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Time of flight =\( \frac{2Usin\theta}{g}\) T = 5, g = 10m/s2 \(5 = \frac {2\times 50sin\theta}{10}\) \(sin\theta =\frac {50}{100}\) \(\theta = 30\) vertical angle = 90 - 30 = 60^\circ

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

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

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

The bubble is formed 20 m below the surface. Pressure at that depth = atmospheric pressure + water pressure due to 20 m of water. Given: Atmospheric pressure = pressure of 10 m of water Therefore, P\(_1 = 20 + 10 = 30 \text{ m of water}\) Just below the surface, the bubble is under atmospheric pressure only: P\(_2 = 10 \text{ m of water}\) Apply Boyle's Law Given: V\(_1 = 4\ \text{cm}^3\) P\(_1V_1 = P_2V_2\) 30\(\times 4 = 10 \times V_2\) V\(_2 = \frac{30 \times 4}{10}\) V\(_2 = 12\ \text{cm}^3\) The volume of the air bubble just below the water surface is 12 cm\(^3\).

Work done by friction = Friction force x displacement from the relation, f = \muR where \mu = coefficient of friction ; R = normal reaction => F = \mu mg (R = mg) = 0.1 x 0.01 x 10 ∴ work done = F x displacement = 0.1 x 0.01 x 10 x 0.2 = 0.002 = 2 x 10\(^{-3}\)

Water and glass are made up of molecules and since the force of attraction between water molecules and glass molecules are stronger than that between water molecules, there is rise in a glass capillary tube.

(a) Diffusion is the process by which different forms of fluids mix with one another due to the kinetic nature of their particles. (b) Factors affecting rate of diffusion are: Density, Temperature, Pressure and Concentration of the substance.

(a) Elasticity is the ability for a body to regain its original shape and size after undergoing a stretching or compression force. (b) Elastic constant is the force that produces a unit extension of the material.

(a) A discharge tube at very high p.d. filled with neon and evacuated to a very low pressure of about 5mm will produce a discharge between the electrodes with a characteristic colour. (b) The colour depends on; - nature of the gas in the tube. -nature of coating inside the tube

(a)(i) A machine is a device by means of which a force or effort applied at one point is used to overcome load at the other point. (ii) Examples of simple machines are: lever, pulley system, incline plane, Jack, wheel and axle and hydraulic press (iii) This means that the distance moved by the effort is 5 times the distance moved by the load at the same time interval. (b)(i) Efficiency of a machine is the ratio of work output to work input expressed in percentage. (iii) The efficiency of a machine can never be 100% because part of the energy supplied to the machine is used to overcome friction and in moving other parts of the machine. (i) Velocity ratio, V.R = \(\frac{2 \pi r}{P} = \frac{2 \pi \times 40}{0.4}\) = 628 (ii) Efficiency = \(\frac{M.A}{V.R}\) x 100% M.A. = \(\frac{\text{Efficiency x V.R}}{100}\) = \(\frac{25 \times 628}{100}\) = 157 (ii) M.A = \(\frac{load}{Effort}\); Effort = \(\frac{load}{M.A}\) = \(\frac{1000}{157}\) = 6.4N

(a)(i) Relative density is the ratio of the density of the substance to the density of water (ii) Characteristics of pressure in liquid are: -pressure increases in direct proportion to the depth of the liquid -pressure at any point in a liquid acts equally in all directions -pressure at all points at the same level within a liquid is the same -pressure applied to an enclosed liquid is transmitted equally throughout the fluid. (b) Force on the door F = Ah g = 0.4 x 500 x 1.03 x 103x 10 = 2.06x 106N (c)(i) Effects of heat other than expansion are: -Rise in temperature -Change of state -Change of colour -Change of electrical resistance (ii) When a liquid and its vapour are in dynamic equilibrium, the vapour is said to be saturated. The pressure or force exerted on unit area of the container of such a saturated vapour is known as saturated vapour pressure. (iii) Heat generated by coil = heat gained by water + container. \(\frac{V^2t}{R}\) = mc\(\theta_{\text{water}}\) + Q\(_c \theta_{\text{container}}\) \(\frac{220^2 \times 2 \times 2 \times 60}{20}\) = m x 4.2 x 10\(^{3}\) x 60 + 100 x 60 290400 = 252000m + 6000 m = \(\frac{290400 - 6000}{252000}\) = 1.13kg

(a) Heisenberg's uncertainty principle states that there is always an uncertainty in any attempt to measure the position and momentum of a particle simultaneously (b) Phenomena explained in terms of particle nature of light are: - photoelectricity, - black body radiation, - compton effect

(a)(i) Principal focus of a convex mirror is a pc.nt on the principal axis on which all rays parallel and close to the principal axis appear to diverge after reflection. (ii) The pole is the centre of the mirror through which the principal axis pass. (iii) Radius of curvature is the radius of the sphere from which the mirror was cut. (b) Advantages of using convex mirror for driving -wide field of view -image is always upright. Disadvantages of using convex for driving: -image is smaller -image appears further away and gives false impression of the distance. (d)(i) \(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}; \frac{1}{u} - \frac{1}{30} = \frac{1}{10}; \frac{1}{u} = \frac{1}{10} + \frac{1}{30}\) = \(\frac{4}{30} = \frac{2}{15}; u = \frac{15}{2}\) = 7.5cm (ii) \(\frac{\text{image size}}{\text{object size}} = \frac{\text{image distance x object size}}{\text{object distance}}\) = \(\frac{30 \times 0.25}{7.5} = 1cm\) (iii) Power = \(\frac{1}{\text{focal length (in metre)}} = \frac{1}{0.1}\) = +10.0 dioptre 0.1

(a)(i) Reactance s the opposition in ohms to the alternating current by an inductor, a capacitor or both. (ii) Impedance is the total opposition is ohms to the alternating current by a combination of resistor as well as a capacitor or an inductor. (b)(i) Resonant frequency fo is to frequency at which the current in the circuit has a maximum value. fo = \(\frac{1}{2 \pi LC}\) (ii) This means that the root mean square value of the voltage is 230v. The actual voltage lies between Vo and -Vo where the voltage amplitude or peak voltage Vo. (c)(i) \(V^2 = V^2_R + (V_L - V_C)^2; 240^2 = 140^2 + (50 - v_c)^2\); 50 - \(V_c = 194.9\) \(V_c = 244.9v\) (ii) X\(_c = \frac{1}{2 \pi fc} = \frac{V}{1} = \frac{1}{2 \pi \times 50 \times c} = \frac{244.9}{10}\) C = \(\frac{10}{2 \pi \times 50 \times 244.9} = 129.97 \mu F\) (iii) \(X_L = 2 \pi fL = \frac{v}{l}; 2 \pi \times 50 \times L = \frac{50}{10}\) L = \(\frac{50}{100x}\) = 0.01159Hz (d)