46 questions. Try each one, then open the answer to check yourself and read the explanation.
The dimensions of electromotive force are
Answer: A (ML2T−3I−1.)
E.m.f. is energy per unit charge. Energy has dimensions ML2T−2 and charge has IT, so e.m.f. = ML2T−2 ÷ IT = ML2T−3I−1.
I. Force (N) II. Torque (Nm−1) III. Current (A) IV. Power (W)
Which of the above are the correct S.I. units of the quantities indicated?
Answer: D (I, III and IV only)
Force in newtons, current in amperes and power in watts are correct. Torque is force × distance, so its unit is N m, not N m−1.
The resultant of two forces 12 N and 5 N is 13 N. What is the angle between the two forces?
Answer: C (90°)
122 + 52 = 144 + 25 = 169 = 132, so the forces form a right-angled triangle (Pythagoras): they act at 90° to each other.
A force F is required to keep a 5 kg mass moving round a cycle of radius 3.5 m at a speed of 7 ms−1. What is the speed, if the force is tripled?
Answer: C (12.1 ms−1)
F = mv2/r, so v2 ∝ F at fixed m and r. Tripling F gives v = 7√3 ≈ 12.1 m s−1.
If a wheel 1.2 m in diameter rotates at one revolution per second, calculate the velocity of the wheel
Answer: B (3.8ms−1.)
In one second a point on the rim travels one circumference: πd = 3.14 × 1.2 ≈ 3.8 m, so v ≈ 3.8 m s−1.
A body of mass 4 kg resting on a smooth horizontal plane is simultaneously acted upon by two perpendicular forces 6 N and 8 N. Calculate the acceleration of the motion.
Answer: A (2.5 ms−1.)
The resultant of perpendicular forces is √(62 + 82) = 10 N. a = F/m = 10 ÷ 4 = 2.5 m s−2.
The diagram above shows plank RS pivoted at its centre of gravity O and is in equilibrium with the weights P and Q. If a weight 2P is added to P, the plank will be in equilibrium again by
Answer: B (moving P nearer to O.)
The load on P's side becomes 3P, so its moment about O increases. To balance again, that moment must be reduced by moving P (now 3P) nearer to O so that 3P × new distance equals Q's moment.
I. All the three forces must be concurrent
II. The upward force is equal to the downward force
III. The algebraic sum of the moment about any point must be zero.
Which of the above conditions must hold for a body acted upon by a system of three coplanar forces in equilibrium?
Answer: D (I,II and III)
Three non-parallel forces in equilibrium must meet at one point, the forces must balance (upward = downward, left = right), and the total moment about any point must be zero. All three statements hold.
What is the frequency of vibration if the balance wheel of a wrist-watch makes 90 revolutions in 25 s?
Answer: D (3.60 Hz)
Frequency = number of revolutions ÷ time = 90 ÷ 25 = 3.6 Hz.
If a body of mass 5 kg is thrown vertically upwards with velocity u, at what height will the potential energy equal the kinetic energy?
Answer: B (h = u2/4g)
Total energy = ½mu2. When PE = KE, each is half the total: mgh = ¼mu2, so h = u2/4g.
Counting of currency notes with moist fingers is based on the principles of
Answer: C (adhesion.)
Water on the fingers clings to both the skin and the paper (attraction between unlike molecules), which is adhesion, so the notes are gripped better.
A motorcycle of mass 100 kg moves round in a circle of radius 10 m with a velocity of 5ms−1. Find the coefficient of friction between the road and the tyres. [g=10ms−2]
Answer: D (0.25)
Friction provides the centripetal force: μmg = mv2/r, so μ = v2/(rg) = 25 ÷ (10 × 10) = 0.25.
The efficiency of the pulley system shown above is 80%. Find the effort E required to lift a load of 1200 N.
Answer: C (375 N.)
The system has 4 pulleys, so VR = 4. MA = 0.8 × 4 = 3.2. Effort = load ÷ MA = 1200 ÷ 3.2 = 375 N.
A spring of force constant 500 Nm−1 is compressed such that its length shortens by 5 cm. The energy stored in the spring is
Answer: A (0.625 J.)
E = ½ke2 = ½ × 500 × (0.05)2 = 0.625 J.
In the Hare's apparatus, water rises to a height of 26.5 cm in one limb. If a liquid rises to a height of 20.4 cm in the other limb, what is the relative density of the liquid?
