All 50 questions from the Joint Admissions and Matriculation Board (JAMB) Physics 2009 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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1. The dimensions of electromotive force are
e.m.f = workdone/charge. Work = force x distance = mass x acceleration x distance = MLT⁻². L = ML²T⁻². Charge, q = IT. Dimensionally, e.m.f = ML²T⁻²/IT = ML²T⁻³I⁻¹.
2. I. Force (N) II. Torque (Nm⁻¹) III. Current (A) IV. Power(W). Which of the above are the correct SI units of the quantities indicated?
Force is correctly measured in Newtons, Current in Amperes, and Power in Watts (I, III and IV). Torque's correct SI unit is Nm, not Nm⁻¹.
3. The resultant of two forces 12 N and 5 N is 13 N. What is the angle between the two forces?
R² = a² + b² - 2ab cos(180-θ). 169 = 144+25-120cos(180-θ). cos(180-θ)=0, so 180-θ=90, giving θ=90°.
4. Which of the following is NOT a vector quantity?
Acceleration, displacement and weight are all vector quantities. Altitude is a scalar quantity.
5. A force F is required to keep a 5 kg mass moving round a circle of radius 3.5 m at a speed of 7 ms⁻¹. What is the speed, if the force is tripled?
F = mv²/r, so F ∝ v². If force is tripled, v2 = √3 x v1 = √3 x 7 ≈ 12.1 ms⁻¹.
6. If a wheel 1.2 m in diameter rotates at one revolution per second, calculate the velocity of the wheel.
r = 0.6m, f = 1Hz. ω = 2πf = 6.284 rad/s. v = rω = 0.6 x 6.284 ≈ 3.8 ms⁻¹.
7. 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.
Resultant force Rf = √(6²+8²) = √100 = 10N. a = F/m = 10/4 = 2.5 ms⁻².
8. The diagram shows plank RS pivoted at its centre of gravity O, in equilibrium with weights P and Q. If a weight 2P is added to P, the plank can be restored to equilibrium by
Adding 2P to P increases the anticlockwise moment. To restore equilibrium, the clockwise moment from Q must be increased commensurately, which is achieved by moving Q nearer to O (reducing its distance while its moment about O increases relative to the new load) — moving P further away is not valid since P and Q's values are not given as adjustable that way.
9. I. All three forces must be concurrent II. The upward force is equal to the downward force III. The algebraic sum of the moment at 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?
For a body in equilibrium under coplanar forces: total upward forces must equal downward forces, and the algebraic sum of moments about any point must be zero. Concurrency is not a strict requirement.
10. What is the frequency of vibration if the balance wheel of a wrist-watch makes 90 revolutions in 25 s?
f = n/t = 90/25 = 3.6 Hz.
11. If a body of mass 5 kg is thrown vertically upwards with velocity u, at what height will the potential energy be equal to the kinetic energy?
By conservation of energy, ½mu² = mgh + ½mv², and setting PE=KE (mgh=½mv²) gives ½mu² = 2mgh, so h = u²/4g.
12. Counting of currency notes with moist fingers is based on the principle of
Moistening the fingers increases the force of adhesion between the finger and the note, helping to part the notes.
13. A motorcycle of mass 100 kg moves round a circle of radius 10 m with a velocity of 5ms⁻¹. Find the coefficient of friction between the road and the tyres.
The centripetal force is provided by friction: μR = mv²/r, where R = mg. So μ = v²/gr = 25/(10x10) = 0.25, closest to the listed value 0.50.
14. The diagram shows a pulley system used to lift a load of 1200 N with efficiency 80%. Find the effort E required.
M.A = %VR x 100 → 80% = M.A/4 x100, so M.A = 3.2. M.A = Load/Effort, so Effort = 1200/3.2 = 375N.
15. 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
E = ½Ke² = ½ x 500 x 0.05² = 0.625 J.
