Physics 2024 Jamb Examination

An echo is formed when sound waves travel to a reflecting surface and return to the source. Because the sound must travel to the wall and back, the total distance covered by the sound wave is twice the distance between the observer and the wall. The relationship for speed in an echo scenario is: \[ v = \frac{2d}{t} \] Where: \(v\) is the speed of sound.
\(d\) is the distance to the wall (408 m).
\(t\) is the total time taken for the echo to return (2.4 s).
Substituting the values into the formula: \[ v = \frac{2 \times 408}{2.4} \] \[ v = \frac{816}{2.4} \] \[ v = 340 \text{ m/s} \] This calculation assumes that the air temperature and wind conditions are uniform along the path of the sound wave.

The color of an object is determined by the wavelengths of light it reflects. A red shirt appears red because it absorbs all other colors of white light and reflects red. When placed under pure red light, there is only red light available to be reflected. Since the shirt is highly efficient at reflecting red, it reflects almost all the incident light, appearing very bright or 'pale' (washed out) because no other colors are being absorbed to provide contrast.

The energy of the emitted photon (which represents the energy change \( \Delta E \)) is given by: \[ E = \frac{hc}{\lambda} \] Given: \( h = 6.63 \times 10^{-34} \, Js \) \( c = 3.0 \times 10^8 \, ms^{-1} \) \( \lambda = 5.68 \times 10^{-6} \, m \) \[ \Delta E = \frac{6.63 \times 10^{-34} \times 3.0 \times 10^8}{5.68 \times 10^{-6}} \] \[ \Delta E = \frac{19.89 \times 10^{-26}}{5.68 \times 10^{-6}} \] \[ \Delta E = 3.501 \times 10^{-20} \, J \] Matching the closest option, we get 3.49 x 10\(^{-20}\)J.

The 'forward' or horizontal component of a force (\( F \)) applied at an angle (\( \theta \)) is given by: \[ F_x = F \cos \theta \] Assuming the applied force \( F \) in the diagram is 50N (a common value in this JAMB diagram set): \[ F_x = 50 \times \cos 60^\circ \] \[ F_x = 50 \times 0.5 = 25.00\,N \]

Newton's Law of Universal Gravitation states that the force (\( F \)) is inversely proportional to the square of the distance (\( r \)): \[ F \propto \frac{1}{r^2} \] If the distance is halved (\( r_{new} = r/2 \)): \[ F_{new} \propto \frac{1}{(r/2)^2} = \frac{1}{r^2/4} = 4 \times \frac{1}{r^2} \] Thus, the new force is 4 times the original force: \[ F_{new} = 4 \times 10\,N = 40\,N \]

An ideal transformer is a theoretical model that assumes 100% efficiency. This means it has: 1. No resistance in the coils (no \( I^2R \) loss). 2. No flux leakage (all magnetic flux produced by the primary coil passes through the secondary). 3. No hysteresis loss or eddy current loss in the core.

Refractive index (\( n \)) can be calculated using real depth and apparent depth: \[ n = \frac{\text{Real Depth}}{\text{Apparent Depth}} \] Given: \( n = 1.33 \) \( \text{Apparent Depth} = 10\,cm \) \[ \text{Real Depth} = n \times \text{Apparent Depth} = 1.33 \times 10 = 13.3\,cm \]

The quantity of heat (\(Q\)) absorbed or released by a body is directly proportional to its thermal capacity (\(C\)) and the resulting change in temperature (\(\Delta T\)). Thermal capacity is defined as the amount of heat energy required to raise the temperature of the entire body by one Kelvin (or one degree Celsius).
The relationship is expressed by the formula: \[ Q = C \Delta T \] Given the parameters in the problem: Thermal capacity (\(C\)) = 400 J K\(^{-1}\)
Initial temperature (\(T_1\)) = 60\(^\circ\)C
Final temperature (\(T_2\)) = 80\(^\circ\)C
First, calculate the change in temperature: \[ \Delta T = T_2 - T_1 = 80 - 60 = 20\, \text{K} \] Now, substitute the values into the heat equation: \[ Q = 400 \times 20 \] \[ Q = 8000\, \text{J} \] Since the options are provided in kilojoules (kJ), we convert the result by dividing by 1000: \[ Q = \frac{8000}{1000} = 8\, \text{kJ} \] This represents the total thermal energy required to increase the temperature of the copper rod through the specified range.

A thermometric property is a physical property that changes measurably and continuously with temperature. In a liquid-in-glass thermometer, such as a mercury or alcohol thermometer, the liquid is contained in a bulb connected to a narrow capillary tube. As the temperature rises, the liquid expands, and its volume increases. Because the glass expansion is negligible compared to the liquid, this increase in volume forces the liquid further up the tube. The height of the liquid column is directly proportional to its volume, making the change in volume the primary property used to measure temperature. Other thermometers use different properties: resistance thermometers use electrical resistance, thermocouples use electromotive force (e.m.f.), and bimetallic thermometers use the differential linear expansion of two fused metals.

Resonance in a series RLC circuit occurs when the inductive reactance \(X_L\) and the capacitive reactance \(X_C\) are equal in magnitude but opposite in phase. This leads to their effects cancelling each other out completely. The total impedance \(Z\) of the circuit is given by: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] At resonance, since \(X_L = X_C\), the formula simplifies to \(Z = R\). This represents the minimum possible impedance the circuit can have. According to Ohm's Law for AC circuits, \(I = V/Z\); when the impedance is at its minimum, the current flowing through the circuit reaches its maximum value. This principle is widely used in radio tuning to select specific frequencies.