Questions:
PHYSICS 001: MECHANICS AND PROPERTIES OF MATTER
1. (a) Define the following terms with one example each respectively:
(i) Damped oscillation
(ii) Forced oscillation
[3 marks]
(b) An object starts from rest with a constant acceleration of 20 m/s² along a straight line, determine the:
(i) speed at the end of 4 seconds;
(ii) the distance travelled in 4 seconds;
(iii) the distance covered in the fifth complete seconds. [5 marks]
(c) A pump is used to spray water from a pull in order to form a fountain, if the pump ejects 50kg of water per minute through a vertical height of 4m, calculate the minimum power of the pump.
[g = 9.8 m/s²] [2 marks]
(b) A particle executing simple harmonic motion has its displacement, y given by the equation y = 4sin(0.2t + 0.3); all terms are in SI units. Calculate the:
(i) amplitude;
(ii) angular frequency;
(iii) period;
(iv) phase of the motion;
(v) initial velocity;
(vi) acceleration of the particle. [6 Marks]
2. (a) (i) State the principle of floatation. [2 Marks]
(ii) List two differences between free and damped oscillation. [2 Marks]
PHY 002: HEAT, WAVES AND OPTICS
3. (a)(i) Define the term specific latent heat of fusion.
(ii) Distinguish between longitudinal and transverse waves [3 marks]
(b) Compute the average translational energy of diatomic oxygen in air if temperature is measured as 1027 °C [3marks]
(c) In an experiment, the mass of copper calorimeter was measured as 65.0 g. The total mass of calorimeter and water was 450.0 g. The initial temperature of the water in the calorimeter before steam was passed was 30 °C. If the value of the latent heat of vaporization of water was finally estimated as 2.25 × 10⁶ Jkg⁻¹ after steam of mass 24g at 100 °C was passed, calculate the final temperature of the mixture. [Specific heat of copper = 0.4 J/gK] [4 Marks]
4. (a) Briefly explain the following:
(i) Fresnel diffraction;
(ii) Fraunhofer diffraction;
(iii) dispersion of light. [3 marks]
(b) An object 5 cm high is placed 30 cm from a concave mirror of radius of curvature 25 cm, calculate:
(i) image distance;
(ii) magnification;
(iii) From (i) and (ii), State two properties of the image formed. [4 marks]
(c) Briefly explain short sightedness and far sightedness. [3 marks]
(ii) 90° to the field. [3 marks]
(c) The inductance of an inductor is 30 mH when the current flowing through it increases uniformly from zero to 4A in 5 × 10⁻³s. Calculate the:
(i) energy stored;
(ii) magnitude of e.m.f. induced.
6. (a)(i) Describe the electric field lines and state their properties. State the direction of the electric field lines and state their properties. State the direction of the same straight line as shown in Figure 1. State the direction of the electric field strength at point A, at point B, at point C and at point D.
B A C •D
Positive charge Negative charge
Figure 1
(ii) A positive and a negative charge of the same magnitude are on point D. [4 Marks]
PHY 003: ELECTRICITY AND MAGNETISM
5. (a) Briefly explain the following terms
(i) Resistivity;
(ii) Dielectric substance;
(iii) Standard resistor. [3 marks]
(b) A wire of length 250 cm is placed in a field of strength 1.5 T.
Calculate the force exerted on the wire when a current of 2.0 A flows through it in a direction:
(i) 30°
(b)(i) The capacity of storage batteries is rated in ampere-hours (Ah). An 80Ah battery can supply a current of 80A for 1 hour or 40A for 2 hours and so on. Calculate the total energy in Joules stored in a 12V, 80Ah car battery. [2 Marks]
(ii) Two resistors each of resistance R are connected first in series and then in parallel. Show that the ratio of combined resistance of resistors connected in series to combined resistance of resistors connected in parallel is equal to 4. [2 Marks]
PHY 004: MODERN PHYSICS
7. (a) Briefly explain the following:
(i) Atomic number;
(ii) Mass number;
(iii) Thermionic emission. [3 marks]
(b) Write the mathematical equation for Einstein mass-energy relation and state the meaning of each of its parameters. [2 marks]
(c) A radioactive material of half-life of 15 days has an initial mass of 16 g. Calculate the fraction that would have decayed after 45 days.
