Physics 2025 Jamb Examination

When the same current passes through different voltameters in series, the mass of elements deposited is directly proportional to their electrochemical equivalents: \( \frac{m_1}{m_2} = \frac{z_1}{z_2} \). \[ \frac{0.2}{1.2} = \frac{0.00028}{z_{\text{silver}}} \] \[ z_{\text{silver}} = \frac{1.2 \times 0.00028}{0.2} = 6 \times 0.00028 \] \[ z_{\text{silver}} = 0.00168 = 1.68 \times 10^{-3} \, \text{gC}^{-1} \]

Heat capacity (C) is the ratio of heat absorbed (Q) to the change in temperature (\( \Delta T \)). \[ C = \frac{Q}{\Delta T} \] Given: \( Q = 48000 \, \text{J} \) and \( \Delta T = 53 \, \text{K} \) (or ºC). \[ C = \frac{48000}{53} \approx 905.66 \, \text{JK}^{-1} \]

In the electromagnetic spectrum, frequency increases as wavelength decreases. The order from longest to shortest wavelength is: Radio waves > Microwaves > Infrared > Visible Light > Ultraviolet > X-rays > Gamma rays. Among the choices, X-rays have the highest frequency and therefore the shortest wavelength.

Stress is defined as Force divided by Area. Force (\( F \)) = \( mg = 1.5 \times 10 = 15 \, \text{N} \). Area (\( A \)) = \( \pi r^2 = 3.142 \times (0.003 \, \text{m})^2 = 3.142 \times 9 \times 10^{-6} \approx 2.827 \times 10^{-5} \, \text{m}^2 \). \[ \text{Stress} = \frac{15}{2.827 \times 10^{-5}} \approx 530597 \, \text{Nm}^{-2} = 5.3 \times 10^5 \, \text{Nm}^{-2} \text{ (approximately } 53 \times 10^4 \, \text{Nm}^{-2} \text{)} \]

Latent heat of fusion is the total amount of heat required to change a given mass of a substance from solid to liquid state at its melting point without any change in temperature. (Note: 'Specific' latent heat would refer to the heat per unit mass, whereas the question asks for the total quantity for a specific 5kg mass, which is simply the Latent Heat of Fusion).

A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. It is highly accurate for measuring low to medium resistances because it is a null-balance method, meaning it does not rely on the calibration of a meter but on the ratio of known resistances. While a potentiometer is used for comparing e.m.f.s or measuring internal resistance, the Wheatstone bridge is the standard laboratory instrument for precise resistance measurement.

In an AC circuit, if the 'instantaneous current' provided in a problem like this refers to the peak current (\(I_0\)), the r.m.s value is calculated using the relationship: \(I_{rms} = \frac{I_0}{\sqrt{2}}\). Given \(I_0 = 7\, \text{A}\) and taking \(\sqrt{2} \approx 1.414\): \[I_{rms} = \frac{7}{1.414} \approx 4.95\, \text{A}\] Rounding to the nearest whole number as per the options gives 5A.

Refractive index (\(n\)) can be defined as the ratio of the real depth to the apparent depth of an object in a medium. The formula is: \[n = \frac{\text{Real Depth}}{\text{Apparent Depth}}\] Given \(n = 1.33\) and apparent depth = 10 cm: \[1.33 = \frac{\text{Real Depth}}{10}\] \[\text{Real Depth} = 1.33 \times 10 = 13.3\, \text{cm}\]

The force (F) on a charge (q) moving in a magnetic field (B) at an angle (\(\theta\)) is given by: \[F = qvB \sin\theta\] Given: \(F = 6\, \text{N}\), \(q = 5 \times 10^{-6}\, \text{C}\), \(v = 3 \times 10^4\, \text{m/s}\), and \(\theta = 45^\circ\). \[6 = (5 \times 10^{-6}) \times (3 \times 10^4) \times B \times \sin 45^\circ\] \[6 = 0.15 \times B \times 0.7071\] \[6 = 0.106065B\] \[B = \frac{6}{0.106065} \approx 56.57\, \text{T}\]

Tension is a force exerted through a string or cable. Since tension is a force, it has the same dimensions as force. Force is mass (M) multiplied by acceleration (LT\(^{-2}\)). Therefore, the dimensions are [M][L][T\(^{-2}\)].