 × ¾ = 570 mmHg.
A stone of mass 1 kg is dropped from a height of 10 m above the ground and falls freely under gravity. Its kinetic energy 5 m above the ground is then equal to
Answer: D (half its initial potential energy)
After falling 5 m of the 10 m, the stone has turned half of its starting potential energy into kinetic energy.
The diagram above is a block-and-tackle pulley system in which an effort of 80 N is used to lift a load of 240 N. The efficiency of the machine is
Answer: B (50%)
There are 6 pulleys, so VR = 6. MA = 240/80 = 3. Efficiency = MA/VR × 100% = 3/6 × 100% = 50%.
If a spherical metal bob of radius 3 cm is fully immersed in a cylinder containing water and the water level rises by 1 cm, what is the radius of the cylinder?
Answer: D (6 cm)
Volume of bob = water displaced: (4/3)π × 33 = πr2 × 1, so 36 = r2 and r = 6 cm.
The resultant of two forces acting on an object is maximum if the angle between them is
Answer: B (0°)
R2 = F12 + F22 + 2F1F2 cos θ is largest when cos θ = 1, i.e. θ = 0°: the forces act in the same direction and simply add.
I. The earth is not spherical but elliptical in shape.
II. Variation in latitude and longitude.
III. Rotation of the earth on its axis.
IV. Variation in the density of the earth.
On which combination of the above does the weight of an object vary on the earth's surface?
Answer: C (I, II and III only)
g changes over the earth's surface because the earth is flattened at the poles, because of the earth's rotation, and so with latitude. So weight varies for reasons I, II and III.
The efficiency of a machine is always less than 100% because the
Answer: D (velocity ratio is always greater than the mechanical advantage.)
Efficiency = MA/VR. Friction and moving parts waste some work, so MA is always less than VR and the efficiency is below 100%.
Which of the following consists entirely of vector quantities?
Answer: A (Velocity, magnetic flux and reaction)
Velocity and reaction are vectors, and the magnetic field (flux) is treated here as a vector. Each other option contains a clear scalar: mass, power or work.
Ice cubes are added to a glass of warm water. The glass and water are cooled by
Answer: C (conduction and convection)
Heat passes from the water into the ice by conduction where they touch, and the cold water sinks and sets up convection currents that cool the rest.
A ray of light strikes a plane mirror at an angle of incidence of 35°. If the mirror is rotated through 10°, through what angle is the reflected ray rotated?
Answer: D (20°)
When a plane mirror turns through an angle θ, the reflected ray turns through 2θ, so 2 × 10° = 20°.
Find the frequencies of the first three harmonics of a piano string of length 1.5 m, if the velocity of the waves on the string is 120 m s−1.
Answer: A (40 Hz, 80 Hz, 120 Hz)
The fundamental has λ = 2L = 3 m, so f0 = 120/3 = 40 Hz. A string gives all multiples: 40 Hz, 80 Hz and 120 Hz.
The terrestrial telescope has one extra lens more than the astronomical telescope. The extra lens is for
Answer: D (erection of the image)
An astronomical telescope gives an upside-down image. The extra (erecting) lens in a terrestrial telescope turns the image the right way up.
The driving mirror of a car has a radius of curvature of 1 m. A vehicle behind the car is 4 m from the mirror. Find the image distance behind the mirror.
Answer: B (4/9)
A driving mirror is convex, so f = −r/2 = −0.5 m. 1/v = 1/f − 1/u = −2 − ¼ = −9/4, so v = −4/9 m: a virtual image 4/9 m behind the mirror.
If a ray travelling in air is incident on a transparent medium as shown in the diagram, the refractive index of the medium is given as
Answer: A (cos α/sin β)
α is measured from the surface, so the angle of incidence is 90° − α and sin(90° − α) = cos α. β is the angle of refraction, so n = cos α/sin β.
The pressure of a given mass of a gas changes from 300 N m−2 to 120 N m−2 while the temperature drops from 127 °C to −73 °C. The ratio of the final volume to the initial volume is
Answer: B (5 : 4)
P1V1/T1 = P2V2/T2 with T1 = 400 K, T2 = 200 K: V2/V1 = (300 × 200)/(120 × 400) = 5/4.
A plane sound wave of frequency 85.5 Hz and velocity 342 m s−1 is reflected from a vertical wall. At what distance from the wall does the wave have an antinode?
