FORM SIX JOINT EXAMINATION SERIES 1 — PHYSICS 2 (131/2)-MWALA_LEARN

Objectives: FORM SIX JOINT EXAMINATION SERIES 1 — PHYSICS 2 (131/2)

FORM SIX JOINT EXAMINATION SERIES 1 — PHYSICS 2 (131/2)
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FORM SIX JOINT EXAMINATION SERIES 1

PHYSICS 2
131/2
Duration: 3:00 Hours
Monday, August 25, 2025
Instructions
  1. This paper consists of a total of six (6) questions.
  2. Answer five (5) questions.
  3. Each question carries twenty (20) marks.
  4. Mathematical tables and non-programmable calculators may be used.
  5. Cellular phones and any unauthorized materials are not allowed in the examination room.
  6. Write your official name on every page of your answer booklet(s).
  7. The following information may be useful.
    1. Acceleration due to gravity, g = 9.8\,\mathrm{m\,s^{-2}}
    2. Density of air, \rho_a = 1.29\,\mathrm{kg\,m^{-3}}
    3. Density of water, \rho_w = 10^3\,\mathrm{kg\,m^{-3}}
    4. Speed of sound in air, v = 340\,\mathrm{m\,s^{-1}}
    5. Speed of light, c = 3.0\times10^{8}\,\mathrm{m\,s^{-1}}
    6. Surface tension of water, \gamma = 0.072\,\mathrm{N\,m^{-1}}
    7. Coulomb constant of free space, k = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}}
    8. Electronic charge, e = 1.6\times10^{-19}\,\mathrm{C}
1.
(a)

You are working in a garage as a mechanical engineer; your customers need knowledge from you why:

  1. Cars need different oils in hot and cold countries. (1.5 marks)
  2. Engine runs more freely as it heats up. (1.5 marks)
  3. Skin lotions are easier to pour in summer than in winter. (1.5 marks)
(b)

A liquid flows steadily between two pipes A and B which are joined end-to-end and whose internal radii are r and 2r respectively. If B is eight times longer than A and the pressure difference between the ends of the composite pipe is 9000 N m−2, what is the pressure difference across A? (3.5 marks)

(c)
  1. A Tanzanian student in a diving training college in South Africa is told to observe the motion of a trainer falling from greatest height. He noted the change in velocity of the diver for some time and later the speed remained constant. Based on the knowledge of fluid dynamics, explain how this happens. (3 marks)
  2. In a viscous-fluid experiment, Mr. Ishengoma dropped a metallic sphere of radius 1.0 × 10−3 m and density 1.0 × 104 kg m−3 to enter a tank of water after free fall through a height H in Earth’s gravitational field. If its velocity remains unchanged after entering water, determine the value of H. (4 marks)
(d)
  1. According to Bernoulli’s principle the pressure of water should remain constant in a pipe of uniform cross-section. But in practice it decreases. Why? (2 marks)
  2. A DAWASCO pressure meter attached to a closed pipe reads 2.5×105 N m−2. On opening the valve the reading drops to 2.0×105 N m−2. Calculate the speed of water flowing through the pipe. (3 marks)
2.
(a)
  1. Msonjo brings you a string and two pieces of wood and wants to learn the formation of standing waves. Using the materials provided, demonstrate how standing waves in a string are formed. (2 marks)
  2. Form Five students are researching why a duck floating on a lake is likely to remain at the same place even as water waves pass. Help them explain how this is possible. (3 marks)
Standing wave with nodes at the supports

Fig. A — Standing wave demonstration on a stretched string between two supports.

(b)
  1. In a concert hall two forks, A and B, produce 4 beats s−1. Fork A is in unison with a 30 cm length of a sonometer wire and fork B with 25 cm at the same tension. Calculate the frequencies of the forks. (3 marks)
  2. “The rise in temperature causes a variation in the velocity of sound.” Is this statement true? If yes, using a mathematical relation explain how the two quantities are related. (3 marks)
(c)

Two stars of equal mass move in a circular orbit of radius r about their common centre of mass. From spectral lines, one star’s wavelength varies from 599.9 nm to 600.1 nm during one revolution.

  1. Calculate the speed of the star. (2 marks)
  2. If the orbital period is 3.5×106 s, find the orbital radius r. (2 marks)
(d)

In a Newton’s rings experiment, the diameter of the 15th dark ring is 0.59 cm and that of the 5th dark ring is 0.336 cm. If the radius of curvature of the plano-convex lens is 100 cm, calculate the wavelength of the light used. (5 marks)

Glass plate Plano-convex lens (R = 100 cm) Newton’s rings

Fig. B — Schematic of Newton’s rings arrangement.

