Physics 2016 Jamb Examination

To calculate the decrease in length due to cooling, we use the linear expansivity formula:\[ \Delta L = L_1 \alpha \Delta\theta \]Given:
Initial length \( L_1 = 10 \; \text{m} \)
Linear expansivity \( \alpha = 3 \times 10^{-5} \; \text{K}^{-1} \)
Temperature change \( \Delta\theta = 50 - 10 = 40 \; ^{\circ}\text{C} \) (or K)

Substituting the values:\[ \Delta L = 10 \times (3 \times 10^{-5}) \times 40 \]\[ \Delta L = 10 \times 40 \times 3 \times 10^{-5} \]\[ \Delta L = 1200 \times 10^{-5} \]\[ \Delta L = 1.2 \times 10^{-2} \; \text{m} \]The decrease in length of the wire is 0.012m or 1.2 × 10\(^{-2}\)m.

Perspiration (sweating) is a primary biological mechanism for thermoregulation. When sweat is produced on the skin, it absorbs thermal energy from the athlete's body to overcome the intermolecular forces holding the liquid together. As this liquid sweat changes phase into water vapour, it carries that heat away into the atmosphere. This process is known as evaporation, and it is highly effective because water has a high latent heat of vaporisation, meaning a small amount of sweat can remove a significant amount of heat from the body.

According to Newton's Law of Cooling, the rate at which an object loses heat is directly proportional to the difference in temperature between the object and its surroundings (the enclosure). If the temperature of the enclosure is significantly lower than that of the liquid, the rate of cooling will be faster. While surface area and the nature of the surface also play roles, among the options provided, the ambient temperature of the environment (enclosure) is the key determining factor for the rate of heat loss.

The quantity of heat required to raise the temperature of a whole body or a specific mass of a substance by 1 Kelvin (or 1°C) is called its heat capacity (or thermal capacity). It is mathematically expressed as \( C = \frac{Q}{\Delta\theta} \). If the definition had specified a 'unit mass' (like 1 kg), the answer would have been 'specific heat capacity'. Since it refers to 'a mass' (implying the total mass of the object in question), the correct term is heat capacity. Latent heats (fusion and vaporisation) refer to phase changes where the temperature does not change.

When two plane mirrors are placed parallel to each other, the angle between them (\( heta \)) is 0 degrees. The formula for the number of images formed by two inclined mirrors is \( n = \frac{360}{\theta} - 1 \). When \( heta = 0 \), the value of \( n \) becomes mathematically undefined, tending towards infinity. In practice, light reflects back and forth between the two surfaces repeatedly, creating a long 'tunnel' of images that only fade away due to the slight absorption of light by the glass and air with each reflection.

In semiconductors, the energy gap between the valence band and the conduction band is relatively small. At low temperatures, few electrons have enough energy to jump this gap, so the material acts as an insulator. As the temperature increases, more thermal energy is provided to the valence electrons, allowing more of them to cross into the conduction band and leave behind 'holes'. Since the number of charge carriers (electrons and holes) increases with heat, the electrical conductivity of the semiconductor increases as temperature rises. This is the opposite of how metallic conductors behave.

According to the Kinetic Theory of Matter, all matter is composed of tiny particles (atoms or molecules) that are in a state of constant, random motion. This constant motion is what explains phenomena like diffusion, gas pressure, and Brownian motion. Therefore, the statement claiming that molecules of matter are 'not in constant motion' is factually incorrect and contradicts the fundamental principles of molecular physics.

A dynamo (or generator) works on the principle of electromagnetic induction. When a coil of wire is rotated within a magnetic field, the changing magnetic flux induces an electromotive force (e.m.f.), which creates an electric current.

The rotation of the coil requires mechanical work (input), which is then transformed by the machine into electrical energy (output). This makes it the functional opposite of an electric motor, which converts electrical energy into mechanical energy.

Saturated vapour pressure (SVP) is the pressure exerted by a vapour in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. The SVP of any liquid depends solely on the nature of the liquid and its temperature. As the temperature of the liquid increases, the kinetic energy of the molecules increases, allowing more of them to escape into the vapour phase. This increase in the concentration of vapour molecules leads to a higher pressure. SVP is independent of the volume of the liquid or the volume of the container.

To accelerate an object vertically upwards, the applied force (F) must overcome the object's weight (mg) and provide the additional force required for the desired acceleration (ma).
Using Newton's Second Law (\( F_{net} = ma \)):\[ F_{applied} - mg = ma \]\[ F_{applied} = m(g + a) \]Given:
Mass \( m = 60 \; \text{kg} \)
Acceleration \( a = 10 \; \text{ms}^{-2} \)
Gravity \( g = 10 \; \text{ms}^{-2} \)

Substituting the values:\[ F_{applied} = 60(10 + 10) \]\[ F_{applied} = 60(20) \]\[ F_{applied} = 1200 \; \text{N} \]A total force of 1200N is required to lift the mass with the specified acceleration.