1. The force, $F$, acting on the wings of an aircraft moving through the air of velocity $v$ and density $\rho$, is given by the equation $F = kv^x\rho^yA^z$, where $k$ is a dimensionless constant and $A$ is the surface area of the wings of the aircraft. Use dimensional analysis to determine the values of $x$, $y$, and $z$.

a. Define strain energy.
b. Write an expression for the energy stored $E$ in a stretched wire of original length $l$, cross-sectional area $A$, extension $e$, and Young's modulus $Y$ of the material of the wire.

a. A projectile is fired at an angle $\theta$ to the horizontal with velocity $u$. Show that at any time $t$ during the motion, the:
i. horizontal component of the velocity is independent of $t$;
ii. vertical component of the velocity depends on $t$.
b. State the assumption on which projectile motion is based.

4. State three differences between geostationary satellites and polar satellites.

a. Using the kinetic theory, explain the term diffusion of fluid molecules.
b. Name one phenomenon that demonstrates that light behaves as a:
i. wave,
ii. particle.

a. State one difference between an intrinsic and an extrinsic semiconductor.

a. What is fibre optics?
b. State two reasons why optical fibres are preferred to copper cables in the telecommunication industry.

a. i. State the reason why simple harmonic motion is periodic.
ii. State two factors that affect the period of oscillation of a simple pendulum.

b. The diagram above illustrates an oscillatory pendulum. Calculate the work done in raising the pendulum to point B if the mass of the bob is 50 g. $[g = 10 \, \text{m/s}^2]$

c. A spiral spring of spring constant $k$ and natural length $l$ has a scale pan of mass 0.04 kg hanging on its lower end while the upper end is firmly fixed to a support. When an object of mass 0.20 kg is placed on the scale pan, the length of the spring becomes 0.055 m, and when the object is replaced with another object of mass 0.28 kg, the length of the spring becomes 0.065 m. Calculate the values of $k$ and $l$. $[g = 10 \, \text{m/s}^2]$

a. Define each of the following terms used with simple machines:
i. Pivot,
ii. Load,
iii. Efficiency.

b. A truck of mass $1.2 \times 10^3 \, \text{kg}$ is pulled from rest by a constant horizontal force of $25.2 \, \text{N}$ on a leveled road. If the maximum speed attainable in the process is 60 km/h, calculate the:
i. work done by the force,
ii. distance traveled by the truck in reaching the maximum speed.

c. State two differences between absolute zero temperature and ice point.

a. i. Why are parabolic mirrors suitable for use in the headlamps of vehicles?
b. i. State two applications of echoes.
ii. An observer standing at a point $P$, on the same horizontal ground as the foot $H$ of a tower, shouts, and 1.20 s later, hears the echo. He then moves to another point $Q$, 40 m from $P$, and shouts again but hears the echo after 1.45 s. Calculate the:
I. distance between $P$ and $H$;
II. speed of sound in air.

c. i. Define the term absolute refractive index of a medium.

a. i. Define the electric potential at a point in an electric field.
ii. An uncharged body $A$ was charged electrostatically by a test charge $B$ using the method of induction and the method of contact. State two differences between the two methods.

b. An important precaution during an electricity experiment is to open the circuit when no readings are being taken. Give two reasons for the stated precaution.

a. State the function of each of the following parts of a modern x-ray tube:
i. heater,
ii. high tension source,
iii. cooling fins.

b. State one reason for each of the following design features of a modern x-ray tube:
i. the glass envelope is highly evacuated,
ii. the target is a metal of very high melting point,
iii. the cooling fins are located outside the glass envelope.

c. In a nuclear fission reaction, a nuclide $^{235}U_{92}$ is bombarded with a neutron to produce $^{93}Kr_{36}$ and $^{141}Ba_{56}$ with additional neutrons. The energy involved in the process is $Q$.
$[ \text{mass of } ^{235}U_{92} = 235.044 \, \text{u}, \text{mass of } ^{93}Kr_{36} = 91.898 \, \text{u}, \text{mass of } ^{141}Ba_{56} = 140.914 \, \text{u}, \text{mass of neutron} = 1.009 \, \text{u}, 1 \, \text{u} = 1.66 \times 10^{-27} \, \text{kg}, c = 3.0 \times 10^8 \, \text{m/s}]$
i. Write down the balanced nuclear reaction equation for the process.
ii. State with reason whether $Q$ is absorbed or released in the process.
iii. Calculate the value of $Q$ in joules.