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R = \(U\sqrt{\frac{2H}{g}}\) H = \(\frac{gR^2}{2U^2} = \frac{10 \times 45^2}{2 \times 15^2}\)

R = \(U\sqrt{\frac{2H}{g}}\) = 0.4 \(\sqrt{\frac{2 \times 20}{10}}\) = 0.8m

(i) unpolarized wave (ii) Planer Polarized Wave

(a) Cations are positive ions that are attracted to the cathode during relectrolysis e.g. cu\(^{2+}\), Ag\(^+\) , H\(^+\), Na\(^+\) etc. (b)

(a) Lightening in fluorescent tubes operate on the principle of electric discharge through low pressure gas. (b) Colour of light from fluorescent tube depend on (i) Nature of the coating inside the tube (ii) Nature of the gas in the tube.

(a) Young's modulus of electricity is the ratio of tensile or compressive stress to tensile or compressive strain. (b) F = Ke K = \(\frac{f}{e} = \frac{20}{(10.01 - 10.00)^{-2}}\) = 2.0 x 10 N/M

(a) Elastic limit is the point on a load/extension graph beyond which Hooke's law is no longer obeyed. (b) Hooke's law of elasticity states that the extension (e) in an elastic material (wire) is directly proportional to the force (load) applied, provided the elastic limit is not exceeded.

(a) Surface tension is the property of a liquid which makes its surface behave as though covered by an elastic skin. (b) The surface tension of a liquid can be reduced by (i) Heating the liquid (ii) Addition of impurities such as oil, alcohol, soap, camphor, kerosene etc.

Matter is made up of molecules which are held together by intermolecular forces which make the molecules to vibrate about their mean positions giving the solids definite shape.

(a) (b)(i) V = rw = 2.5 x 10\(^{-2}\) x 0.4 \(\pi\) = 3.142 x 10\(^{-2}\)m/s (ii) a = rw\(^2\) = 2.5 x 1.0\(^{-2}\) x (0.4 \(\pi^2\)) (c) (i) \(\frac{k}{m}\) = w. H is the rate of change of angular displacement. H is measured in radians per second (ii) (1) K.E\(_{\text{max}} \frac{1}{2}MV^2_{\text{max}} = \frac{1}{2} mr^2w^2\) But w = \(\sqrt{\frac{k}{m}} = w^2 = \frac{k}{m} = \frac{30}{0.3} = 100 rad/s^2\) K.E\(_{\text{max}} = \frac{1}{2}mr^2w^2 = \frac{1}{2} \times 0.30 \times (0.015)^2\) x 100 = 3.38 x 10\(^{3}\)J T\(_{\text{max}}\) = Weight + Ke = Mg + Ke = 0.30 x 10 + 30 x 0.015 = 3.45N

(a) Specific latent heat of a substance is the quantity of heat energy required to change a unit mass of a substance from one state to another without change in temperature. The unit specific latent heat is Jkg\(^{-1}\). (b)(i) Mass of empty calorimeter = M; Mass of cal. + water = M\(_2\) Mass of cal. + water + ice = M\(_3\); Temp. of warm water = \(\theta_1\) Final temp. when all the is has melted = \(\theta_2\); Sp. heat capacity of cal = Cc Sp. heat capacity of water = C\(_w\) latent heat of ice = L Mass of water = M\(_2\) - M\(_1\) Mass of ice = M\(_3\) — M\(_2\) Heat lost by cal. and water = (m\(_1\)Cc + (M\(_2\) - M\(_1\))C x ( \(\theta_1\) - \(\theta_2\)) Heat gained by ice in melting to water of 0^\circC = (M\(_3 - M_2\))L Heat gained by ice water from 0^\circC = (M\(^3\) - M\(_2\))C\(_ w \theta_2\), Total heat gained = Heat lost (M\(_3\) - M\(_2\)L + (M\(_3\) - M\(_2\)) C\(_w \theta_2\) = (M\(_1\)Cc + (M\(_2\) - M\(_1\)) C\(_w\) (\(\theta_2 - \theta_2\) L = \(\frac{M_1C_c + (M_2 - M_1) C_w(\theta_1 - \theta_2) - (M_3 M_2)C_w\theta_2}{(M_3 - M_2)}\) (ii) Precautions - Stir gently - Ensure that ice is dry before adding to water - Avoid parallax error in reading the balance and thermometer. (c) If M\(_s\) = mass of steam ; Heat lost by steam at 100^\circC = M\(_s\)l\(_v\) = M\(_s\) x 2.3 x 10\(^3\)(J) Heat lost by hot water from 100^\circC = 0^\circC ; = \(M_sC_w \Delta \theta\) = \(M_s\) x 4.2 x 100 (J) Heat gained by ice at 0\(^oC\) = M\(_{\text{ice}}\) L\(_f\) = 20 x 3.4 x 10\(^2\) = 6800J; Heat lost by steam + hot water = Heat gained by ice; M\(_sl_v\) + M\(_s\)C\(_w\)\(\Delta\) = M\(_{\text{ice}}\)L\(_f\); M\(_s\) (2.3 x 10\(^3\) + 4.2 x 100) = 6800; M\(_s\) = \(\frac{6800}{2720}\) = 2.5g Mass of water in container = mass of melted ice + mass of water + mass of condensed steam. = 20 + 100 + 2.5 = 122.5g