3.
(a)
  1. Mr. Kazimoto of Kazulamimba Secondary School throws a piece of chalk through a window; it hits the wall and then a bucket full of water. A student tries to pick it up but finds lots of bubbles emitted in all directions. Explain why this happened. (2 marks)
  2. A Form One student dips a capillary tube in water and the water level rises to 2 mm. What level would you expect if a capillary tube of half the radius is used? (3 marks)
r r/2 Water rise = 2 mm rise = ?

Fig. C — Capillary rise for tubes of radius r and r/2.

(b)

A spherical drop of water has radius 1 mm. Explain the pressure difference between the inside and outside of the drop. (4 marks)

(c)
  1. Someone attempts to measure a temperature of −5 K and fails to even start for an hour. Explain why temperatures less than the absolute zero 0 K are impossible. (2 marks)
  2. At what temperature is the root-mean-square speed of oxygen molecules equal to the escape speed from Earth’s surface if the escape speed is 11.2 km s−1? (4 marks)
(d)

What will be the density of lead under a pressure of 2×108 N m−2? Take the density of lead as 11.4×103 kg m−3 and the bulk modulus as 8×109 N m−2. (5 marks)

4.
(a)
  1. Two friends argue about the proper method for testing electric charge—repulsion or attraction. Side with one and convince the rest that repulsion is the only sure test for charge. (2 marks)
  2. Two charges −5 μC and 20 μC are brought into contact briefly and then separated by 10 cm. Find the force between them after separation. (3 marks)
(b)
  1. Two equipotential surfaces never cross. Explain briefly why. (2 marks)
  2. Two positive point charges of 16×10−10 C and 12×10−10 C are placed 10 cm apart. Find the work done in bringing the two charges 4 cm closer. (2 marks)
(c)

Two capacitors C₁ and C₂ each of plate area 20 cm² and separation 2 cm have capacitances 4 μF and 5 μF respectively. Capacitor C₁ is charged to 90 V and C₂ to 120 V. They are then connected with like plates joined together.

  1. What is the loss of energy transferred as heat in the wires during connection? (3 marks)
  2. Find the energy-loss density (energy per unit volume). (2 marks)
(d)

Two point charges of +5 μC and −3 μC are placed at points A and B as shown. Calculate the work done in moving a charge of −3 μC from P and from Q. (6 marks)

Q P +5 μC −3 μC 900 mm 1200 mm

Fig. D — Charges on axes (Q at origin; P at −600 mm on x-axis; symmetric right point shown).

5.
(a)

Distinguish between the following, giving due explanation:

  1. Stress and strain. (2 marks)
  2. Force and stress. (2 marks)
  3. Tensile stress and compressive stress. (2 marks)
(b)

A member is formed by connecting a steel bar to an aluminium bar as shown. Assuming the bars are prevented from buckling sideways, calculate the force F which will cause the total length of the member to decrease by 0.30 mm. Take the elastic moduli of steel and aluminium as 2×105 N mm−2 and 6.5×104 N mm−2, respectively. (4 marks)

Steel bar (E = 2×10⁵ N/mm², L = 10 cm) Aluminium bar (E = 6.5×10⁴ N/mm², L = 10 cm) Cross-section (example): 20 cm² (schematic) Axial force F causing total contraction ΔL = 0.30 mm

Fig. E — Composite bar: steel + aluminium in series (schematic dimensions as in the question).

(c)
  1. State Coulomb’s law. (1 mark)
  2. Deduce Coulomb’s law from Gauss’s theorem. (4 marks)
  3. A proton of mass 1.673×10−27 kg falls through a distance of 1.5 cm in a uniform electric field of magnitude 2.0×104 N C−1. Neglect air resistance and gravity; calculate its time of fall. (5 marks)
6.
(a)
  1. Give a concrete reason for the straight-line propagation of light irrespective of its wave nature. (3 marks)
  2. In a Young’s double-slit experiment, green mercury light of wavelength 0.54 μm is used with a pair of slits separated by 0.6 mm. If the screen is at 40 cm, calculate the fringe separation. (4 marks)
(b)
  1. Identify two cases in which there is no Doppler effect in sound. (2 marks)
  2. A car sounds a horn of frequency 500 Hz. If it approaches and then passes a stationary observer Q at a steady speed of 20 m s−1, calculate the change in pitch of the note as heard by Q. (5 marks)
(c)
  1. What properties of a medium are responsible for the propagation of a wave through it? Give two points. (2 marks)
  2. A horizontal stretched elastic string of length 3.0 m and mass 12 kg is subjected to a tension of 1.6 N. If a transverse wave of frequency 40 Hz travels along the string, determine the distance between successive crests. (4 marks)
PHYSICS 2 — Answer Key with Visuals (HTML + SVG)