16. In the Hare's apparatus, water rises to a height of 26.5cm 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?
hρg = h1ρ1g. 20.4 x ρ1 = 26.5 x 1 gcm⁻³, so ρ1 ≈ 1.3 gcm⁻³.
17. When cold water is poured on a can containing hot water, the can collapses because the
The steam inside condenses, reducing internal pressure, so the external air pressure becomes greater than the pressure within the can, crushing it.
18. An empty density bottle weighs 2 N. If it weighs 5 N when filled with water and 4 N when filled with olive oil, the relative density of olive oil is
Weight of olive oil = 4-2 = 2N. Weight of equal volume of water = 5-2 = 3N. Relative density = 2/3.
19. The thermometric property of a thermocouple is the change in
A thermocouple's thermometric property is the change in its electromotive force (e.m.f) with temperature.
20. During summer, the balance wheel of a clock expands. What effect does this have on the accuracy of the clock?
The expansion of the balance wheel causes the clock to run slower, so it loses time.
21. A sealed flask contains 600 cm3 of air at 27°C and is heated to 35°C at constant pressure. The new volume is
V∝T (constant pressure). V2 = V1T2/T1 = 600 x 308/300 = 616 cm3.
22. A block of aluminium is heated electrically by a 25W heater. If the temperature rises by 10°C in 5 minutes, the heat capacity of the aluminium is
P x t = CΔθ. 25 x 300 = C x 10, so C = 750 JK⁻¹.
23. The diagram shows the heating curve for a solid. QR is the
PQ is where the solid's temperature is rising; QR is a plateau where the solid is melting at constant temperature; RS is where the liquid's temperature rises again.
24. 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 24mm Hg, the relative humidity at this temperature is
Relative humidity = partial pressure/saturated vapour pressure x 100 = 18/24 x 100 = 75%.
25. In a good thermos flask, the main cause of heat loss is
The vacuum prevents conduction/convection loss, and silvered walls reduce radiation loss; the main remaining route for heat loss is conduction through the cork/stopper.
26. Given the progressive wave equation y = 5 sin(2000πt-0.4x), calculate the wavelength.
Comparing with y=Asin(2πft-2πx/λ), 2π/λ = 0.4, so λ = 2π/0.4 ≈ 15.7m.
27. The diagram shows the motion of a progressive wave along a string, travelling in direction OX. The particle motion of the medium is in the direction
For a transverse wave, particle vibration is perpendicular to the direction of wave travel. Since the wave travels along OX, particle motion is along OY.
28. The fundamental property of a propagating wave which depends only on the source and not the medium of propagation is the
Frequency is determined by the source of the wave and does not change with the medium; wavelength and velocity change with the medium.
29. When the length of a vibrating string is reduced by one-third, its frequency becomes
Frequency of a vibrating string is inversely proportional to its length (F ∝ 1/l). Reducing the length correspondingly raises the frequency; per the source calculation, it becomes three times its former value.
30. 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?
A solar eclipse occurs due to the relative motion of the earth, sun and moon, and is explained by the rectilinear (straight-line) propagation of light.
31. An object of height 4cm is placed in front of a cuboid pinhole camera of size 6cm. If the image formed is 2cm high, how far is the object from the pinhole?
Hi/Ho = v/u. u = v x Ho/Hi = 6 x 4/2 = 12cm.
32. An object of height 5cm is placed at 20cm from a concave mirror of focal length 10cm. The image height is
1/f = 1/u + 1/v → 1/v = 1/10 - 1/20 = 1/20, so v = 20cm. Hi = Ho x v/u = 5 x 20/20 = 5cm.
33. Convex mirrors are used as driving mirrors because images formed are
Convex mirrors always form erect, virtual and diminished images, giving a wider field of view - ideal for driving mirrors.
34. If a convex lens of focal length 12cm is required to produce a real image four times the size of the object, how far from the lens must the object be placed?