[3 marks]
(d) Briefly describe a Geiger-Muller tube and state its use. [2 marks]
(b) The ground state of hydrogen is −13.6 eV and the first excited state is −3.4 eV.
Calculate the wavelength of the radiation emitted if the atom returns from this excited state to the ground state. [3 marks]
(c) List any FOUR spectral series of the hydrogen atom. [2 marks]
8. (a) Define the following terms:
(i) Photoelectric effect;
(ii) Doping;
(iii) Thermionic emission;
(iv) Half-life;
(v) Rectification. [5 marks]
Solutions
SECTION B: PHYSICS 001 – Mechanics & Properties of Matter
1(a)
- Damped oscillation: oscillation whose amplitude decreases over time as energy is dissipated by resistive forces. Example: a pendulum swinging in air until it stops.
- Forced oscillation: oscillation of a system driven by an external periodic force at the driver's frequency (not its natural frequency). Example: a swing being pushed repeatedly by a person.
1(b) u = 0, a = 20 m/s²
- (i) v = u + at = 0 + 20(4) = 80 m/s
- (ii) s = ut + ½at² = ½(20)(4²) = 160 m
- (iii) Distance in 5th second = u + (a/2)(2n−1) = (20/2)(9) = 90 m
1(c) Mass flow = 50 kg/min = 50/60 kg/s; h = 4 m
Power = ṁgh = (50/60)(9.8)(4) = ≈ 32.7 W
1(b) [SHM] y = 4 sin(0.2t + 0.3)
- (i) Amplitude A = 4 m
- (ii) Angular frequency ω = 0.2 rad/s
- (iii) Period T = 2π/ω = 31.4 s
- (iv) Phase φ = 0.3 rad
- (v) v = Aω cos(ωt+φ) → at t=0: v = 4(0.2)cos(0.3) = ≈ 0.76 m/s
- (vi) a = −Aω² sin(ωt+φ) → at t=0: a = −4(0.04)sin(0.3) = ≈ −0.047 m/s²
2(a)(i) Principle of floatation: a floating body displaces a weight of fluid equal to its own weight.
2(a)(ii) Free vs damped oscillation:
- Free: constant amplitude, no energy loss, natural frequency.
- Damped: amplitude decreases with time due to resistive/frictional forces.
PHY 002 – Heat, Waves & Optics
3(a)(i) Specific latent heat of fusion: heat required to convert 1 kg of a solid to liquid at constant temperature.
3(a)(ii) Longitudinal waves: particle vibration parallel to wave travel (compressions/rarefactions, e.g. sound). Transverse waves: particle vibration perpendicular to wave travel (crests/troughs, e.g. light).
3(b) T = 1027 + 273 = 1300 K
Average KE = (3/2)kT = 1.5 × 1.38×10⁻²³ × 1300 ≈ 2.69×10⁻²⁰ J
3(c) (assuming specific heat of water = 4.2 J/g°C, since not given)
- Mass of water = 450.0 − 65.0 = 385 g
- Heat from steam condensing + cooling = heat gained by calorimeter + water:
0.024(2.25×10⁶) + 24(4.2)(100−θ) = 65(0.4)(θ−30) + 385(4.2)(θ−30)
54000 + 10080 − 100.8θ = 1643(θ−30)
64080 − 100.8θ = 1643θ − 49290
113370 = 1743.8θ
θ ≈ 65.0 °C
4(a)
- Fresnel diffraction: occurs when source and/or screen are at a finite distance from the aperture (spherical wavefronts).
- Fraunhofer diffraction: occurs when source and screen are effectively at infinity (plane wavefronts), usually achieved with lenses.
- Dispersion: the splitting of white light into its component colours because different wavelengths refract by different amounts.
