Physics 2018 Jamb Examination

To find the resistance of the lamp, we use the relationship between power (P), voltage (V), and resistance (R). The standard formula for power in an electrical circuit is:\[ P = \frac{V^2}{R} \]By rearranging this formula to solve for resistance, we get:\[ R = \frac{V^2}{P} \]Given that the power \( P = 40 \; \text{W} \) and the voltage \( V = 12 \; \text{V} \), the calculation is as follows:\[ R = \frac{12^2}{40} = \frac{144}{40} \]\[ R = 3.6 \; \Omega \]

This problem is solved using Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the two media.

The formula is:\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]Where:
\( n_1 = 1 \) (refractive index of air)
\( \theta_1 = 30^\circ \) (angle of incidence)
\( n_2 = 4/3 \approx 1.33 \) (refractive index of water)
\( \theta_2 \) is the angle of refraction.

Substituting the values:\[ 1 \times \sin 30^\circ = \frac{4}{3} \times \sin \theta_2 \]\[ 0.5 = \frac{4}{3} \sin \theta_2 \]\[ \sin \theta_2 = 0.5 \times \frac{3}{4} = 0.375 \]\[ \theta_2 = \sin^{-1}(0.375) \approx 22^\circ \]

The electrical energy supplied by the heater is converted into heat energy absorbed by the water.
1. Calculate Electrical Energy (E):\[ P = 1 \; \text{kW} = 1000 \; \text{W} \]\[ t = 2 \; \text{mins} = 120 \; \text{s} \]\[ E = P \times t = 1000 \times 120 = 120,000 \; \text{J} \]2. Calculate Heat Gained by Water (Q):\[ Q = mc\Delta\theta \]\[ 120,000 = 2 \times 4000 \times (T_f - 30) \]\[ 120,000 = 8000(T_f - 30) \]\[ T_f - 30 = \frac{120,000}{8000} = 15 \]\[ T_f = 15 + 30 = 45^\circ\text{C} \]

Earthing or grounding involves connecting a charged body to the Earth, which acts as a vast reservoir of charge. A positively charged conductor has a deficit of electrons. When it is connected to the Earth, electrons (which are negatively charged and mobile) flow from the Earth into the conductor to neutralise the positive charge. Protons are bound within the nucleus and do not flow through conductors in this manner.

According to the Kinetic Theory of Matter, the temperature of a substance is a macroscopic measure of the microscopic motion of its constituent particles. Specifically, temperature is directly proportional to the average kinetic energy of the molecules. While total kinetic energy depends on the amount of substance (mass), the temperature reflects the average energy per molecule. As heat is added, molecules move more vigorously, increasing their average kinetic energy and thus the temperature.

Impulse is defined as the product of the average force applied to an object and the time interval over which that force acts. The formula is:\[ J = F \Delta t \]Impulse is a vector quantity and, according to the impulse-momentum theorem, it is equal to the change in momentum of the object.

Diffusion and Brownian motion provide direct evidence that matter is composed of discrete particles in constant motion. Esterification is a chemical reaction, which also implies the rearrangement of discrete atoms/molecules. Diffraction, however, is a phenomenon specifically associated with the wave nature of matter and light. It occurs when a wave encounters an obstacle or an opening that is comparable in size to its wavelength, causing the wave to bend around the corners.

According to the Law of Floatation, a floating body displaces its own weight of the liquid in which it floats.
1. Calculate density of the cube (\( ho_c \)):\[ \text{Volume} = 0.5 \times 0.5 \times 0.5 = 0.125 \; \text{m}^3 \]\[ \rho_c = \frac{\text{Mass}}{\text{Volume}} = \frac{75}{0.125} = 600 \; \text{kg/m}^3 \]2. Calculate density of the liquid (\( ho_l \)):
If 1/3 of the height is above, then 2/3 is submerged (\( V_{sub} = \frac{2}{3}V_{total} \)).\[ \text{Weight of cube} = \text{Weight of displaced liquid} \]\[ \rho_c V_{total} g = \rho_l V_{sub} g \]\[ 600 \times V_{total} = \rho_l \times \frac{2}{3} V_{total} \]\[ \rho_l = 600 \times \frac{3}{2} = 900 \; \text{kg/m}^3 \]3. Relative Density (R.D.):\[ R.D. = \frac{\rho_l}{\rho_{water}} = \frac{900}{1000} = 0.90 \]

First, we find the speed of sound (\( v \)) using the wave equation:\[ v = f\lambda \]\[ v = 260 \times 1.29 = 335.4 \; \text{ms}^{-1} \]For an echo, the sound travels to the hill and back, covering a total distance of \( 2d \), where \( d \) is the distance to the hill. \[ 2d = v \times t \]\[ 2d = 335.4 \times 2 \]\[ 2d = 670.8 \]\[ d = 335.4 \; \text{m} \]

A fuse is a safety device designed to protect an electrical circuit from excessive current. It consists of a short piece of wire made of a material that has a low melting point. When the current exceeds a safe limit, the heat generated by the resistance of the wire reaches its melting point quickly, causing the wire to melt and break the circuit, thereby preventing damage to appliances or fires.