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(a) Vector quantity is any quantity that has both magnitude and direction, e.g. velocity. (b)(i) (ii) x y -3 cos 45 = -2.121 -12.000 0.000 V_x = -14.121 + 3 sin 45 = 2.121 0000 -5000 V_y = -2.879 R = \(\sqrt{V_x^2 + Vy^2}\) = \(\sqrt{-14.121^2} + -2.879^2\) = 14.4m/s Ta n \(\theta = \frac{2.879}{14.121} = 0.2039\) \(\theta = tan^{-1} 0.2039 = 11.5^o\) R = 14.4m/s S78.5\(^o\)W (c)(i) Mass/g Weight W/N Ext.e/cm 50 100 150 200 250 0.5 1.0 1.5 2.0 2.5 6,5 11.0 15.0 20.0 25.0 (iii) Force constant = slope \(\frac{\Delta W}{\Delta e} = \frac{3.1 - 1.0}{30 - 11} = \frac{2.1}{9} = 0.1105\) (iv) Nature length = 38.0 - 25 = 13cm

a)(i) Advantages of alcohol over mercury as a thermometric liquid are: - Alcohol is cheaper -Alcohol is easily available -Alcohol has higher expansivity - Alcohol has lower freezing point. (ii) The glass bulb of the thermometer first got heated and expands, therefore the mercury level in it falls. Then the mercury expands and increases more than that of the glass and then rises. (b) Factors that affect the rate of evaporation of a liquid, temperature exclusively are: - Pressure, area of liquid surface exposed, humidity, nature of the liquid, wind and dryness of air, etc. (c)(i) Q = mc \(\Delta \theta = 100 \times 120 \times (320 - 40)\) ii) Q = Ml = 100 x 0.25 x 10\(^5)\) = 2500000J = 2.5MJ ii) Pt = ml t = \(\frac{ml}{p} = \frac{2500000}{10000} = 250s\) (d) Precautions to be considered are: - Calorimeter should be well lagged. - Use only dry steam. - Stir the mixture gently and continually. - Shield the calorimeter from heat sources.

(i) An eclipse is a shadow that results from the obstruction of light from the sun by the moon or the earth. (ii) Types of eclipse: -Eclipse of the sun or solar eclipse. -Annular eclipse - Eclipse of the moon or lunar eclipse. (b i) The eye defect is long sight or hypermetropia. (ii) The type of lens to correct the defect is convex or converging lens. (iii) Power of lens = \(\frac{1}{f} = \frac{1}{0.1} = dioptre(D)\) (c) Velocity of an echo = \(\frac{2d}{t}\) d = \(\frac{vt}{2} = \frac{340 \times 5 \times 10^{-3}}{2} = 0.952 m\) (d) M = \(\frac{v}{u}\) U = \(\frac{V}{M} = \frac{9}{0.6} = 15cm\) \(\frac{1}{f} = \frac{1}{u} + \frac{1}{v} = \frac{1}{15} + \frac{1}{-9}\) f = -22.5cm

(a) Mutual Induction: Mutual Induction is a phenomenon which occurs when the current in a coil is changing, an e.m.f will be induced in a tear-by circuit due to some of the magnetic flux produced by the first circuit linking the second circuit. (b) The uses of electromagnets are in: - electric bells or telephone earpieces - generators or electric motors - industrial robots - separation of iron scraps from debris - electromagnetic switches or magnetic relays - cranes fbr lifting or transporting heavy magnetic materials - magnetic resonance scanners, i.e. in medical diagnosis. (i) The changing magnetic flux in X induces changing magnetic flux in Y which induces the current that light up the bulb. (ii) As the distance between X and Y decreases, the magnetic flux density linking coil Y increases, hence the induced e.m.f. increase hence the brightners of the lamp. (iii) The insulated soft iron wires increases the magnetic flux through coil Y, hence increase in the induced current in Y, therefore, the filament of the lamp glows brighter. (d) Total e,m,f. E = 2V Total internal resistance r \(\frac{1}{r} + \frac{1}{r_2} = \frac{1}{0.4} + \frac{1}{0.1}\) e = 0.08\(\Omega\) E = I(R + r) 2 = I(5 + 0.08) I = \(\frac{2}{5.08}\) = 0.394A