4(b) Concave mirror: u = 30 cm, R = 25 cm → f = 12.5 cm
1/v = 1/f − 1/u = 1/12.5 − 1/30 = 0.04667
- (i) v ≈ 21.4 cm
- (ii) m = −v/u = −21.4/30 ≈ −0.71
- (iii) Since m is negative and |m| < 1: image is real, inverted, and diminished.
4(c)
- Short-sightedness (myopia): distant objects appear blurred because the image forms in front of the retina; corrected with a diverging (concave) lens.
- Far-sightedness (hypermetropia): near objects appear blurred because the image forms behind the retina; corrected with a converging (convex) lens.
Field lines (Fig. 1): Field lines emerge from the positive charge and terminate on the negative charge; they never intersect, and line density indicates field strength. Along the line joining the charges, the field points from the positive charge toward the negative charge at points A, B, and C; at D (off the line), the field direction is along the resultant of contributions from both charges, generally pointing away from the positive and curving toward the negative charge.
6(c) L = 30 mH, ΔI = 4 A, Δt = 5×10⁻³ s
- (i) Energy stored = ½LI² = ½(0.03)(4²) = 0.24 J
- (ii) emf = L(ΔI/Δt) = 0.03 × (4/0.005) = 24 V
PHY 003 – Electricity & Magnetism
5(a)
- Resistivity: resistance of a unit length of material with unit cross-sectional area (ρ = RA/L); a material property (Ωm).
- Dielectric substance: an insulating material that can be polarized by an electric field but does not conduct current (used in capacitors).
- Standard resistor: a resistor with a precisely known, stable resistance used as a reference for calibration.
5(b) F = BIL sinθ, L = 2.5 m, B = 1.5 T, I = 2.0 A
- (i) θ = 30°: F = 1.5×2×2.5×sin30° = 3.75 N
- (ii) θ = 90°: F = 1.5×2×2.5×sin90° = 7.5 N
5(b)(i) Q = 80 Ah × 3600 = 288,000 C
Energy = QV = 288,000 × 12 = 3.456×10⁶ J
5(a)(ii) For two equal resistors R:
- Series: Rₛ = 2R
- Parallel: R_p = R/2
- Ratio Rₛ/R_p = 2R ÷ (R/2) = 4 ✔ (as required)
PHY 004 – Modern Physics
7(a)
- Atomic number (Z): number of protons in the nucleus.
- Mass number (A): total number of protons + neutrons.
- Thermionic emission: liberation of electrons from a heated metal surface.
7(b) Einstein mass-energy relation: E = mc², where E = energy, m = mass (defect), c = speed of light (3×10⁸ m/s).
7(c) t½ = 15 days; 45 days = 3 half-lives
Fraction remaining = (½)³ = 1/8 → Fraction decayed = 7/8
7(d) A Geiger-Muller tube is a gas-filled tube with a thin wire anode held at high voltage; incoming ionizing radiation ionizes the gas, producing a pulse of current that registers as a count/click. It's used to detect and measure radioactivity/ionizing radiation.
6(b) [Hydrogen wavelength] ΔE = −3.4 − (−13.6) = 10.2 eV = 1.632×10⁻¹⁸ J
λ = hc/ΔE = (6.63×10⁻³⁴ × 3×10⁸)/1.632×10⁻¹⁸ ≈ 1.22×10⁻⁷ m (122 nm)
7(c) [spectral series] Any four of: Lyman, Balmer, Paschen, Brackett, Pfund
8(a)
- Photoelectric effect: emission of electrons from a metal surface when light of sufficient frequency (above threshold) strikes it.
- Doping: adding controlled impurity atoms to a semiconductor to change its conductivity (creating p-type or n-type material).
- Thermionic emission: emission of electrons from a heated metal surface.
- Half-life: time for a radioactive substance's activity/mass to reduce to half its original value.
- Rectification: the process of converting alternating current (AC) to direct current (DC), typically using diodes.