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all the parallel forces must be equal in magnitude and direction

- the total energy at any point is a combination of the P.E and K.E - the sum of PE and KE at any point is always constant not the ratio of P.E to K.E

P = Pa + ρgh = (1.00 \times 10\(^5\)) + (950 \times 10 \times 1000) P = 10\(^5\) + (95 \times 10\(^5\)) = 10\(^5\)(1 + 95) = 96 \times 10\(^5\) P = 9.6 \times 10\(^6\) N/m\(^2\)

First condition

- I & II are in neutral equilibrium. They will roll continuously on the table - III is a body with high centre of gravity (unstable) - IV is a body with high centre of gravity (stable)

Potential energy = mgh = (mg)h = force \times distance ⇒ 0 \times d = 0

ρ\(_m\)h\(_m\) = ρ\(_a\)h\(_a\) 13.6(760 - p) \times 10\(^{-3}\) = 13 \times 10\(^{-5}\)(20 \times 10\(^3\)) 760 - p = 13 \times 10\(^{-5}\) \times 20 \times 10\(^{3}\) 13.6 \times 10\(^{-3}\) = 19.12 \times 10\(^{1}\) 760 - p = 191.2 p = 760 - 191.2 ≈ 570mmHg

½Ke\(^{2}\) = ½mv\(^{6}\) ½ x 200 x (0.05)\(^{2}\) = ½ x 0.02 x v\(^{2}\) v\(^{2}\) = 25 v = 5 m s\(^{-1}\)

The expected answer is (a) Identification of labelled physical quantities P - initial velocity/ velocity of projection b - angle of projection H - maximum height reached R - range/horizontal distance (covered) (b) Equation showing relationship between P, g and Rmax Rmax = \(\frac{p^2}{g}\)

In unstable equilibrium, when the cone is disturbed, it tends to fall further from its equilibrium position, leading to a decrease in height and thus an increase in potential energy.

\omega = 2\piF = 2\pi \times 2 = 4\pirad\(^{-1}\) Centripetal force = mr\omega\(^2\) ⇒ 0.5 \times 2 \times (4\pi)\(^2\) ⇒ 157.75N Approximately = 158N.

Stable equilibrium brings about increase in potential energy as the height rises after displacement.

(a) Definition of diffusion; The process by which molecules of different substances move randomly among one another. OR Intimate mixing of molecules/atoms/particles of different substance (as a result of kinetic energy) (b) Factors that affect the rate of diffusion - density of substance - mass of substance - temperature

(a) (i) Newton’s law of Universal Gravitation; Any two bodies in the universe attract each other with a force that is (directly) proportional to the product of their masses and inversely proportional to the square of the distance between them. (ii) Definition of gravitational field; A region/space in which gravitational force is felt / experienced. (b) (i) Derivation of the equation relating G and g at the surface of the earth F = \(\frac{GMm}{R^2}\) mg = \(\frac{GMm}{R^2}\) g = \(\frac{GM}{R^2}\) (ii) Assumptions for which equation holds; - mass of the earth is concentrated at its centre - earth is spherical - earth is not rotating - possesses uniform density. (c) Calculation of the force of attraction between a star and the earth; F = \(\frac{GM_sM_e}{r_2}\) = 6.67 x 10\(^{11}\) [\(\frac {(2 \times 10^{30}) (5.98 \times 10^{24})} {(1.5 \times 10^{11})^2}\)] = 3.55 x 10\(^{22}\)N (d) (i) Definition of escape velocity; The minimum uni-directional speed/velocity required by a body to leave the gravitational field/influence of a planet (ii) Differences between acceleration of free fall (g) and universal gravitational constant (G) g G Its unit is N m2 kg-2 Its unit is m s-2 / N kg-1 It is constant everywhere It varies from place to place It is a scalar quantity It is a vector quantity

(a)(i) Explanation of latent heat When a substance is changing state, it absorbs/gives out thermal/heat energy which does not result in temperature change. This heat absorbed or given out during change of state is known as latent heat. (ii) Factors that affect the rate of evaporation of a liquid - exposed surface area of the liquid - temperature of the liquid - wind / draught - humidity / amount of water vapour - nature of the liquid - air pressure. (b) Explanation of observations (i) Water in a clay pot is cooler than water in a closed plastic container The clay pot has pores which allow evaporation to take place. In the process of evaporation, molecules take latent heat from the bulk of the water, leaving the water cooler; but the plastic container does not have pores (to allow for evaporation). (ii) Food gets cooked faster in a pressure cooker than in an ordinary cooking pot With the pressure cooker, increased pressure raises the boiling point of water within a short period. This leads to faster cooking. Ordinary cooking pot operates at normal atmospheric pressure. (c) Effects of heat on a substance Change of/in: - state - temperature - dimension - colour - electrical resistance (d) (i) Determination of latent heat of fusion of the body Heat supplied by electric heater in the first 1400 s IVt\(_1\) = mlf mlf = 12 x 40 x 1400 = 6.72 x 105J (ii) Determination of Specific heat capacity of the body IVt\(_2\) = mc\(\Delta \theta\) c = \(\frac{IVt_2}{m \Delta \theta}\) = \(\frac{12 \times 40 \times 72}{1.5 \times 60}\) = 384 Jk\(^{-1}\) K\(^{-1}\)