Answer: C (1 m)
λ = v/f = 342/85.5 = 4 m. There is a node at the wall, and the first antinode is λ/4 = 1 m from it.
A string is fastened tightly between two walls 24 cm apart. The wavelength of the second overtone is
Answer: B (16 cm)
The second overtone is the third harmonic, with three loops: 3 × λ/2 = 24 cm, so λ = 16 cm.
A gas with initial volume 2 × 10−6 m3 is allowed to expand to six times its initial volume at constant pressure of 2 × 105 N m−2. The work done is
Answer: A (2.0 J)
W = PΔV = 2 × 105 × (12 − 2) × 10−6 = 2.0 J.
The thermometric substance of an absolute thermometer is
Answer: C (helium)
The absolute (thermodynamic) scale is realised with a constant-volume gas thermometer, and helium behaves almost like an ideal gas down to very low temperatures.
A cell of internal resistance r supplies current to a 6.0 Ω resistor and its efficiency is 75%. Find the value of r.
Answer: D (2.0 Ω)
Efficiency = R/(R + r): 0.75 = 6/(6 + r), so 6 + r = 8 and r = 2.0 Ω.
In the diagram above, the current I is
Answer: B (9/11 A)
10 Ω and 5 Ω in parallel give 10/3 Ω. Total resistance = 3 + 1 + 10/3 = 22/3 Ω. With a 6 V cell, I = 6 ÷ 22/3 = 9/11 A.
The diagram above shows two capacitors P and Q of capacitances 2 μF and 4 μF respectively connected to a d.c. source. The ratio of energy stored in P to Q is
Answer: D (1 : 2)
P and Q are in parallel, so they have the same voltage. Energy = ½CV2 is proportional to C, so the ratio is 2 : 4 = 1 : 2.
A resistance R is connected across the terminal of an electric cell of internal resistance 2 Ω and the voltage was reduced to 3/5 of its nominal value. The value of R is
Answer: A (3 Ω)
Terminal p.d. = E × R/(R + r) = 3/5 E, so 5R = 3R + 6 and R = 3 Ω.
The diagram above shows three capacitors C1, C2 and C3 of capacitances 2 μF, 6 μF and 3 μF respectively. The potential differences across C1, C2 and C3 respectively are
Answer: D (6 V, 2 V and 4 V)
In series: 1/C = ½ + ⅙ + ⅓ = 1, so C = 1 μF and Q = 1 × 12 = 12 μC. V = Q/C gives 12/2 = 6 V, 12/6 = 2 V and 12/3 = 4 V.
A student is at a height 4 m above the ground during a thunderstorm. Given that the potential difference between the thundercloud and the ground is 107 V, the electric field created by the storm is
Answer: B (2.5 × 106 N C−1)
Taking the 4 m as the distance over which the 107 V acts, E = V/d = 107/4 = 2.5 × 106 N C−1.
A working electric motor takes a current of 1.5 A when the p.d. across it is 250 V. If its efficiency is 80%, the power output is
Answer: A (300.0 W)
Power input = IV = 1.5 × 250 = 375 W. Output = 80% of 375 = 300.0 W.
The cost of running five 60 W lamps and four 100 W lamps for 20 hours if electrical energy costs N10.00 per kWh is
Answer: D (N140.00)
Total power = 5 × 60 + 4 × 100 = 700 W = 0.7 kW. Energy = 0.7 × 20 = 14 kWh, costing 14 × N10 = N140.00.
In a Daniell cell, the depolarizer, positive and negative electrodes are respectively
Answer: A (copper sulphate, copper and zinc)
A Daniell cell has a copper positive pole in copper sulphate solution (the depolariser) and a zinc negative pole.
The diagram above shows a closed square box of side 0.5 m in a uniform electric field E in the direction shown by the arrows. What is the flux ϕ for the box?
Answer: D (0.0 E)
In a uniform field every field line that enters the closed box also leaves it, so the flux in equals the flux out and the net flux is zero.
A bread toaster uses a current of 4 A when plugged in a 240 volts line. It takes one minute to toast slices of bread. What is the energy consumed by the toaster?
Answer: A (5.76 × 104 J)
Energy = IVt = 4 × 240 × 60 = 57 600 J = 5.76 × 104 J.
In the circuit diagram above, the ammeter reads a current of 3 A when R is 5 Ω and 6 A when R is 2 Ω. Determine the value of x.
