Physics 2018 Jamb Examination

To determine the operating voltage, we utilize the electrical power formula that relates power (P), voltage (V), and resistance (R). The relationship is expressed as:\[ P = \frac{V^2}{R} \]By rearranging this equation to isolate the voltage, we get:\[ V^2 = P \times R \]\[ V = \sqrt{P \times R} \]Given that the power \( P = 40 \; \text{W} \) and the resistance \( R = 90 \; \Omega \), we substitute these values into the formula:\[ V = \sqrt{40 \times 90} \]\[ V = \sqrt{3600} \]\[ V = 60 \; \text{V} \]

The shape of a liquid on a surface is determined by the competition between cohesive forces (attraction between like molecules) and adhesive forces (attraction between unlike molecules). In the case of mercury on glass, the cohesive forces between the mercury atoms are significantly stronger than the adhesive forces between the mercury atoms and the glass molecules. As a result, the mercury molecules pull toward each other to minimize surface area, forming spherical 'balls' rather than spreading out and 'wetting' the glass surface.

Based on the Principle of Conservation of Heat Energy, the heat lost by the hot water must equal the heat gained by the cold water in an isolated system. The formula for heat change is \( Q = mc\Delta\theta \). Let the final temperature be \( T \):
1. Heat lost by hot water:\[ Q_{\text{lost}} = m_1 c (\theta_1 - T) = 150 \times c \times (60 - T) \]2. Heat gained by cold water:\[ Q_{\text{gain}} = m_2 c (T - \theta_2) = 300 \times c \times (T - 20) \]Equating both sides (and cancelling specific heat capacity \( c \)):\[ 150(60 - T) = 300(T - 20) \]\[ 60 - T = 2(T - 20) \]\[ 60 - T = 2T - 40 \]\[ 100 = 3T \]\[ T = \frac{100}{3} \approx 33.33^\circ\text{C} \]

Brownian motion is the random, erratic movement of microscopic particles (like pollen or smoke particles) suspended in a fluid (liquid or gas). This movement is caused by the constant, rapid, and uneven collisions between the suspended particles and the invisible molecules of the fluid. This phenomenon provides direct physical evidence for the Kinetic Theory, proving that molecules are in a constant state of random motion.

Nuclear fusion is the process where light atomic nuclei, such as protons (hydrogen nuclei), combine to form a heavier nucleus, such as a helium atom. Because the mass of the resulting helium nucleus is slightly less than the sum of the masses of the original protons, the difference in mass is converted into a vast amount of energy according to Einstein's mass-energy equivalence formula, \( E = mc^{2} \). This specific process is what powers the sun and other stars, where it is often referred to as thermonuclear fusion due to the extreme temperatures required.

During nuclear fusion reactions (like those occurring in stars or experimental reactors), common products include Helium nuclei (also known as alpha particles), neutrons, and high-energy electromagnetic radiation in the form of Gamma (\( \gamma \)) rays. X-rays, however, are typically produced by the transitions of electrons in the outer shells of atoms or by the sudden deceleration of fast-moving electrons (Bremsstrahlung), rather than being a direct fundamental product of the nuclear fusion process itself.

There are three modes of heat transfer: conduction, convection, and radiation. Conduction requires direct contact, and convection involves the bulk movement of warmed air currents (which mostly rise upwards). For a person standing away from the fire, the primary method they receive heat is through infrared waves. These waves travel through space without needing a medium and transfer energy directly to the person's body. This process is known as radiation.

The Molecular Theory (or Kinetic Theory) of matter explains phenomena based on the motion and arrangement of particles. Conduction is explained by molecular collisions; convection by the movement of groups of molecules; and expansion by the increased spacing between molecules as they vibrate faster. Radiation, however, consists of electromagnetic waves (photons) and does not require a material medium or the presence of molecules to propagate. It is an electromagnetic phenomenon rather than a mechanical one explained by molecular interactions.

Viscosity is the measure of a fluid's resistance to flow or gradual deformation by shear stress. On a molecular level, it can be thought of as internal friction between adjacent layers of the fluid that are moving at different velocities. A 'thick' fluid like honey has high viscosity because it has high internal friction, whereas a 'thin' fluid like water has low viscosity.

According to the Principle of Conservation of Linear Momentum, the total momentum before the split must equal the total momentum after the split.
Total Initial Momentum = 0 (since it was at rest).
Let the mass of the second particle be \( M_2 = M - M_1 \) and its velocity be \( V_2 \).\[ 0 = M_1 V_1 + M_2 V_2 \]\[ 0 = M_1 V_1 + (M - M_1)V_2 \]\[ -(M - M_1)V_2 = M_1 V_1 \]\[ (M_1 - M)V_2 = M_1 V_1 \]\[ V_2 = \frac{M_1 V_1}{M_1 - M} \]The negative sign (implied in the denominator) indicates that the second particle moves in the opposite direction to the first.