JAMB Physics 1983

B: Altitude

Altitude is a height measured from a reference level, so it has magnitude without a vector direction. Force, weight, displacement and acceleration are vectors.

D: II and III only

Horizontal equilibrium gives P₃ = P₁ cos θ₁ + P₂ cos θ₂. Vertical equilibrium gives P₁ sin θ₁ = P₂ sin θ₂. Statement I is not a general equilibrium identity: the two angles need not be equal. Therefore II and III must hold.

A: It increases if the pull increases while the brick remains at rest

While the brick remains at rest, static friction acts leftwards and matches the rightward pull. Increasing that pull increases static friction until its limiting value is reached. The limiting value can change with normal force, but the actual static friction still balances the applied pull.

E: Weight.

Weight is the gravitational force acting on an object: W = mg. Mass measures the amount of matter and is measured in kilograms; weight is measured in newtons.

B: 2.0 × 10⁸ m/s

Refractive index n = c/v, so v = c/n = (3.0 × 10⁸)/1.5 = 2.0 × 10⁸ m/s. Light travels more slowly in this liquid than in a vacuum.

A: 380g

Relative density 19 means a density of 19 g/cm³. Mass = density × volume = 19 × 20 = 380 g. Immersion changes apparent weight, not the mass of the metal.

E: At a particular depth depends on the shape of the vessel.

For a liquid at rest, pressure due to the liquid is p = ρgh. At a given depth it depends on density and depth, not on the shape of the container.

C: I and II only

Long-sightedness makes close objects difficult to focus on; short-sightedness makes distant objects blurred. Short-sightedness is corrected using diverging lenses, so I and II are correct but III is false.

D: Shorter than 400nm

Gamma rays have much shorter wavelengths than visible light. Their wavelengths are therefore shorter than 400 nm.

A: 25 cm³

For a fixed amount of ideal gas, PV/T is constant. V₂ = V₁(P₁/P₂)(T₂/T₁) = 100 × ½ × ½ = 25 cm³. Both changes reduce the volume.

A: Source, slit, converging lens, prism, converging lens, screen.

The slit provides a narrow source. The first converging lens makes the rays parallel before the prism separates the colours; the second converging lens focuses them onto the screen to form a pure spectrum.

B: I and II only

For a given transmitted power, a higher voltage requires a smaller current. Heating loss is I²R, so a smaller current reduces heating and allows a smaller conductor cross-section for the same loss limit. Higher voltage does not mean that power travels faster.

C: 10.06 cm³

For a solid, volume expansivity is approximately 3α. V = V₀(1 + 3αΔT) = 10(1 + 3 × 2 × 10⁻⁵ × 100) = 10.06 cm³.

B: 4 A

Each parallel branch has the full 24 V across it. The current in each 6 Ω resistor is I = V/R = 24/6 = 4 A. The total current through all four branches is 16 A.

E: 2.268 × 10⁻³ kg

The charge passed is Q = It = 5 × 3600 = 18000 C. Deposited mass m = ZQ = 0.126 × 10⁻⁶ × 18000 = 2.268 × 10⁻³ kg.

E: Can be refracted and diffracted.

Both water ripples and light can change direction through refraction and spread around edges or openings through diffraction. They do not need to have the same speed or wavelength to show these wave behaviours.

B: 2 × 10⁻⁹ m

One drop has mass (5 × 10⁻⁴)/1000 = 5 × 10⁻⁷ kg. Its volume is m/ρ = 10⁻⁹ m³. Film thickness = volume/area = 10⁻⁹/0.5 = 2 × 10⁻⁹ m.

B: 10.00 cm

Hooke’s law makes extension proportional to load. An extra 10 g increases the length by 2 cm, so the 20 g load produces a 4 cm extension. The natural length is 14 − 4 = 10 cm.

B: II only

Atomic number is the number of protons, so II is correct. Mass number counts protons plus neutrons. A neutral atom has equal numbers of electrons and protons, not protons plus neutrons.

C: 0.18 J/(g·°C)

Electrical energy supplied is I²Rt = 3² × 20 × 10 = 1800 J. Using Q = mcΔT, c = 1800/(1000 × 10) = 0.18 J/(g·°C), equivalent to 180 J/(kg·°C).

C: 0.40 ohms

The current through the external resistor is I = 2/4 = 0.5 A. The internal voltage drop is 2.2 − 2.0 = 0.2 V, so internal resistance r = 0.2/0.5 = 0.40 Ω.

E: East

Point your right thumb upwards along the current. Your curled fingers show the magnetic-field direction around the wire. At a point south of the wire the tangent to this circle points east, so the field at P is eastwards.

C: Heat → kinetic energy → electricity → heat and light

The steam engine changes thermal energy into mechanical motion. The generator changes that motion into electrical energy, and the lamp changes electrical energy into light and heat.

D: I and III

Copper expands more than steel, so it becomes the outside of the bend. With copper above steel, the free end bends downwards towards the steel side, away from the contact above. Reversing the layers makes it bend upwards, allowing contact. Thus I and III are correct.

B: II and III only

A wet-and-dry bulb hygrometer uses evaporative cooling to determine humidity. A hair hygrometer uses the change in hair length with humidity. A manometer measures pressure; a hydrometer measures liquid density.

D: Vertical

Reflection in a plane mirror preserves length and reverses the component perpendicular to the mirror. Reflecting a horizontal line in a line inclined at 45° changes its orientation to vertical. The image is finite and the same size as the rod.

B: 2.25 × 10⁸ m/s

The refractive index is n = c/v. Therefore v = (3.0 × 10⁸)/(4/3) = 2.25 × 10⁸ m/s.

C: 20.0 N/C

Electric field strength is force per unit charge: E = F/q = 4/0.2 = 20 N/C.

D: Polarization

Polarization requires vibrations perpendicular to the direction of travel. Longitudinal waves vibrate along their direction of travel, so they cannot be polarized.

D: The tube is completely filled with water and P is lower than W

A continuous water column must first fill the tube, and the outlet P must be below the tank’s water surface W for gravity to drive outward flow. The inlet O only needs to remain submerged; it need not reach the bottom, and P need not be lower than O.