Answer: C (10 Ω)
R and x are in parallel across E: E = 3 × 5x/(5 + x) = 6 × 2x/(2 + x). So 15(2 + x) = 12(5 + x), giving 3x = 30 and x = 10 Ω.
When a piece of rectangular glass block is inserted between two parallel plate capacitor, at constant plate area and distance of separation, the capacitance of the capacitor will
Answer: A (increase)
Glass has a higher permittivity than air, and C = εA/d, so putting a glass dielectric between the plates increases the capacitance.
The ratio of electrostatic force FE to gravitational force FG between two protons each of charge e and mass m, at a distance d is
Answer: D (e2/(4πεoGm2))
FE = e2/(4πεod2) and FG = Gm2/d2. Dividing, d2 cancels: FE/FG = e2/(4πεoGm2).
What is the angle of dip at the magnetic equator?
Answer: B (0°)
At the magnetic equator the earth's field is horizontal, so a dip needle rests level: the angle of dip is 0°.
A cell can supply currents of 0.4 A and 0.2 A through a 4.0 Ω and 10.0 Ω resistors respectively. The internal resistance of the cell is
Answer: A (2.0 Ω)
E = 0.4(4 + r) = 0.2(10 + r), so 1.6 + 0.4r = 2 + 0.2r, giving 0.2r = 0.4 and r = 2.0 Ω.
Which of the following graphs correctly represents the variation of mass of a given material deposited with time for constant current in Faraday's law of electrolysis?
Answer: C (Graph C)
m = ZIt, so with constant current the mass is proportional to time: a straight line through the origin, which is graph C.
In the diagram above, determine the r.m.s. current
Answer: B (48 A)
Impedance Z = √(42 + 32) = 5 Ω, so Irms = 240/5 = 48 A.
The particle emitted when K decays to K is
Answer: A (gamma)
The nucleus stays potassium (same element, same atomic number), so no charged particle left it; it only lost energy as a gamma ray.
The current through a resistor in an a.c. circuit is given as 2 sin ωt. Determine the d.c. equivalent of the current.
Answer: D (√2 A)
The d.c. equivalent is the r.m.s. value: Irms = I0/√2 = 2/√2 = √2 A.
I. Low pressure
II. High pressure
III. High p.d.
IV. Low p.d.
Which combination of the above is true of the conduction of electricity through gases?
Answer: B (I and III only)
A gas conducts well (as in a discharge tube) when its pressure is low and a high p.d. is applied across it.
Which of the following metals will provide the greatest shield against ionizing radiation?
Answer: D (Lead)
Lead is very dense and has a high atomic number, so it absorbs ionising radiation best.
The primary coil of a transformer has N turns and is connected to a 120 V a.c power line. If the secondary coil has 1,000 turns and a terminal voltage of 1,200 volts, what is the value of N?
Answer: B (100)
Np/Ns = Vp/Vs: N/1000 = 120/1200, so N = 100.
The process of energy production in the sun is
Answer: B (nuclear fusion)
In the sun, light nuclei (hydrogen) fuse to form helium, releasing large amounts of energy: nuclear fusion.
At resonance, the phase angle in an a.c. circuit is
Answer: C (0°)
At resonance XL = XC, so the circuit acts like a pure resistance and current and voltage are in phase: cos θ = R/Z = 1, θ = 0°.
The force on a current carrying conductor in a magnetic field is greatest when the
Answer: D (conductor is at right angles with the field.)
F = BIL sin θ is greatest when sin θ = 1, i.e. when the conductor is at 90° to the field.
A transistor functions mainly as a
Answer: A (switch and an amplifier)
A transistor's main uses are as an amplifier (a small base current controls a large collector current) and as an electronic switch.
Energy losses through eddy currents are reduced by using
Answer: B (insulated soft iron wires)
A core made of insulated soft-iron wires (or laminations) breaks up the paths of eddy currents, so less energy is lost as heat.
A capacitor of 20 × 10−12 F and an inductor are joined in series. The value of the inductance that will give the circuit a resonant frequency of 200 kHz is [π2 = 10]
Answer: D (1/32 H)
At resonance f = 1/(2π√(LC)), so L = 1/(4π2f2C) = 1/(4 × 10 × (2 × 105)2 × 20 × 10−12) = 1/32 H.
The magnetic force on a charged particle moving with velocity v is
Answer: A (proportional to both the magnitude of the charge and the velocity v)
F = qvB sin θ, so the force is proportional to both the charge q and the velocity v.