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(a) The incident light rays must be parallel and close to the principal axis (b) Spherical aberration as a defect of curved mirrors: When a wide parallel beam is incident on a spherical mirror, it is not brought to the same focus. This makes the image distorted. (c) SEE THE DIAGRAM ABOVE (d) Accommodation is the ability of the eyes to alter its focal length to form a clear image (e) Quantitatively, (i) far point = infinity, Near point = 25 cm P\(_{near point}\) = \(\frac{1}{f}\) = \(\frac{1}{u}\) + \(\frac{1}{v}\) (ii) for near point, u = 0.25 m P\(_{near point}\) = \(\frac{1}{f}\) = \(\frac{1}{0.25}\) + \(\frac{1}{v}\) similarly, for far point, u = infinity(\infty) P\(_{far point}\) = \(\frac{1}{f}\) = \(\frac{1}{u}\) + \(\frac{1}{v}\) P\(_{far point}\) = \(\frac{1}{\infty}\) + \(\frac{1}{v}\) = 0 + \(\frac{1}{v}\) So, change in optical power \DeltaP = P\(_{near point}\) - P\(_{far point}\) \DeltaP = 4 + \(\frac{1}{v}\) - \(\frac{1}{v}\) \DeltaP = 4 dioptres.

When light travels from a less dense medium (like air) to a denser medium (like glass or water), its speed decreases due to the higher optical density of the new medium. The frequency of light remains constant when it passes from one medium to another. Although the speed changes, the frequency is determined by the source of the light and does not change with the medium.

Chromatic aberration occurs because different wavelengths of light are refracted by different amounts when passing through a lens. Chromatic aberration can be corrected by using a combination of diverging (concave) and converging (convex) lenses, which help focus different colors of light to the same point.

Twice the focal length of the lens: this is because, for a real image to be formed, the object must be placed outside the focal length of the lens, typically at a distance greater than twice the focal length.

Diameter = 20cm The radius of curvature, R = 10cm But, focal length, f = \(\frac{R}{2} = \frac{10}{2}\) = 5 cm. Because the inside portion is polished, light reflects off the hollow, caved-in interior. A mirror that reflects light from its inner surface is concave.

The formation of a rainbow is primarily due to dispersion, as it involves the separation of light into its constituent colors when it passes through water droplets in the atmosphere, it is refracted and dispersed due to varying wavelengths.

Loudness does not affect the speed of sound.

The uses of ferromagnetic materials are: (i) Electromagnets (ii) Magnetic Storage (iii) Magnetic Sensors (iv) Magnetic Shielding (v) Permanent Magnets (vi) Inductive Components, others are transformers, electric bells, electric generators, etc.

(ai) Increasing the temperature of a liquid decreases the viscosity of the liquid. (aii) Increasing the temperature of a gas increases the viscosity of the gas (b) Factors that determine the magnitude of the moment of a force about a point are: 1. Angle between the distance from the turning point and the line of action of the force. 2. magnitude of the applied force. 3. perpendicular distance from the pivot to the line of action of the applied force. (c) SEE THE DIAGRAM ABOVE. (ii) Taking a moment about the support: clockwise moment = anti-clockwise moment 400 x 10 = m x (\(\frac{L}{2}\) - 10) -- ------- from figure 1 above 4000 = m x (\(\frac{L}{2}\) - 10) - - - -- - - (i) 400 x 6 = m x (\(\frac{L}{2}\) - 15) - - - - -- - - -(ii) divide eqn i by ii \(\frac{4000}{2400}\) = \(\frac{m \times \frac{L}{2} - 10)}{m \times \frac{L}{2} - 15)}\) \(\frac{5}{3}\) = \(\frac{\frac{L}{2} - 10)}{\frac{L}{2} - 15)}\) 3 x (\(\frac{L}{2}\) - 10) = 5 x (\(\frac{L}{2}\) - 15) \(\frac{3L}{2}\) - 30) = \(\frac{5L}{2}\) - 75) \(\frac{5L}{2}\) - \(\frac{3L}{2}\) = 75 - 30 = 45 L = \(\frac{2L}{2}\) = 45 cm From equation (ii) 400 x 6 = m x (\(\frac{L}{2}\) - 15) 2400 = m x (\(\frac{45}{2}\) - 15) 2400 = m x 7.5 m = \(\frac{2400}{7.5}\) = 320 g Therefore, I. m = 320g and II. L = 45 cm (d) Reasons for less pressure at the top of a mountain: The lower pressure at the top of a mountain is due to the reduced number of air molecules in the atmosphere above that elevation, resulting in a lighter air column and fewer molecular collisions, which together create lower atmospheric pressure compared to sea level. (e)(i) Density = \(\rho\) = \(\frac{m}{v}\) m = v x \(\rho\), but v = A x h m = A x h x \(\rho\) = 13.6 x 10\(^3\) x 40 x 20 x 10\(^{-6}\) = 10.88kg (e)(ii) pressure exerted by the surface of the mercury P\(_t\) = P\(_{atm}\) + pressure of mercury P\(_{atm}\) = P\(_t\) - \(\rho\) x h x g = 1.42 x 10\(^5\) - 13.6 x 10\(^3\) x 0.2 x 10 = 1.148 x 10\(^5\)Pa

