Physics 2018 Jamb Examination

Evaporation is the process by which molecules at the surface of a liquid gain enough kinetic energy to escape into the gas phase. Unlike boiling, which occurs at a specific temperature (the boiling point) throughout the entire volume of the liquid, evaporation occurs spontaneously at any temperature and only at the liquid's surface. Regelation refers to the melting of ice under pressure, while sublimation is the direct transition from solid to gas.

The Kinetic Molecular Theory explains that the state of matter is determined by the balance between the kinetic energy of particles and the attractive forces between them. In solids, intermolecular forces are very strong and spacing is minimal, leading to fixed shapes. In liquids, forces are weaker, allowing molecules to slide past each other while staying close. In gases, the molecules are far apart with negligible attractive forces, allowing them to fill any container. Therefore, the spacing and intermolecular forces are the defining factors for these states.

Convex mirrors (diverging mirrors) are preferred for vehicle side-view and rear-view mirrors because they always produce an upright (erect) and smaller (diminished) virtual image.

Because the image is diminished, it allows for a much wider field of view compared to a plane or concave mirror, enabling the driver to see more of the traffic behind them.

Quality, also known as timbre, is the characteristic of sound that allows the ear to distinguish between two sounds that have the same pitch and loudness. This difference arises because most musical instruments do not produce a pure sine wave; instead, they produce a fundamental frequency accompanied by various overtones or harmonics. The unique blend and relative strengths of these overtones give each instrument its distinct 'colour' or quality.

This diagram illustrates the 'divided touch' method of magnetisation. In this method, the ends of the steel bar where the stroking magnets finish their stroke always acquire the opposite polarity to the stroking pole used. Since the south poles (S) of both magnets start at the centre and move outwards towards ends T and V, they 'pull' the north poles of the internal molecular magnets toward those ends. Therefore, both ends T and V will acquire North polarities.

Domestic circuits are connected in parallel for several vital reasons. Firstly, in a parallel circuit, every appliance receives the full mains voltage (e.g., 240V). Secondly, it allows each appliance to be controlled by its own switch independently. If they were in series, turning off one lamp would break the circuit and turn off everything else. While not explicitly listed as a 'true' option in the standard sense, the context of JAMB questions often implies that parallel circuits are used so that each device operates at its rated voltage and independently of others.

The relationship between linear velocity (\(v\)) and angular velocity (\(\omega\)) in circular motion is given by the formula:\[ v = r\omega \]Given:
Linear speed \(v = 1 \; \text{ms}^{-1}\)
Radius \(r = 0.5 \; \text{m}\)

Substituting the values into the rearranged formula:\[ \omega = \frac{v}{r} \]\[ \omega = \frac{1}{0.5} = 2 \; \text{rads}^{-1} \]

First, we determine the Velocity Ratio (V.R.) of the machine. For a lever-type machine, the V.R. is the ratio of the effort arm length to the load arm length:\[ V.R. = \frac{\text{Effort Arm}}{\text{Load Arm}} = \frac{2}{1} = 2 \]Next, we use the efficiency (\(\eta\)) formula to find the Mechanical Advantage (M.A.):\[ \eta = \frac{M.A.}{V.R.} \times 100\% \]\[ 90 = \frac{M.A.}{2} \times 100 \]\[ M.A. = \frac{90 \times 2}{100} = 1.8 \]Finally, we use the definition of M.A. to find the effort (\(E\)):\[ M.A. = \frac{\text{Load}}{\text{Effort}} \]\[ 1.8 = \frac{180}{E} \]\[ E = \frac{180}{1.8} = 100 \; \text{N} \]

1. Capacitors in parallel:\[ C_p = C_1 + C_2 + C_3 =2 + 2 + 2 = 6\,\mu\text{F}\] 2. Total capacitance in series:\[ \frac{1}{C_T} = \frac{1}{C_p} + \frac{1}{C_4} + \frac{1}{C_5} \]\[= \frac{1}{6} + \frac{1}{2}  + \frac{1}{3}\]\[= \frac{1}{6} + \frac{3}{6}  + \frac{2}{6}\]\[= \frac{1 + 3 + 2}{6}  = \frac{6}{6} = 1\] \[ C_T = 1\,\mu\text{F}\]  

A vernier calliper is equipped with internal jaws specifically designed to measure the internal diameters of hollow objects like test tubes or pipes. While a micrometer screw gauge is more precise, it is generally used for external dimensions of very small objects. A metre rule lacks the necessary precision and physical accessibility for inner diameters, and dividers would require an additional scale to read the measurement.