45 questions. Try each one, then open the answer to check yourself and read the explanation.
Which of the following is a set of vectors?
Answer: B (Acceleration, velocity and moment)
Acceleration, velocity and moment (torque) all have direction. Mass, volume and density are scalars, so every other set contains a scalar.
The magnitude of the resultant of two mutually perpendicular forces, F1 and F2 is 13 N. If the magnitude of F1 is 5 N, what is the magnitude of F2?
Answer: C (12.0 N)
For perpendicular forces 13² = 5² + F2², so F2 = √(169 − 25) = 12 N.
Two points on a velocity-time graph have co-ordinates (5 s, 10 m s−1) and (20 s, 20 m s−1). Calculate the mean acceleration between the two points
Answer: A (0.67 m s−2)
a = change in velocity ÷ time = (20 − 10)/(20 − 5) = 10/15 ≈ 0.67 m s−2.
The figure above shows a uniform circular object, centre R and diameter PS. A circular section, centre Q and diameter PR is cut away from it. If PQRS is a straight line, where is the centre of gravity of the figure?
Answer: D (A point between R and S)
Removing material on the P side of R shifts the centre of gravity of what is left away from the hole, to a point between R and S.
A simple pendulum of mass m moves along an arc of a circle radius R in a vertical plane as shown in the figure above. What is the work done by gravity in a downward swing through the angle θ to 0°?
Answer: B (mgR (1 − cos θ))
At angle θ the bob is R(1 − cos θ) higher than at the bottom, so gravity does work mgR(1 − cos θ) as it swings down.
A block of mass m is held in equilibrium against a vertical wall by a horizontal force. If the coefficient of friction between the block and the wall is μ, the minimum value of the horizontal force is
Answer: D (mg/μ)
The horizontal force F is the normal reaction, so the wall can give an upward friction of at most μF. This must hold up the weight: μF = mg, so F = mg/μ.
A thin film of liquid is trapped between two glass plates. The force required to pull the plates apart will increase if the
Answer: C (area of the liquid surface in contact with the plates is increased.)
The plates are held together by surface tension acting over the wetted area, so a larger area of liquid in contact makes them harder to separate.
A block-and-tackle system is used to lift a load of 20 N through a vertical height of 10 m. If the efficiency of the system is 40%, how much work is done against friction?
Answer: C (300 J)
Useful work = 20 × 10 = 200 J. Input = 200 ÷ 0.4 = 500 J. Work against friction = 500 − 200 = 300 J.
In the figure above W1 = 200 g and W2 = 450 g. Calculate the extension of the spring per unit load. [g = 10 m s−2]
Answer: C (6.0 × 10−3 m N−1)
Extension per unit load = (6.5 − 5.0) cm ÷ (4.5 − 2.0) N = 0.015 m ÷ 2.5 N = 6.0 × 10−3 m N−1. (The pointer moves down 1.5 scale divisions when the load goes from 200 g to 450 g.)
Which of the following devices are used to measure pressure? I. Aneroid barometer II. Hydrometer III. Hygrometer IV. Manometer
Answer: D (I and IV.)
Barometers and manometers measure pressure. A hydrometer measures relative density and a hygrometer measures humidity.
A piece of wood of mass 40 g and uniform cross-sectional area of 2 cm2 floats upright in water. The length of the wood immersed is
Answer: C (20 cm)
A floating body displaces its own mass of water: 40 g = 40 cm3. Immersed length = 40 ÷ 2 = 20 cm.
A column of air 10.0 cm long is trapped in a tube at 27°C. What is the length of the volume at 100°C?
Answer: A (12.4 cm)
At constant pressure V ∝ T (kelvin), and V ∝ length for a uniform tube: L = 10 × 373/300 ≈ 12.4 cm.
A mass of gas at 7°C and 70 cm of mercury has a volume of 1200 cm3. Determine its volume at 27°C and pressure of 75 cm of mercury.
Answer: A (1200 cm3)
V2 = V1 × (p1/p2) × (T2/T1) = 1200 × (70/75) × (300/280) = 1200 cm3.
An electric heater is used to melt a block of ice, mass 1.5 kg. If the heater is powered by a 12 V battery and a current of 20 A flows through the coil, calculate the time taken to melt the block of ice at 0°C. (Specific latent heat of fusion of ice = 336 × 103 J kg−1).
Answer: B (35.0 min)
Heat needed = 1.5 × 336 000 = 504 000 J. Power = 12 × 20 = 240 W. t = 504 000/240 = 2100 s = 35 min.
