Physics 2015 Jamb Examination

In mechanics, a couple consists of two parallel forces that are equal in magnitude but opposite in direction and do not share a common line of action. Because the two forces are equal and opposite, they satisfy the condition for translational equilibrium, meaning their vector sum is exactly zero. However, since they act at different points, they produce a turning effect known as a torque or moment. Therefore, while a couple can cause an object to rotate, it cannot cause it to move linearly because the resultant (net) force is always zero.

Physical quantities are categorised into two main groups: scalars and vectors. Scalar quantities, such as mass or time, are fully described by their magnitude (size) alone. In contrast, vector quantities, such as velocity, force, and acceleration, require both a magnitude and a specific direction in space to be fully defined. Mentioning only the magnitude of a force, for example, tells us how strong it is, but not where it will move an object; the direction is essential for a complete physical description.

Fire alarms, thermostats, and bimetallic thermometers all function specifically by utilizing the thermal expansion of solids. They typically use a bimetallic strip made of two different metals that expand at different rates, causing the strip to bend and complete or break an electrical circuit. In a simple pendulum, thermal expansion is actually a disadvantage or a source of error rather than a functional requirement. If the metal rod of a pendulum expands due to heat, its length increases, which changes its period of oscillation. Therefore, expansion is not 'required' for the pendulum to work; it is an unwanted physical effect that needs to be compensated for in precision clocks.

Energy associated with the position or configuration of an object is known as potential energy. When an object is lifted to a certain height against the force of gravity, work is done on the object, and this work is stored as gravitational potential energy. Since the object is described as being at a 'stationary point', it has no velocity and therefore no kinetic energy. The energy it possesses solely due to its elevated position is its potential energy, which would be converted into kinetic energy if the object were allowed to fall.

To find the gravitational force of attraction between two masses, we use Newton's Law of Universal Gravitation:\[ F = \frac{Gm_1m_2}{r^2} \]Given:
\(G = 6.67 \times 10^{-11} \; \text{Nm}^2\text{kg}^{-2}\)
\(m_1 = 10^{24} \; \text{kg}\)
\(m_2 = 10^{27} \; \text{kg}\)
\(r = 10^{20} \; \text{m}\)
Substituting the values into the formula:\[ F = \frac{6.67 \times 10^{-11} \times 10^{24} \times 10^{27}}{(10^{20})^2} \]\[ F = \frac{6.67 \times 10^{(-11 + 24 + 27)}}{10^{40}} \]\[ F = \frac{6.67 \times 10^{40}}{10^{40}} \]\[ F = 6.67 \; \text{N} \]The calculation results in a force of 6.67 Newtons.

One of the fundamental characteristics of an image formed by a plane mirror is that the image is as far behind the mirror as the object is in front of it. Given that Mr. Abioye (the object) is 4.7m from the mirror, his virtual image will be formed 4.7m behind the mirror. To find the total distance between the observer's eye and the image, we add the object-to-mirror distance and the mirror-to-image distance:\[ \text{Total Distance} = \text{m (object to mirror)} + \text{m (mirror to image)} \]\[ \text{Total Distance} = 4.7 + 4.7  \]\[ \text{Total Distance} = 9.4 \; \text{m} \]

Primary colours of light are those that can be mixed in different proportions to create a wide gamut of other colours, including white. For additive colour mixing (light), the primary colours are Red, Green, and Blue (RGB). This is distinct from subtractive primary colours used in paints and pigments, which are Cyan, Magenta, and Yellow (CMY). When the three primary colours of light are projected together at equal intensities, they produce white light.

The electron was the first subatomic particle to be discovered. In 1897, the British physicist J.J. Thomson discovered it while performing experiments with cathode ray tubes. He demonstrated that cathode rays were composed of previously unknown negatively charged particles, which he calculated to have much smaller mass than atoms and a very large charge-to-mass ratio.

James Chadwick later discovered the neutron in 1932, and Isaac Newton is famous for his work on gravity and laws of motion, not subatomic particles.

The efficiency of a machine measures how much of the work put into the machine is converted into useful work output. It is mathematically defined as the ratio of Work Output to Work Input. Since Mechanical Advantage (MA) represents the ratio of Load to Effort and Velocity Ratio (VR) represents the ratio of distance moved by Effort to distance moved by Load, the efficiency can be simplified to the ratio of MA to VR. To express this as a percentage, the ratio is multiplied by 100. Thus, the correct mathematical relationship is efficiency \(e = \frac{MA}{VR} \times 100\%\).

While a meter rule can measure length, it lacks the precision for accurate measurements of small objects. A micrometer screw gauge is used for very small thicknesses or diameters (like a wire). However, the Vernier caliper is specifically designed with 'outside jaws' to measure the external dimensions, such as the outer diameter of a cylinder or the width of a block, with high accuracy (typically up to 0.01 cm). It also features inside jaws for internal diameters and a depth probe, making it the most versatile and common instrument for measuring the external parts of mechanical objects accurately.