FORM SIX JOINT EXAM SERIES 1 — PHYSICS 2 (131/2)

1. Fluids & Bernoulli

(a) Everyday viscosity facts
  • Hot vs cold oils: Viscosity decreases when temperature increases. Hot climates need higher-viscosity (or higher multigrade index) oils to keep a protective film; cold climates need lower-viscosity for easy start.
  • Engine runs freer when warm: Oil thins → frictional/viscous losses drop → smoother running.
  • Lotions pour easier in summer: Same viscosity–temperature effect.
(b) Composite pipe (Poiseuille)

Laminar flow pressure drop: ΔP &propto \(\) L / r4. Let A have radius r, B have 2r, and B is 8 times longer.

(ΔP)B / (ΔP)A = (8) / (24) = 8/16 = 1/2

Total: ΔPtot = ΔPA + ΔPB = (3/2)ΔPA = 9000 Pa

Answer: ΔP across A = 6000 Pa.

(c) Falling sphere & terminal speed
Weight mg Drag FD &propto v2 Terminal speed when mg = FD → speed constant

At terminal speed the forces balance, so velocity is constant.

Sphere radius r = 1.0×10−3 m; densities: 1.0×104 and 1.0×103 kg m−3; water viscosity η = 1.0×10−3 Pa·s.

vt = [2 r2 ( ρs − ρw) g] / (9 η) ≈ 19.6 m s−1
v = √(2 g H) = vt &Rightarrow H = vt2 / (2 g) ≈ 19.6 m

Answer: required height H ≈ 19.6 m.

(d) Why Bernoulli seems to fail & speed from pressure drop
  • Bernoulli assumes no viscosity. Real pipes have viscous dissipation → pressure decreases along the pipe.

Meter closed: 2.5×105 Pa; open: 2.0×105 Pa. Dynamic pressure ΔP = 0.5×105 Pa.

v = √(2 ΔP / ρ) = √(2 × 5×104 / 1000) ≈ 10 m s−1

2. Waves, Beats & Orbits

(a) Standing waves and ducks on lakes
L = n λ / 2 at resonance

Nodes at supports; antinodes between. Energy moves, medium points mostly oscillate.

Duck stays near same place because water-particle paths in surface waves are nearly closed orbits → little net transport of water.

(b) Beats with sonometer

Same tension → frequency f &propto 1/L.

fA = k / 0.30,   fB = k / 0.25,   |fA−fB| = 4
k = 6 &Rightarrow fA = 20 Hz,   fB = 24 Hz
(c) Binary star speed & radius

Wavelength swings 599.9–600.1 nm → Δλ = 0.1 nm, λ ≈ 600 nm.

v / c = Δλ / λ &Rightarrow v ≈ 5.0×104 m s−1
r = v T / (2π) = (5.0×104 × 3.5×106) / (2π) ≈ 2.8×1010 m
(d) Newton’s rings
Dark rings at contact

Plano-convex lens on a plate produces concentric rings.

For dark rings: Dn2 − Dm2 = 4 R λ (n − m)

λ = (0.592 − 0.3362) / (4 × 100 × 10) cm = 5.88×10−7 m (588 nm)

3. Surface Tension & Thermal Physics

(a) Chalk bubbles & capillarity

Chalk bubbles: pores trap air; when immersed, air escapes as bubbles.

radius r radius r/2 rise = 2 mm rise = 4 mm

Capillary rise h &propto 1/r → halving radius doubles the rise.

(b) Pressure inside a drop

Surface tension jump: ΔP = 2γ / r. With r = 1.0×10−3 m and γ = 0.072 N m−1:

ΔP = 2 × 0.072 / 0.001 = 1.44×102 Pa
(c) Absolute zero & oxygen speed
  • No −5 K: Thermodynamic temperature has a lower bound at 0 K; negative values would contradict the Kelvin scale for ordinary matter.