From the kinetic theory of gases, temperature is a
Answer: D (physical property and is proportional to the average kinetic energy of the molecules.)
Temperature is not itself energy; it is a property of the gas that is proportional to the average kinetic energy of its molecules.
Which of the following correctly represents the variation of the saturated vapour pressure of water with temperature?
Answer: A (A)
Saturated vapour pressure rises with temperature, slowly at first and then more and more steeply, giving the upward-curving graph A.
A vibrator of frequency 60 Hz is used in generating transverse stationary waves in a long thin wire. If the average distance between successive nodes on the wire is 45 cm, find the speed of the transverse waves in the wire.
Answer: B (54 m s−1)
Successive nodes are half a wavelength apart, so λ = 90 cm = 0.9 m. v = fλ = 60 × 0.9 = 54 m s−1.
The air column as shown in the figure above is set into vibration by the tuning fork. In this state of resonance, the waves in the air column will be
Answer: B (stationary and longitudinal)
Sound waves in air are longitudinal, and at resonance the incident and reflected waves form a stationary wave in the column.
When the tension in a sonometer wire is doubled, the ratio of the new frequency to the initial frequency is
Answer: C (√2)
f ∝ √T, so doubling the tension multiplies the frequency by √2.
In a sound wave in air, the adjacent rarefactions and compressions are separated by a distance of 17 cm. If the velocity of the sound wave is 340 m s−1 determine the frequency.
Answer: C (1000 Hz)
A compression and the next rarefaction are half a wavelength apart, so λ = 34 cm. f = v/λ = 340/0.34 = 1000 Hz.
In which of the following diagrams is the length of the tube equal to one wavelength?
Answer: C (C)
Each loop of a stationary-wave pattern (node to node) is half a wavelength, so the tube is one wavelength long when it holds two complete half-wave loops between antinodes at the open ends, as in C.
Light of wavelength 5000 × 10−8 cm travels in free space with a velocity of 3 × 108 m s−1. What is its wavelength in glass of refractive index 1.5?
Answer: A (3333 × 10−8 cm)
The frequency stays the same and the speed falls by 1.5 times, so the wavelength also falls: 5000 ÷ 1.5 ≈ 3333 × 10−8 cm.
An object is placed 5.6 × 10−4 m in front of a converging lens of focal length 1.0 × 10−3 m. The image formed is
Answer: B (virtual, erect and magnified)
The object is closer to the lens than its focal length, so the lens acts as a magnifying glass: the image is virtual, upright and magnified.
The magnification of the image of an object placed in front of a convex mirror is 1/3. If the radius of curvature of the mirror is 24 cm, what is the distance between the object and its image?
Answer: D (32 cm)
f = 12 cm (virtual). With v = u/3 behind the mirror: 1/u − 3/u = −1/12, so u = 24 cm and v = 8 cm. The image is behind the mirror, so they are 24 + 8 = 32 cm apart.
The plane mirrors in a kaleidoscope are usually placed
Answer: A (at an angle of 60°)
Kaleidoscope mirrors are set at 60°, giving 360/60 − 1 = 5 images that form a symmetrical pattern.
A far sighted person cannot see objects that are less than 100 cm away. If this person wants to read a book at 25 cm, what type and focal length of lens does he need?
Answer: C (convex, 33 cm)
The lens must form a virtual image at 100 cm of a book at 25 cm: 1/f = 1/25 − 1/100 = 3/100, so f ≈ 33 cm, converging (convex).
When a yellow card is observed through a blue glass, the card would appear
Answer: A (black)
A yellow card reflects red, green and yellow light but no blue. Blue glass lets only blue through, so no light reaches the eye and the card looks black.
Dispersion of light by a glass prism is due to the
Answer: B (different speeds of the various colours in glass)
Each colour travels at a different speed in glass, so each is refracted by a different amount and the colours separate.
Which of the following pairs is NOT part of the electromagnetic spectrum? I. Radio waves II. Beta rays III. Gamma rays IV. Alpha rays
Answer: D (II and IV.)
Beta and alpha 'rays' are streams of particles. Radio waves and gamma rays are electromagnetic waves.
Two insulated charged spheres of different sizes and carrying opposite charges are connected together by a metallic conductor. Current will flow from one sphere to the other until both spheres
Answer: B (are at the same potential)
Charge flows from high to low potential and stops when the two spheres are at the same potential.