(a)i The charged particle must be in motion or have velocity and the particle's velocity must be inclined to the magnetic field at an angle \(\theta\) (ii) F = Qv\(\beta\)sin\(\theta\) (iii) for a charged particle moving parallel to the magnetic field, \(\theta\) = 0 and F = Qv\(\beta\)sin\(\theta\) F = Qv\(\beta\)sin 0 = 0 Thus, F = 0 (b)The main parts of an electrical transformer are the coil, Soft iron core (ii) An alternating current in the primary coil produces a changing magnetic field in the primary coil. The changing magnetic field around the core gives rise to a changing magnetic flux linking the secondary coil thereby inducing an alternating e.m.f in the secondary coil as stated in Faraday's law. c(i) Why the speed of the proton remains constant: The speed of the proton remains constant because the magnetic force acts perpendicular to its velocity, providing centripetal acceleration without doing work on it. This means the force changes the direction of the proton's motion but not its speed, resulting in constant kinetic energy and a uniform speed throughout its circular path. (ii) I. radius of curved path qv\(\beta\) = \(\frac{mv^2}{r}\) r = \(\frac{mv}{q\beta}\) r = \(\frac{1.7 \times 10^{-27}}{1.6 \times 10^{-19}}\) = 0.24 m. II. time taken by the proton to move through the magnetic field, t = \(\frac{\pi r}{2v}\) = \(\frac{3.14 \times 0.24}{2 \times 4.5 \times 10^6}\) = 8.37 x 10\(^{-8}\)s

(v) M(g) W\(_A\)(N) W\(_W\)(N) U\(_1\) = W\(_A\) - W\(_W\). W\(_L\)(N) U\(_2\) = W\(_A\) - W\(_L\) 20.0 0.20 0.16 0.04 0.18 0.02 40.0 0.40 0.33 0.07 0.36 0.04 60.0 0.60 0.49 0.11 0.54 0.06 80.0 0.80 0.66 0.14 0.72 0.08 100.0 1.00 0.82 0.18 0.90 0.10 (vi) SEE THE GRAPH ABOVE (vii) s = \(\frac{\Delta U_1}{\Delta U_1}\) = \(\frac{0.162 - 0.2}{0.09 - 0.067}\) = \(\frac{0.042}{0.023}\) = 1.826 (viii) K = \(\frac{1}{\text{s}}\) = \(\frac{1}{1.826}\) = 0.5476 (ix)(I) I avoided errors due to parallax when reading the spring balance. (II) I cleared the mass thoroughly before immersing it in liquid L b(i) Archimedes's principle states that when a body is completely or partially immersed in a fluid, it experiences an upthrust which is equal to the weight of fluid displaced. (ii) Density has a unit whereas relative density has none. (II) The value of density is different in different systems of measurement, whereas relative density is the same in all systems of measurement.

