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To keep the block of mass m in equilibrium against a vertical wall using a horizontal force F: The normal reaction N = F The frictional force f must balance the weight: f = mg Maximum friction available: f = \muN = \muF For the minimum horizontal force: \muF = mg F = mg / \mu

From the diagram given in the question Change in length = (6.5 - 5.0) x 10\(^{-2}\)m Change in force(wg) = (420 - 200) x 10 x 10\(^{-3}\) = 2.5N ( g changed to kg) extension per unit x = \(\frac{\Delta l}{\Delta F}\) = \(\frac{1.5 \times 10^{-2}}{2.5}\) = 6.0 x 10\(^{-3}\)

(a) A wave motion is succession of pulses propagated with time from one region of space to another. Energy is transmitted in the process. A is the amplitude. It is the maximum displacement from equilibrium position of the wave particle. \(\lambda\) - the wavelength, is the distance between two successive points on the wave that is in phase. (b) Experiment to determine the frequency of a note emitted by a source of sound Assuming that the source of sound is a turning fork. The vibrating tube turning fork is held close to the top of a moveable tube as shown. The tube is deeped in a cylinder that is 3/4 filled with water. Starting with the air column of length, I, with the turning fork sounding gently close to the top, the length I is gradually increased; The, sound coming from the air column is heard to increase. When the sound is loudest the air has been set into resonance by the fork. The length of I of the air column is measured and recorded. The length of the air column can be shown to be \(\frac{\lambda}{4}\) neglecting end correction. Thus using the equation: \(f = \frac{V}{\lambda} = \frac{V}{4l}\) where V is the velocity of sound in air, f the frequency of the turning-fork the source of sound, the frequency is then determined. (ii) Using \(f = \frac{V}{\lambda} = \frac{V}{4l}\) = \(\frac{340}{4 \times 1} = 85 Hz\) (c) A sound wave : (i) requires material medium for propagation. (ii) is a longitudinal wave motion. While radio wave (i) does not require material medium for propagation. (ii) is a transverse wave motion.

a(i) Photoelectric emission occurs when electrons are emitted from the surface of metal plate when it is illuminated by light of sufficient high frequency. Threshold frequency is the minimum frequency of the illuminating light which will just be sufficient to cause photoelectric emission. Below this frequency, electrons will not be emitted. (ii) In the Einstein's photoelectric equation \(E = hf - hf_{0}\), E - is the maximum kinetic energy of the emitted electron ; hf - is the energy of the illuminating light; \(hf_{0}\) - is the work function. It represents the minimum energy required to liberate electrons from the surface of the metal \(f_{0}\) - is the threshold frequency. (b) Using \(E = hf - hf_{0}\) \(f = \frac{E + hf_{0}}{h}\) (d) The duality of matter means that matter can exhibit wave properties as well as have particle properties. This double nature of matter is general in nature e.g. particles like electrons can have wave properties. Waves such as X-rays can have particle properties. This is equally illustrated by photoelectric effect. De Broglie equation for the waves carried with particle is \(\lambda = \frac{h}{mv} = \frac{h}{p}\) mv = p is momentum of particle of mass m; h - planks constant.

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

On a displacement–time graph, the slope (\(\frac{\Delta y}{\Delta x}\)) represents velocity, and a straight-line slope indicates that this velocity is constant (uniform).

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

I. Forces can be represented by the sides of a triangle in equilibrium. II. The lines of action of the forces meet at a point or are parallel. III. The magnitude of one force equals the resultant of the other two. IV. Any one force can act as the equilibrant of the other two.

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

H\(_{max}\) = \(\frac{(V_0)^2 Sin^2\theta}{2g}\)

As the catapult is drawn back, it stores elastic potential energy. When released, this energy is converted into the stone's kinetic energy, which can then be converted into gravitational potential energy as the stone rises.

Time to move up: V = U - gt 0 = 50 - 10t t = 5. Total time spent on air = 2t = 10.0s

P1/T1 = P2/T2 80/(273+47) = P1/(273+27) = 75Nm-2

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

Refraction: change in direction of propagation of any wave as a result of its traveling at different speeds at different points along the wave front.