(a)(i) Transmutation is the change of one chemical element into another by radioactive disintegration or nuclear bombardment with particles. Example is the conversion of mercury to gold. (ii) Stopping potential is the p.d of the anode of a photocell with respect to the cathode at which no electrons will reach the anode stopping potential Vs = \(\frac{ht}{e} - \frac{Wo}{e}\) (b) \(^{23}_{11}A + ^2_1B + ^1_1P\) P + 1 = 23 + 2 P = 24 q + 1 = 11 + 1 q = 11 \(^{24}_{11}C \to ^r_sE + ^o_{-1}B\) r + 0 = 24; r = 24 S - 1 = 11; S = 12 (c) (i) W = 1.6eV = 1.6 x 1.6 x 10\(^{-19}\) = 2.56 x 10\(^{-19}\)J E = \(\frac{hc}{\lambda} = \frac{6.6 \times 10{-34} \times 3 \times 10^{8}}{3.6 \times 10^{-7}}\) E = W + K.E\(_{max}\) ii) K.E = \(\frac{1}{2}mv^2\) 2.94 x 10\(^{-19}\) = \(\frac{1}{2} \times 9 \times 10^{-3} \times V^2_{max}\) V\(_{max} = 8.04 \times 10^5 m/s\) (d) No effect.

Properties of cathode rays that show particle nature of matter: - Casting of shadows of objects along their path. - They have momentum - Heat up objects that stop thorn, that is they obey energy conservation law. - They are deflected in electric or magnetic fields, showing they are tiny particles of matter, etc.

Observation /table of values Mass mo = 400g. S/N mo(g) m(g) (M=mo+m)g R = \(\frac{M(g)}{100}\) F(N) 1 400.0 0.00 400.0 4.00 1.70 2 400.0 200.0 600.0 6.00 2.40 3 400.0 400.0 800.0 8.00 3.60 4 400.0 600.0 1000.0 10.00 5.20 5 400.0 800.0 1200.0 12.00 6.30 Slope, s = \(\frac{\bigtriangleup{F}}{\bigtriangleup{R}} = \frac{F_{2}-F_{1}}{R_{2}-R_{1}}\) Slope (S) = \(\frac{6.4-2.3}{12.0-6.0}\) S = \(\frac{4.1}{6.0}\) = 0.68 PRECAUTION; i - Avoided parallax error in reading spring balance. - Tapped the wood/load slightly to avoid sticking to the table. - Repeated readings are shown in the table. - Zero error of the spring balance. (b)i. Coefficient of static friction: This is the ratio of the frictional force F (when the body is just about to move) to the normal reaction R (between the two surfaces in contact). ii. \(\mu\) = \(\frac{F}{R} = \frac{2}{5}\) = 0.5

The velocity of sound in air, V∝\(\sqrt{T}\), where T is the absolute temperature Thus V = K\(\sqrt{T}\) or K = \(\frac{\text{V}}{\sqrt{T}}\) V is independent of pressure and density at a fixed temperature. ∴ \(\frac{V_1}{\sqrt{T_1}}\) = \(\frac{V_2}{\sqrt{T_2}}\) T\(_1\) = 16 + 273 = 289K, V\(_1\) = 340ms\(^{-1}\) T\(_2\) = 127 + 273 = 400K, V\(_2\) = ? \(\frac{340}{\sqrt{289}}\) = \(\frac{V_2}{\sqrt{400}}\) ∴ V\(_2\) = \(\frac{340 \sqrt{400}}{\sqrt{289}}\) = 400m/s

The process of a substance changing from solid to liquid upon heating is called fusion. It happens when the temperature reaches the melting point, allowing particles to gain enough energy to move freely as a liquid.

P = 0.72 x 1000 = 720

The maximum force of static friction (\(f_{s}\)) is directly proportional to the normal reaction force (\(R\)) pressing the two surfaces together (\(f_s = \mu_s R\)). On a flat, horizontal surface, the normal reaction force is exactly equal to the weight of the body (\(R = mg\)). Therefore, static friction depends directly on the body's weight.

A particle is in dynamic equilibrium if the resultant force acting on it is zero. This means that the sum of all forces acting on the particle is zero, resulting in no acceleration or change in velocity. Therefore, the particle can either be at rest or moving with a constant velocity

R = 110 + 90 = 200

No expanded working has been attached for this question yet. The verified answer is Option B.

from, H = \(\frac{1}{2}\)gt\(^2\) 45 = \(\frac{1}{2}\) x 10 x t\(^2\) 45 = 0.5 x 10 t\(^2\) 45 = 5t\(^2\) t\(^2\) = \(\frac{45}{5}\) = 9 t = \(\sqrt{9}\) = 3s But distance = velocity x time V = \(\frac{D}{t}\) = \(\frac{30}{3}\) = 10m/s