Answer: D (1.3)
Both columns are held up by the same pressure difference, so ρliquidhliquid = ρwaterhwater. Relative density = 26.5 ÷ 20.4 ≈ 1.3.
When cold water is poured on a can containing hot water, the can collapses because the
Answer: D (external pressure becomes greater than the pressure within the can.)
Cooling condenses the steam inside, so the pressure inside falls far below atmospheric pressure. The greater outside air pressure crushes the can.
The thermometric property of a thermocouple is the change in
Answer: B (electromotive force.)
A thermocouple produces an e.m.f. that changes with the temperature difference between its two junctions.
During summer, the balance wheel of a clock expands. What effect does this have on the accuracy of the clock?
Answer: C (The clock loses time)
A larger balance wheel swings more slowly (longer period), so the clock ticks fewer times per hour and loses time.
A sealed flask contains 600 cm3 of air at 27°C and is heated to 35°C at constant pressure. The new volume is
Answer: D (616 cm3.)
Charles's law with kelvin temperatures: V2 = 600 × 308/300 = 616 cm3.
A block of aluminium is heated electrically by a 25 W heater. If the temperature rises by 10°C in 5 minutes, the heat capacity of the aluminium is
Answer: B (750JK−1.)
Heat supplied = Pt = 25 × 300 = 7500 J. Heat capacity = heat ÷ temperature rise = 7500 ÷ 10 = 750 J K−1.
The diagram above is the heating curve for a solid. QR is the
Answer: A (melting region.)
PQ shows the solid warming up. Along QR the temperature stays constant while heat is absorbed as the solid turns to liquid, so QR is the melting region.
If the partial pressure of water vapour at 27°C is 18mm Hg and the saturated vapour pressure of the atmosphere at the same temperature is 24 mm Hg, the relative humidity at this temperature is
Answer: C (75%.)
Relative humidity = actual vapour pressure ÷ saturated vapour pressure × 100% = 18/24 × 100% = 75%.
In a good thermos flask, the main cause of heat loss is
Answer: A (conduction through the cork.)
The vacuum stops conduction and convection through the walls and the silvering cuts radiation, so most of the heat that still escapes is conducted through the cork stopper.
Given the progressive wave equation y=5 sin (2000 πt − 0.4x), calculate the wavelength
Answer: B (15.7m.)
Compare with y = A sin(ωt − 2πx/λ): 2π/λ = 0.4, so λ = 2π ÷ 0.4 = 15.7 m.
The above figure shows the motion of a progressive wave along a string. The particle motion of the medium is in the direction
Answer: B (Parallel to OY)
On a string the wave is transverse. The wave moves along OX (the arrow), while each particle of the string moves up and down, parallel to OY.
The fundamental property of a propagating wave which depends only on the source and not the medium of propagation is the
Answer: C (frequency.)
When a wave passes into another medium its speed and wavelength change, but its frequency stays the same because it is set by the vibrating source.
I. Total internal reflection of light
II. Conservation of light energy
III. Relative motion of the earth, sun and moon
IV. Rectilinear propagation of light.
Which of the above is a phenomenon of total solar eclipse?
Answer: D (III and IV only)
A solar eclipse happens when the moon moves between the sun and earth (relative motion) and casts a shadow because light travels in straight lines.
An object of height 4cm is placed in front of a cuboid pinhole camera of size 6 cm. If the image formed is 2 cm high, how far is the object from the pinhole?
Answer: C (12.0 cm)
Magnification = image height ÷ object height = image distance ÷ object distance. 2/4 = 6/u, so u = 12 cm.
An object of height 5cm is placed at 20 cm from a concave mirror of focal length 10 cm. The image height is
Answer: D (5 cm.)
The object is at 2f (the centre of curvature), so the image is also at 20 cm, inverted and the same size: 5 cm high.
Convex mirrors are used as driving mirrors because images formed are
Answer: A (erect, virtual and diminished.)
A convex mirror always gives an upright, virtual and smaller image, so it shows a wide field of view behind the driver.
If a convex lens of focal length 12 cm is used to produce a real image four times the size of the object, how far from the lens must the object be placed?
Answer: B (15cm)
Magnification 4 means v = 4u. 1/u + 1/4u = 1/12 gives 5/4u = 1/12, so u = 15 cm.