For O2, set vrms = vesc:

vrms = √(3kT/m) = 11.2 km s−1 &Rightarrow T ≈ 1.6×105 K
(d) Density of lead under pressure

Bulk modulus: B = −ΔP / (ΔV/V) → ρ' = ρ(1 + ΔP/B).

ρ' = 11.4×103 × (1 + 2×108 / 8×109) = 1.1685×104 kg m−3

4. Electrostatics

(a) Sure test of charge & contact problem

Repulsion is the only certain test (attraction can be charge–neutral by induction).

Contact: total charge = −5 + 20 = +15 μC → 7.5 μC each. Separation 0.10 m.

F = k q2 / r2 = 9×109 (7.5×10−6)2 / 0.12 = 50.6 N (repel)
(b) Equipotentials & bringing charges closer

Equipotential surfaces can’t cross (a point cannot have two different potentials).

ΔU = k q1 q2 (1/rf − 1/ri) = 9×109 (16×10−10)(12×10−10) (1/0.06 − 1/0.10) = 1.15×10−7 J
(c) Connecting charged capacitors (like plates)

C1=4 μF at 90 V; C2=5 μF at 120 V.

Q = C1V1 + C2V2 = 9.6×10−4 C
Vf = Q / (C1 + C2) = 106.67 V
Ui = ½ C1V12 + ½ C2V22 = 0.0522 J
Uf = ½ (C1+C2) Vf2 = 0.0512 J
Energy lost = 0.0010 J; with dielectric volume 8×10−5 m3 → loss density 12.5 J m−3
(d) Work with two point charges
+5 μC −3 μC P Q 900 mm 600 mm

Interpreting the figure: Q at origin; P at (−0.6 m, 0); charges at (0, ±0.9 m).

Potential at a point: V = k (q1/r1 + q2/r2).

VQ = 9×109(5×10−6/0.9 + (−3×10−6)/0.9) = 2.00×104 V
VP = 9×109(5×10−6/1.0825 + (−3×10−6)/1.0825) = 1.664×104 V

Work to move test charge q0=−3 μC from P to Q:

W = q0(VQ − VP) = (−3×10−6) (3.36×103) = −1.01×10−2 J

Negative: the field does positive work as it moves from P to Q.

5. Strength of Materials & E&M

(a) Definitions
  • Stress σ = F/A (N m−2) vs Strain ε = ΔL / L (no unit).
  • Force total push/pull vs Stress force per area inside a material.
  • Tensile (stretching) vs Compressive (squeezing) stress (opposite sign).
(b) Composite bar shortened by 0.30 mm
Steel (E = 2×105 N/mm2) Al (E = 6.5×104 N/mm2)

Bars in series under the same axial force F.

Total contraction:

ΔL = F ( Ls / (As Es) + La / (Aa Ea) ) = 0.30 mm
F = 0.30 / [ Ls/(AsEs) + La/(AaEa) ] (N)

Insert the actual lengths and cross-sections from your figure to get the numeric F.

(c) Coulomb & Gauss; proton in E-field

Coulomb’s law: F = k |q1 q2| / r2 along their line.

From Gauss on a sphere: E 4πr2 = q / ε0 &Rightarrow E = (1/4πε0) q / r2.

Proton: s = 0.015 m, E = 2.0×104 N C−1, q = 1.6×10−19 C, m = 1.673×10−27 kg.

a = qE/m → t = √(2s/a) = 1.25×10−7 s

6. Optics & Waves on a String

(a) Straight-line light & Young fringes

When apertures/obstacles » wavelength, diffraction is negligible, so rays travel straight.

Young’s double slit: fringe spacing β = λ D / d.

β = (5.4×10−7 m × 0.40 m) / (6×10−4 m) = 0.36 mm
(b) Doppler effect
  • No Doppler when source & observer are stationary.
  • No Doppler when both move together with same velocity in same direction (no radial relative speed).

Car horn 500 Hz, car speed 20 m s−1, sound speed 340 m s−1.

fapproach = v/(v − u) f ≈ 531.25 Hz
frecede = v/(v + u) f ≈ 472.22 Hz
Change Δf = 59 Hz
(c) Wave needs & string wavelength
  • Elasticity (restoring force) and Inertia (mass/density) are required for propagation.

String: L = 3.0 m, m = 12 kg → linear density μ = m/L = 4 kg m−1, tension T = 1.6 N.

v = √(T/μ) = 0.632 m s−1,   λ = v/f = 0.632/40 = 1.58×10−2 m (crest-to-crest)
λ shown as distance between crests

Transverse wave on a stretched string.

Reference Book: N/A

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