(a)(i) Refraction of a wave is the change in the direction of the wave as it moves from one medium to another of different density. (ii) Critical angle is the angle of incidence in the denser medium beyond which total internal reflection occurs. (b) (i) The conditions necessary for total internal reflection of wave to occur are:- - The wave must be travelling from a denser medium to a less dense medium - The angle of incidence of the wave in the denser medium must be greater than the critical angle of the medium. (ii) The conditions necessary for interference pattern to be formed are:- - Two or more sources must be involved. - The distance between the sources must be of the order of the wave length of the waves (c) V = \(f \lambda\) F = \(\frac{v}{\lambda} = \frac{3.6}{0.45}\) = 8.0Hz (d) (i) (ii) n = \(\frac{sin i}{sin r}\) r = sin\(^{-1} (\frac{sin i}{n})\) = sin\(^{-1} (\frac{sin 30}{1.5})\) = 19.5\(^o\) Deviation = i - r = 30 - 19.5 = 10.5\(^o\)

(a)(i) Electric potential is the work done in moving a unit positive charge from infinity to a point in an electric field. H is measured in volts or J/C. (ii) Electric potential energy is the work done or energy required to move a charged particle from infinity to a point in an electric field. The unit is Joules. (ii) Electric potential unit is in volts v. Electric potential energy is measured in Joules (J) (b) (i) Electric field intensity E = \(\frac{Q}{4 \pi \varepsilon_or^2}\) (ii) Electric potential V = \(\frac{Q}{4 \pi \varepsilon_or}\) (iii) \(\frac{E}{v} = \frac{I}{r}\) OR E = \(\frac{Y}{4 \pi \varepsilon_o r}\) (c) E = \(\frac{v}{d} = \frac{5 \times 10^4}{5 \times 10^{-3}} = 10^7 v/m\) (ii) F = qE = 1.6 x 10\(^{-19}\) x 10\(^{7}\) = 1.6 x 10\(^{-12}\) N (iii) F = ma a = \(\frac{F}{m}\) = \(\frac{1.6 \times 10^{-12}}{9.1 \times 10^{-31}}\) = 1.76 x 10\(^{18}\) m/s\(^2\)

The wave particle paradox supposes that light exhibits wave properties such as reflection, diffraction, interference etc. and can also exist as a particle called photons. However light cannot behave as a wave and as particle at the same time.

(a)(i) In nuclear fission reaction results in splitting a heavy nucleus into two parts of nearly equal masses while in nuclear fusion process two light nuclei combine together to form a heavier nucleus. (ii) Nuclear fission releases less energy per nuclear while nuclear fusion releases more energy per nuclear. (iii) Nuclear fission can take place at room temperature while nuclear fusion takes place at very high temperature. (ii) Peaceful uses of atomic energy are: - Production of laser beams - Production of x-rays - Production of energy in discharge tubes. (b)(i) The neutrons produced as a result of fission of a nucleus can cause further fission if they strike other nuclei. This rapid multiplication of a fission process by fissile neutrons is called chain reaction. (ii) (i) Conditions necessary for chain reaction to occur are: - The mass of fissile material must exceed the critical mass - In addition to the two nuclei produced during the fission, one to three neutrons must be produced per parent nucleus. (ii) Components in a nuclear reactor used to control chain reactions are; - Boron steel - Heavy water or denterium oxide - Graphite or carbon rod. (c)(i) The type of nuclear reaction is fusion. T\(_{\frac{1}{2}} = \frac{0.693}{\lambda}\); \(\lambda = \frac{0.693}{T_{\frac{1}{2}}}\) = \(\frac{0.693}{5.40 \times 10^{3}}\) = 1.28 x 10\(^{-4}\)S\(^{-1}\)