A bar magnet is most effectively demagnetized by
Answer: D (heating the magnet.)
Strong heating makes the domains vibrate out of line and destroys the magnetism completely.
The resistance of a 5 m uniform wire of cross-sectional area 0.2 × 10−6 m2 is 0.425 Ω. What is the resistivity of the material of the wire?
Answer: D (1.70 × 10−8 Ω m)
ρ = RA/L = 0.425 × 0.2 × 10−6/5 = 1.7 × 10−8 Ω m.
Three resistors, with substances 250 Ω, 500 Ω and 1 kΩ are connected in series. A 6 V battery is connected to either end of the combination. Calculate the potential difference between the ends of the 250 Ω resistor.
Answer: B (0.86 V)
Total = 1750 Ω, so I = 6/1750 A. V = 250 × 6/1750 ≈ 0.86 V.
A calibrated potentiometer is used to measure the e.m.f. of a cell because the
Answer: C (potentiometer takes no current from the cell)
At the balance point no current flows from the cell, so there is no voltage lost in its internal resistance and the true e.m.f. is measured.
In the above circuit diagrams, A is the ammeter and V the voltmeter. Which of the circuits is correct for finding the value of the resistance R?
Answer: A (I)
The ammeter must be in series with R and the voltmeter in parallel across R, as in circuit I.
Three 2-μF capacitors are arranged as shown in the above circuit. The effective capacitance between E and F is
Answer: B (1.33 μF)
The two in parallel give 4 μF, in series with 2 μF: C = (2 × 4)/(2 + 4) ≈ 1.33 μF.
The function of a 5-A fuse included in a circuit supplying a household refrigerator with power is to keep the
Answer: B (current supplied to the refrigerator below 5A)
The fuse melts and breaks the circuit if the current goes above 5 A, protecting the fridge and wiring.
The total power drawn from the cell in the circuit diagram above is
Answer: B (24 W)
The two 4 Ω in parallel give 2 Ω; with the series 4 Ω the total is 6 Ω. P = V²/R = 12²/6 = 24 W.
Which of the following correctly represents the relationship between the temperature rise θ and the current I in an experiment to illustrate the heating effect of electric current?
Answer: D (D)
Heat produced = I²Rt, so the temperature rise is proportional to I². A graph of θ against I² is a straight line through the origin, as in D.
An ammeter of resistance 0.1 Ω has a full-scale deflection of 50 mA. Determine the resultant full-scale deflection of the meter when a shunt of 0.0111 Ω is connected across its terminals.
Answer: C (500 mA)
At full scale the p.d. is 0.1 × 0.05 = 0.005 V. The shunt carries 0.005/0.0111 ≈ 0.45 A, so the total is 0.05 + 0.45 = 0.5 A = 500 mA.
The electrochemical equivalent of silver is 0.0012 g/C. If 36.0 g of silver is to be deposited by electrolysis on a surface by passing a steady current for 5.0 minutes, the current must be
Answer: B (100 A)
m = zIt, so I = 36/(0.0012 × 300) = 100 A.
The figure above shows a conductor PQ carrying a current I in the direction shown. At a particular position near the conductor is a compass needle K. Neglecting the earth's magnetic field, the compass needle will
Answer: C (settle in a fixed direction whether conductor PQ is a magnetic material or not)
Any current produces a magnetic field around it, whatever the wire is made of, so the needle settles along that field.
When a radiation strikes a metal surface, electrons may be ejected from the metal. The maximum kinetic energy which may be acquired by an ejected electron depends on the
Answer: C (wavelength of the radiation)
By Einstein's equation, maximum KE = hf − W = hc/λ − W, so it depends on the wavelength (frequency). Intensity only changes how many electrons come out.
Eight alpha decays and six beta decays are necessary before an atom of 23892U achieves stability. The final product in the chain has an atomic number of
Answer: C (82)
Each alpha decay lowers the atomic number by 2 and each beta decay raises it by 1: 92 − 16 + 6 = 82.
A beam of radiation is passed between a pair of charged plates as indicated in the diagram above. Beam P is undeflected while Q is deflected to the left. P and Q respectively could be I. γ-rays, β-rays II. x-rays, β-rays III. γ-rays, x-rays IV. x-rays, x-rays
Answer: C (I and II)
P is uncharged, so it could be γ-rays or X-rays. Q bends towards the positive plate, so it is negative: β-rays. Both I and II fit.