Physics 2015 Jamb Examination

To find the volume of the gas at Standard Temperature and Pressure (S.T.P), we use the General Gas Equation, which combines Boyle's and Charles's laws. Standard conditions are defined as a temperature of 273K and a pressure of 760mmHg.
Given parameters:
Initial Pressure \(P_1 = 800 \text{ mmHg}\)
Initial Volume \(V_1 = 76 \text{ cm}^3\)
Initial Temperature \(T_1 = 27 + 273 = 300 \text{ K}\)
Final Pressure at S.T.P \(P_2 = 760 \text{ mmHg}\)
Final Temperature at S.T.P \(T_2 = 273 \text{ K}\)
We need to find the final volume \(V_2\):\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]\[ \frac{800 \times 76}{300} = \frac{760 \times V_2}{273} \]\[ \frac{60800}{300} = \frac{760 V_2}{273} \]\[ 202.667 = \frac{760 V_2}{273} \]\[ 760 V_2 = 202.667 \times 273 \]\[ 760 V_2 = 55328 \]\[ V_2 = \frac{55328}{760} \]\[ V_2 \approx 72.8 \text{ cm}^3 \]The calculation shows that the volume of the gas when adjusted to standard conditions is approximately 72.8cm\(^{3}\).

Boyle's law describes the relationship between the pressure and volume of a confined gas at a constant temperature. It states that the pressure of a given mass of an ideal gas is inversely proportional to its volume. Mathematically, this is expressed as \(P \propto 1/V\), which leads to the constant product relationship \(PV = k\). For a gas changing from one state to another at a fixed temperature, the product of the initial pressure and volume must equal the product of the final pressure and volume. This gives us the equation \(P_1 V_1 = P_2 V_2\). Option B relates to Charles's Law, while Option D is an incorrect attempt at the General Gas Equation.

In optics, light is often modeled as travelling in straight lines to simplify the study of reflection and refraction. A single, infinitesimally thin line that represents the direction and path of light propagation is termed a 'ray'. While a 'beam' refers to a collection or stream of multiple rays (which can be parallel, converging, or diverging), the specific term for the individual path itself is a ray. A 'locus' is a mathematical term for a set of points satisfying a condition, and 'lines' is too general a term for this specific physical concept.

Inductive reactance (\(X_L\)) is the opposition that an inductor offers to alternating current. It is determined by the frequency of the current and the inductance of the coil. The formula for inductive reactance is:\[ X_L = 2\pi f L \]Given:
Reactance \(X_L = 1 \; \Omega\)
Frequency \(f = \frac{50}{\pi} \text{ Hz}\)
Substituting the values into the formula to solve for \(L\):\[ 1 = 2 \times \pi \times \left(\frac{50}{\pi}\right) \times L \]\[ 1 = 2 \times 50 \times L \]\[ 1 = 100L \]\[ L = \frac{1}{100} \]\[ L = 0.01 \text{ H} \]The inductance required to produce a reactance of 1Ω at the specified frequency is 0.01H.

A stroboscope is an instrument used to make a cyclically moving object appear to be slow-moving or stationary. It works by illuminating the object with periodic flashes of light. When the frequency of the flashes matches the frequency of the wave or the rotation of the object, the object is illuminated at the exact same point in its cycle every time. To the human eye, this creates the optical illusion that the wave is frozen in place or 'stationary'. This is a vital tool in physics laboratories for measuring the frequency and wavelength of ripples in a ripple tank.

In physics, collisions are classified based on whether kinetic energy is conserved. In an elastic collision, both the total linear momentum of the system and the total kinetic energy of the system are conserved. This means the objects bounce off each other without any loss of energy to heat, sound, or permanent deformation. In an 'inelastic' collision, momentum is still conserved, but kinetic energy is not. Therefore, statements I and IV correctly describe the conditions of an elastic collision. Statements II and III are incorrect as they imply energy loss or gain, which contradicts the definition of an elastic process.

The Law of Floatation, which is a corollary of Archimedes' Principle, states that a floating object displaces a weight of fluid equal to its own weight. For an object to stay on the surface, the upward buoyant force (upthrust) must equal the downward force of gravity (weight). Since upthrust is equal to the weight of the fluid displaced, the object must displace exactly its own weight of the fluid to remain in equilibrium. Option A describes an object that is completely submerged, where it displaces its own volume, but not necessarily its own weight.

The General Gas Law (or Combined Gas Law) is formed by combining Boyle's Law, Charles's Law, and Gay-Lussac's Law. It states that the ratio of the product of pressure and volume to the absolute temperature of a gas is constant for a fixed mass of gas. Mathematically, this is expressed as \(\frac{PV}{T} = k\). Option B represents Boyle's Law (constant temperature), Option C represents Charles's Law (constant pressure), and Option D represents Gay-Lussac's Law (constant volume). Option A is the only one that accounts for all three variables simultaneously.

The phenomenon described is a mirage, specifically a 'road mirage'. On a hot, sunny day, the asphalt road becomes very hot and warms the layer of air immediately above it. This creates a gradient where the air near the ground is hot (less dense) and the air higher up is relatively cooler (more dense). As light rays from the sky travel downward towards the road, they pass through these layers of varying density and undergo refraction, eventually hitting the hot layer at a very shallow angle and undergoing total internal reflection. The light is bent back up towards the observer's eyes. The brain interprets these light rays as coming from the ground, creating the illusion of a reflecting pool of water, which is actually just an image of the sky.

A luminous object is one that generates and emits its own light due to internal processes (like nuclear fusion in stars or chemical combustion in a candle). The Sun, stars, and a lit candle are all examples of luminous sources. Non-luminous objects, on the other hand, do not produce their own light; they are only visible because they reflect light from a luminous source. The Moon is a non-luminous object; it shines only because it reflects sunlight towards the Earth. Despite its brightness in the night sky, it does not possess its own light-generating mechanism.