1. The load-extension graph of an elastic material is illustrated above. Use the graph to determine the work done in stretching the material.

2. (a) Name two artificial satellites.
   (b) A geostationary satellite moves in an orbit of radius 6300 km. Calculate the speed with which it moves in the orbit. π = 22/7

3. A projectile is fired at an angle of 30° to the horizontal with a velocity of 40 m/s. Calculate the velocity attained after 1 s. [g = 10 m/s²]

4. The circuit diagram below is a simple current rectifier circuit. Use it to answer the questions that follow:
   (a) State the function of each of the parts labeled A and B.
   (b) Sketch the output signal produced.

5. (a) Explain the wave-particle duality of light.
   (b) A particle with a wavelength of $4.2 \times 10^{-11} \, \text{m}$ travels with a momentum of $1.6 \times 10^{-23} \, \text{kg·m/s}$. Determine the value of Planck's constant, $h$.

Question 6

State three observable phenomena where a particle behaves like waves.
State the scientific principle underlying the operation of fibre optics.

(b) Explain each of the following terms as used in fibre optics:
(i) Core
(ii) Cladding

Question 7

(a)
(i) State Hooke's law.
(ii) A spring has a length of 0.20 m when a mass of 0.30 kg hangs on it, and a length of 0.75 m when a mass of 1.95 kg hangs on it. Calculate:

• The force constant of the spring.
• The length of the spring when it is unloaded.
  [Take $g = 10 \, \text{m/s}^2$]

(b)
(i) What is diffusion?
(ii) State two factors that affect the rate of diffusion of a substance.
(iii) State the relationship between the rate of diffusion of a gas and its density.

(c) A satellite of mass $m$ orbits the earth of mass $M$ with a velocity $v$ at a distance $R$ from the center of the earth. Derive the relationship between the period $T$ of orbit and $R$.

Question 8

(a)
(i) Define dew point.
(ii) Explain why dew forms more quickly on the metal parts than on the rubber parts of a bicycle placed in the open overnight.

(b)
(i) Explain the statement: The specific heat capacity of copper is 400 J/kg/K.
(ii) Two metals, $P$ and $Q$, are supplied with the same quantity of heat.

• If the ratio of the specific heat capacity of $P$ to $Q$ is 3:1 and their masses are in the ratio 1:2, calculate the ratio of the temperature rise of $P$ to $Q$.

(c)
(i) Define the coefficient of thermal conductivity of a material.
(ii) A composite bar of iron and copper is insulated along its sides. The bar has a diameter of 10 mm. The length and thermal conductivity of the iron are 0.15 m and 40 W/m/K, respectively, while those of copper are 0.05 m and 360 W/m/K, respectively. If the free ends of the iron and copper are kept at 100°C and 0°C, respectively, calculate:

• The temperature at the interface between the bars.
• The rate of heat flow along the bar.

Question 9

(a)
(i) Define the following terms as they relate to converging lenses:

• Focal length.
• Optical center.
  (ii) Draw a ray diagram to illustrate how a converging lens is used to produce a virtual image of an object.

(b)
(i) Name the primary colors of light.
(ii) Match each primary color to its corresponding complementary color.

(c) A ray passes symmetrically through a glass prism with an angle of 60° and a refractive index of 1.5. Calculate:
(i) The angle of incidence.
(ii) The angle of minimum deviation.

Question 10

(a)
(i) What is meant by the root-mean-square value of an alternating current?
(ii) Define the impedance of an alternating current circuit.

(b) An electrical device rated 120 V, 60 W operates on a 240 V, 50 Hz mains supply. The circuit has a capacitor connected in series with the electrical device and the supply. Calculate the capacitance of the capacitor. [Use $\pi = 3.142$].

(c)
(i) Define the capacitance of a capacitor.
(ii) Two capacitors with capacitances $C_1$ and $C_2$ are connected in series across a 2 V source.

• Obtain an expression for the total capacitance in terms of $C_1$ and $C_2$.
• Calculate the potential difference across each capacitor.

11.
(a)
(i) State the principal factor that determines the relative stability of a radioactive nucleus.

(ii) Arrange the following radioactive nuclei in decreasing order of stability. Justify your answer:

(b)
(i) Explain the term ionization potential.

(ii) The diagram illustrates energy levels in the hydrogen atom, where $E_0$ is the energy of the ground state.

• When an electron makes a transition from level $n = 3$ to $n = 1$, it emits a photon of wavelength $1.02 \times 10^{-7} \ \text{m}$. Calculate $E_0$.
• Calculate the ionization potential of the hydrogen atom.

(c)
(i) Explain the statement: "The work function of sodium is 2.0 eV."

(ii) Light of wavelength $160 \ \text{nm}$ is shone on the surface of a sodium metal with a work function of 2.0 eV. Determine whether photoelectrons will be emitted.