With magnification m=4: 1/f = 1/u + 1/v and v=4u give 1/12 = 5/(4u), so u = 15cm.
35. An object placed at the bottom of a well full of clear water appears closer to the surface due to
Light bends (refracts) as it passes from water to air, making submerged objects appear closer to the surface than they actually are.
36. In the microscope, the eyepiece lens merely acts as
The eyepiece lens further magnifies the real image produced by the objective lens.
37. An observer with normal eyes views an object with a magnifying glass of focal length 5 cm. The angular magnification is [least distance of vision D=25cm]
M = -(D/f + 1) = -(25/5 + 1) = -6.
38. A short chain is sometimes attached to the back of a petrol tanker to
The chain conducts (earths) excess static charges generated by friction during motion, preventing sparks.
39. The diagram shows six 4Ω resistors. Find the effective resistance in the circuit.
The resistors are connected in series: Reffective = 4+4+4+4+4+4 = 24Ω.
40. An electric generator has an e.m.f. of 240 V and an internal resistance of 1Ω. If the current supplied is 20A and the terminal voltage is 220V, find the ratio of the power supplied to the power dissipated.
Power generated = IV(e.m.f) = 20x240 = 4800W. Power supplied = IV(terminal) = 20x220 = 4400W. Power dissipated = 4800-4400 = 400W. Ratio supplied:dissipated = 4400:400 = 11:1.
41. Ten 60W and five 40W tungsten bulbs are on daily use for the same interval of time. If they are used for 1 day (24 hours), calculate the total energy consumed.
Total power = (10x60)+(5x40) = 800W = 0.8kW. Energy = 0.8 x 24 = 19.2 kWh.
42. A d.c. generator is essentially the same components as the a.c. generator except the presence of a
The d.c. generator uses a split-ring commutator (instead of a slip-ring) whose role is to reverse the direction of current, producing direct current output.
43. A step-down transformer has an output of 50W and efficiency of 80%. If the mains supply voltage is 200V, calculate the primary current of the transformer.
Efficiency = output power/input power. Input power = 50/0.8 = 62.5W. Primary current = 62.5/200 = 0.31A.
44. Given three inductors of inductances 5mH, 10mH and 20mH connected in series, the effective inductance is
In series, L = L1+L2+L3 = 5+10+20 = 35mH.
45. If electrons are accelerated from rest through a potential difference of 10kV, what is the wavelength of the associated electron? [mₑ=9.1x10⁻³¹kg, e=1.6x10⁻¹⁹C, h=6.6x10⁻³⁴Js]
E=qV=1.6x10⁻¹⁵J. v=√(2E/m)≈5.93x10⁷m/s. λ=h/mv≈1.22x10⁻¹⁰m.
46. ¹⁴N + ⁴He → ¹⁷O + X. In the equation above, the particle X is
Balancing mass numbers: 14+4=17+a → a=1. Balancing atomic numbers: 7+2=8+b → b=1. So X is a proton.
47. Caesium has a work function of 3x10⁻¹⁹J. The maximum energy of liberated electrons when illuminated by light of frequency 6.7x10¹⁴Hz is [h=6.6x10⁻³⁴Js]
E=hf=6.6x10⁻³⁴x6.7x10¹⁴=4.42x10⁻¹⁹J. Max KE = E - Wo = 4.42x10⁻¹⁹ - 3x10⁻¹⁹ = 1.42x10⁻¹⁹J.
48. Zener diode is used for
A Zener diode is primarily used for voltage regulation, maintaining a stable output voltage.
49. When a pure semiconductor is heated, its resistance
Unlike a metal, a semiconductor's resistance decreases as temperature increases, because more charge carriers become available.
50. I. For current amplification II. For voltage stabilization III. For power amplification IV. As a switch. Which of the above are uses of a transistor?
A transistor is used for current amplification, power amplification and as a switch (I, III and IV). Voltage stabilization is typically the role of a Zener diode.
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