JAMB Physics 2004

C: v/f − 1

For a real image, using positive object and image distances, 1/f = 1/u + 1/v. Multiplying by v gives v/f = v/u + 1. The magnitude of linear magnification is v/u = v/f − 1; the image itself is inverted.

D: Frequency

For a pure tone, pitch is primarily determined by frequency: higher frequency is heard as higher pitch. Timbre or quality distinguishes sounds with different waveform and harmonic content, rather than defining the frequency of a pure tone.

B: Be parallel

Two nonzero vectors with an angle of 0° point in the same direction and are parallel. Their cross product is zero and their dot product equals the product of their magnitudes; perpendicular vectors instead have a 90° angle.

A: I, II, III and IV

All four involve equal and opposite forces on different bodies. Engines push exhaust backwards and receive forward thrust; a gun pushes a bullet forward and recoils. When walking, the foot pushes the ground backwards and the ground exerts forward friction on the foot.

B: 4 m²

The transmitted pressure is F₁/A₁ = 40/0.4 = 100 Pa. The load piston must have area A₂ = F₂/P = 400/100 = 4 m². This gives the same pressure at both pistons in the ideal hydraulic press.

D: 13 N rightwards

Take rightwards as positive. The horizontal components add to −4 + 10 + 8 cos 60° + 6 cos 60° = −4 + 10 + 4 + 3 = 13 N. The angled forces both contribute rightwards, although their vertical components oppose each other.

C: X_L = X_C

At series resonance the inductive and capacitive reactances cancel. Since the net reactance is X_L − X_C, it vanishes when X_L = X_C. The ideal series impedance is then purely resistive.

A: λ = h/p

The de Broglie relation is λ = h/p, where p is particle momentum and h is Planck’s constant. It associates a wavelength with matter. The formulas c/f and hc/E apply directly to photons in vacuum, and 2d sin θ describes first-order Bragg diffraction.

D: Their resistance decreases with temperature

A negative temperature coefficient means resistance falls as temperature rises over the stated operating range. In many semiconductors, heating creates additional mobile carriers, which can increase conductivity and reduce resistance.

B: Excitation of the gas followed by fluorescence of the phosphor coating

An electric discharge excites mercury atoms in the tube. They emit ultraviolet radiation, which the phosphor coating absorbs and re-emits as visible light. The process uses excitation and fluorescence rather than simply heating a filament until it glows.

C: Minority carriers

Before reverse breakdown, the small reverse current in a junction diode is associated with minority carriers: electrons on the p side and holes on the n side. The reverse field sweeps these carriers across the junction.

D: 9.0 × 10⁻² J

The magnetic energy stored in a linear inductor is U = ½LI². With L = 5 × 10⁻³ H and I = 6 A, U = ½ × 0.005 × 36 = 0.090 J, or 9.0 × 10⁻² J.

A: Have wavelengths comparable to atomic-plane spacings

X-ray wavelengths can be comparable to the spacing between atomic planes in a crystal. The resulting diffraction pattern depends on that spacing and arrangement, allowing crystal structure to be studied. Speed and invisibility alone do not provide this spatial resolution.

C: 1.2 A

The net reactance is 16 − 10 = 6 Ω. Thus Z = √(8² + 6²) = 10 Ω, and the rms current is I = V/Z = 12/10 = 1.2 A. Reactances subtract because their voltage contributions have opposite phases.

B: Polarization

Polarization selects a direction of transverse oscillation. A purely longitudinal wave oscillates along its direction of propagation and cannot be polarized in this way. Diffraction, reflection and refraction can occur for both types of wave.

D: Increase in the volume of water

Water expands when it freezes into ordinary ice, whose open molecular arrangement gives it a lower density. In a full, rigid bottle there is insufficient space for the increased volume, so the resulting pressure can crack the bottle.

A: 0.05 m³

The ice volume is 450/900 = 0.50 m³. The same mass of water occupies 450/1000 = 0.45 m³. The volume therefore decreases by 0.50 − 0.45 = 0.05 m³; mass is conserved during melting.

C: 250 N

The first extension is 20.01 − 20.00 = 0.01 m. The required extension is 0.05 m, five times larger. Within the Hooke’s-law range, force is proportional to extension, so the required force is 5 × 50 = 250 N.

B: Radiation

A shiny silver surface has low thermal emissivity, so it emits less thermal radiation than a dull surface at the same temperature. The coating does not remove heat transfer by air convection or conduction through the pot and its supports.

A: 500 J kg⁻¹ K⁻¹

In 10 minutes the heater supplies Q = Pt = 50 × 600 = 30 000 J. Using Q = mcΔT gives c = 30 000/(5 × 12) = 500 J kg⁻¹ K⁻¹. A rise of 12°C equals a rise of 12 K.

B: Electrophorus

An electrophorus uses a charged insulating base and a removable conducting plate. Bringing the plate near the base, grounding it, disconnecting the ground and lifting it produces a charged plate. The sequence can be repeated to obtain charges of the same sign.

A: Characteristic X-rays arise from electronic transitions; nuclear gamma rays arise from nuclear transitions

Characteristic X-rays arise from transitions involving atomic electrons. Nuclear gamma rays arise from transitions between nuclear energy levels. Both are uncharged electromagnetic radiation, and their energy ranges can overlap, so origin is the useful distinction here.

B: 1 : 2

Both parallel resistors have the same 12 V across them. Their powers are P₆ = 12²/6 = 24 W and P₃ = 12²/3 = 48 W. Thus P₆ : P₃ = 24 : 48 = 1 : 2.

A: Grape juice

Grape juice contains mobile ions from dissolved acids and mineral salts, so it conducts electricity as an electrolytic solution. Pure sugar solution is molecular rather than ionic, while pure alcohol and paraffin do not supply comparable mobile ions.

C: 0.1 μF

Connecting all three capacitors in series gives the smallest equivalent capacitance. In μF units, 1/C = 1/0.3 + 1/0.5 + 1/0.2 = 31/3. Thus C = 3/31 ≈ 0.0968 μF, which rounds to 0.1 μF to one decimal place.