An object placed at the bottom of a well full of clear water appears closer to the surface due to
Answer: C (refraction.)
Light from the object bends away from the normal as it leaves water for air, so the object appears raised (apparent depth). This is refraction.
In the microscope, the eyepiece lens merely acts as
Answer: D (a magnifier.)
The objective forms a real image, and the eyepiece acts as a simple magnifying glass to enlarge that image further.
An observer with normal eyes views an object with a magnifying glass of focal length 5 cm. The angular magnification is [least distance of distinct vision D = 25cm]
Answer: C (5.)
For a relaxed normal eye (final image at infinity), angular magnification = D/f = 25 ÷ 5 = 5.
A short chain is sometimes attached to the back of a petrol tanker to
Answer: D (conduct excess charges to the earth.)
Friction with the air charges the tanker. The metal chain touching the road conducts the charge to earth so a spark cannot ignite the petrol.
An electric generator has an e.m.f. of 240 V and an internal resistance of 1 Ω. If the current supplied by the generator is 20 A when the terminal voltage is 220 V, find the ratio of the power supplied to the power dissipated.
Answer: C (12:11.)
Power supplied by the generator = EI = 240 × 20; power delivered to the external circuit = VI = 220 × 20. Ratio = 240 : 220 = 12 : 11.
A generator is on daily use and in the process, ten 60 W and five 40 W tungsten bulbs are on for the same time interval. The energy consumed daily is
Answer: D (19.20 kWh)
Total power = 10 × 60 + 5 × 40 = 800 W = 0.8 kW. In 24 hours the energy is 0.8 × 24 = 19.2 kWh.
The d.c. generator has essentially the same components as the a.c. generator except the presence of
Answer: C (split ring)
A d.c. generator uses a split-ring commutator instead of slip rings, so the output current always flows the same way.
A step-down transformer has a power output of 50W and efficiency of 80%. If the mains supply voltage is 200V, calculate the primary current of the transformer.
Answer: A (0.31A.)
Input power = output ÷ efficiency = 50 ÷ 0.8 = 62.5 W. Primary current = 62.5 ÷ 200 ≈ 0.31 A.
Given three inductors of inductances 5mH, 10mH and 20mH connected in series, the effective inductance is
Answer: D (35.00 mH.)
Inductors in series add like resistors: 5 + 10 + 20 = 35 mH.
If electrons are accelerated from rest through a potential difference of 10 kV, what is the wavelength of the associated electron? [me=9.1 × 10−31kg, e=1.6 × 10−19C, h=6.6 × 10−34Js]
Answer: A (1.22 × 10−11m)
Kinetic energy eV = 1.6 × 10−15 J, so v = √(2eV/m) ≈ 5.9 × 107 m s−1. De Broglie wavelength λ = h/mv = 6.6 × 10−34 ÷ (9.1 × 10−31 × 5.9 × 107) ≈ 1.22 × 10−11 m.
14N + 4He → 17O + X
In the equation above, the particle X is
Answer: A (a proton.)
Mass numbers: 14 + 4 = 17 + 1. Atomic numbers: 7 + 2 = 8 + 1. X has mass number 1 and atomic number 1, so it is a proton.
Caesium has a work function of 3 × 10−19J. The maximum energy of liberated electrons when it is illuminated by light of frequency 6.7 × 1014Hz is [h=6.6 × 10−34Js]
Answer: A (1.42 × 10−19J.)
Photon energy hf = 6.6 × 10−34 × 6.7 × 1014 = 4.42 × 10−19 J. Maximum kinetic energy = hf − W = 4.42 × 10−19 − 3.00 × 10−19 = 1.42 × 10−19 J.
Zener diode is used for
Answer: C (voltage regulation.)
In reverse breakdown a Zener diode keeps an almost constant voltage across itself even when the current changes, so it is used to regulate (stabilise) voltage.
When a pure semiconductor is heated, its resistance
Answer: B (decreases.)
Heating frees more electrons and holes in a pure semiconductor, so more charge carriers are available and its resistance falls.
I. For current amplification II. For voltage stabilization
III. For power amplification IV. As a switch.
Which of the above are the uses of a transistor?
Answer: B (I,III and IV only)
A transistor can amplify current and power and can act as a switch (I, III and IV). Voltage stabilisation (II) is done by a Zener diode, not listed as a transistor use.