QUESTIONS:
PHYSICS 001: MECHANICS AND PROPERTIES OF MATTER
- (a) Define the following terms with one example each respectively:
(i) Damped oscillation
(ii) Forced oscillation [3marks]
(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. [5marks]
(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 = 9.8m/s²] [2marks]
- (a) (i) State the principle of floatation. [2 Marks]
(ii) List two differences between free and damped oscillation. [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]
PHY 002: HEAT, WAVES AND OPTICS
- (a)(i) Define the term specific latent heat of fusion. [3marks]
(ii) Distinguish between longitudinal and transverse waves.
(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 passed was 30°C. If the value of the latent heat of vaporization of water was finally estimated as 2.25 × 10⁶ J·kg⁻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]
(c) The inductance of an inductor is 30 mH when the current flowing through it increases uniformly from zero to 4A in 5 x 10⁻³s.
Calculate the:
(i) energy stored;
(ii) magnitude of e.m.f. induced.
- (a) (i) Describe the electric field lines and state their properties. [4 Marks]
(ii) A positive and a negative charge of the same magnitude are on 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.
Figure 1: [B (positive charge, +) — A — D — C (negative charge, −), points arranged left to right on a line] [2 Marks]
(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 stored 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
- (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]
- (a) Define the following terms:
(i) Photoelectric effect;
(ii) Doping;
(iii) Thermionic emission;
(iv) Half-life;
(v) Rectification. [5 marks]
Solutions
PHY 001: Mechanics and Properties of Matter
1(a)
- Damped oscillation: an oscillation whose amplitude decreases over time due to resistive/frictional forces (e.g., a swinging pendulum in air, or a car's suspension after hitting a bump).
- Forced oscillation: an oscillation driven by an external periodic force, made to oscillate at the driver's frequency (e.g., a child's swing being pushed periodically).
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 the 5th second: sₙ = u + (a/2)(2n−1) = (20/2)(2×5−1) = 10(9) = 90 m
1(c) Mass flow rate = 50 kg per 60 s
Power = mgh/t = (50 × 9.8 × 4)/60 = 1960/60 = 32.7 W
2(a)(i) Principle of floatation: a floating body displaces its own weight of the fluid it floats in.
(ii) Free oscillation has constant amplitude and occurs at the natural frequency with no external/resistive force; damped oscillation has decreasing amplitude due to resistive forces acting on the system.
2(b) y = 4sin(0.2t + 0.3), compared to y = A sin(ωt + φ):
- (i) Amplitude A = 4 m
- (ii) Angular frequency ω = 0.2 rad/s
- (iii) Period T = 2π/ω = 31.4 s
- (iv) Phase = (0.2t + 0.3) rad, initial phase φ = 0.3 rad
- (v) v = dy/dt = 0.8cos(0.2t+0.3); at t=0: v = 0.8cos(0.3) = 0.76 m/s
- (vi) a = −ω²y = −0.16sin(0.2t+0.3); at t=0: a = −0.16sin(0.3) = −0.047 m/s²
PHY 002: Heat, Waves and Optics
3(a)(i) Specific latent heat of fusion: the heat energy required to convert unit mass of a solid to liquid without change in temperature.
(ii) Longitudinal waves have particle vibration parallel to the direction of wave travel (e.g., sound); transverse waves have particle vibration perpendicular to the direction of travel (e.g., light, water ripples).
3(b) T = 1027°C = 1300 K
Average translational KE = (3/2)kT = 1.5 × (1.38×10⁻²³) × 1300 ≈ 2.69×10⁻²⁰ J
3(c) m_cu = 65 g, m_water = 450−65 = 385 g, T_i(water) = 30°C, steam = 24 g at 100°C, L = 2.25×10⁶ J/kg, c_cu = 0.4 J/gK, c_water = 4.2 J/gK (standard value)
Heat lost by steam = mL + mc_water(100−T) = 24(2250) + 24(4.2)(100−T) = 54000 + 10080 − 100.8T
Heat gained = (m_cu·c_cu + m_water·c_water)(T−30) = (65×0.4 + 385×4.2)(T−30) = 1643(T−30)
64080 − 100.8T = 1643T − 49290
113370 = 1743.8T
T ≈ 65.0°C
Electricity & Magnetism
5(c) L = 30 mH, ΔI = 4A, Δt = 5×10⁻³s
- (i) Energy stored = ½LI² = ½(0.03)(4²) = 0.24 J
- (ii) e.m.f. = L(ΔI/Δt) = 0.03 × (4/0.005) = 24 V
6(a)(i) Electric field lines: imaginary lines showing the direction a positive test charge would move. Properties: they start on positive charges and end on negative charges; never cross; closer spacing = stronger field; they're perpendicular to the surface of a conductor.
(ii) With B(+) and C(−) as the charges, and A, D lying on the line between them: the fields from both charges point in the same direction between them (away from + and toward −), so at A and D the field points from B toward C (left to right). Immediately at B the field points radially away from B; at C it points radially into C.
(b)(i) Q = 80 Ah = 80×3600 = 288,000 C
Energy = VQ = 12 × 288,000 = 3.456×10⁶ J
(ii) Series: Rs = R + R = 2R. Parallel: Rp = R²/(2R) = R/2.
Ratio Rs/Rp = 2R ÷ (R/2) = 4 ✔ (as required)
PHY 004: Modern Physics
7(a)
- Atomic number (Z): number of protons in the nucleus of an atom.
- Mass number (A): total number of protons + neutrons in the nucleus.
- Thermionic emission: emission of electrons from a heated metal surface.
7(b) E = mc², where E = energy released/equivalent, m = mass (defect), c = speed of light in vacuum (3×10⁸ m/s).
7(c) Half-life = 15 days, 45 days = 3 half-lives
Remaining = 16 × (½)³ = 16/8 = 2 g
Decayed = 16 − 2 = 14 g
Fraction decayed = 14/16 = 7/8 (87.5%)
7(d) Geiger-Müller tube: a gas-filled tube with a thin mica window and central wire anode at high voltage; incoming radiation ionizes the gas, producing a pulse of current that's counted electronically. Used to detect and measure ionizing radiation (radioactivity).
8(a)
- Photoelectric effect: emission of electrons from a metal surface when light of sufficient frequency falls on it.
- Doping: adding impurity atoms to a pure (intrinsic) semiconductor to alter its electrical conductivity.
- Thermionic emission: emission of electrons from a heated metal surface.
- Half-life: the time taken for half the atoms in a radioactive sample to decay.
- Rectification: the process of converting alternating current (AC) to direct current (DC).