(vii) L(cm) L\(_x\)(cm) L\(_y\)(cm) R\(_1\) = (\(\frac{L_y}{L_x})R_x\)\(\Omega\) L\(_{x2}\) L\(_{y2}\) R\(_2\) = \(\frac{L_{y2}}{L_{x2}}R_x\)\(\Omega\) 100.0 5.2 94.8 18.2 21.5 78.5 3.6 90.0 6.0 94.0 15.7 22.5 77.5 3.4 80.0 6.8 93.2 13.7 23.4 76.6 3.3 70.0 7.6 92.4 12.2 24.5 75.5 3.1 60.0 8.4 91.6 10.9 25.6 74.4 2.9 (viii) SEE THE GRAPH ABOVE (ix) Slope = \(\frac{\Delta R_2}{\Delta R_1}\) = \(\frac{3.5 - 3.3}{17.0 - 14.6}\) = \(\frac{0.2}{2.4}\) = 0.083 (x) K = \(\sqrt{0.083}\) = 0.2881 (xi) I Tight connection/clean terminal was ensured II. Key removed when readings were not being taken. b(i) I. A potentiometer can be used for measuring the internal resistance of a cell and also to compare the e.m.f. of two cells. II. A potentiometer gives the exact value of potential difference across any two points in a circuit. (ii) It refers to the opposition to the flow of current offered by the cells and batteries themselves resulting in the generation of heat.

(a)i c = 50.0cm (ii) M\(_R\) = 90.0 g (vii) d = 0.8m (ix) S/N h(cm) t(s) T= \(\frac{t}{20}\)s T\(^2\)s\(^2\) 1 40.0 26.12 1.306 1.7056 2 50.0 27.80 1.390 1.9321 3 60.0 30.68 1.534 2.3532 4 70.0 34.60 1.730 2.9929 5 80.0 35.80 1.790 3.2041 (x) SEE THE GRAPH ABOVE (xi) Slope, s = \(\frac{\DeltaT^2}{\Delta h}\) = \(\frac{3.0 - 1.75}{75 - 46}\) = \(\frac{1.25}{29}\) = 0.431s\(^2\)cm\(^{-1}\) (xii) K = \(\frac{\text{S}}{\text{Q}}\) where, Q = \(\frac{2}{25d^2}\) = \(\frac{2}{25 \times (0.8)^2}\) = 0.125 K = \(\frac{\text{S}}{\text{Q}}\) = \(\frac{0.431}{0.125}\) = 0.3448 b(i) A couple, as related to oscillatory motion, refers to a pair of forces that are equal in magnitude but opposite in direction, and act on opposite sides of a pivot or fulcrum, causing rotation or torsion. b(ii) I. Wrenches: When using a wrench to tighten or loosen a bolt, the force applied creates a couple that produces rotational motion. II. Steering Wheels: Turning the steering wheel of a car applies a couple that rotates the front wheels, allowing for directional change. III. Door Handles: When pushing or pulling on one side of a door handle, a couple is created that rotates the door about its hinges. IV. Bicycle Pedals: When pedaling a bicycle, the force applied to the pedals generates a couple that turns the crankshaft, propelling the bike forward.

Gases that are less dense than air are collected by downward displacement of air. Examples include ammonia and hydrogen. Sulphur dioxide (SO\(_2\)) is not collected by downward displacement of air. It is collected by upward displacement of air because it is heavier than air.Also, chlorine is collected by upward displacement of air, not downward displacement. This is because although, it is heavier and denser than air, it is soluble in water. Instead, chlorine is collected by upward displacement of air.

High boiling point is primarily caused by strong intermolecular forces, particularly hydrogen bonding which is the main reason for water's high boiling point, as water molecules can form multiple hydrogen bonds with each other, requiring more energy to separate them and vapourize. Consequently, water, ethanol and aquous sodium chloride would have relatively high boiling points, owing to the presence of hydrogen bonds while tetrachloromethane has no hydrogen bonding, hence, it is has the lowest boiling point.