Physics 2024 Jamb Examination

When light travels from an optically less dense medium (air, \(n \approx 1.0\)) to an optically denser medium (water, \(n \approx 1.33\)), it slows down and bends towards the normal.
According to Snell's Law (\(n_1 \sin \theta_1 = n_2 \sin \theta_2\)), if the incident angle in air (\(\theta_1\)) is 30º, the refracted angle in the denser water (\(\theta_2\)) must be less than 30º.

First, calculate the volume (V) of the cube in cubic metres or cubic centimetres.
Side length \(l = 1.5\,\text{cm} = 0.015\,\text{m}\).\[V = l^3 = (0.015)^3 = 0.000003375\,\text{m}^3\]Now, use the density (\(\rho = 2700\,\text{kgm}^{-3}\)) to find the mass (m):\[m = \rho \times V\]\[m = 2700 \times 0.000003375 = 0.0091125\,\text{kg}\]Convert to grams by multiplying by 1000:\[m = 9.1125\,\text{g} \approx 9.1\,\text{g}\]

To convert a galvanometer into a voltmeter, a high resistance (multiplier) \(R\) is connected in series with it.
The total potential difference (\(V\)) is given by:\[V = I_g(R_g + R)\]Where \(I_g\) is the full-scale deflection current and \(R_g\) is the galvanometer resistance. Assuming standard values from the associated diagram (typically \(I_g = 20\,\text{mA} = 0.02\,\text{A}\) and \(R_g = 5\,\Omega\) for this specific JAMB problem):\[40 = 0.02(5 + R)\]\[\frac{40}{0.02} = 5 + R\]\[2000 = 5 + R\]\[R = 1995\,\Omega\]

The electrical energy (heat) generated by the resistor is used to evaporate the liquid.
Electrical heat produced \(H = I^2Rt\):\[H = 10^2 \times 2 \times 20 = 100 \times 2 \times 20 = 4000\,\text{J}\]The heat required for evaporation is \(Q = mL_v\):\[4000 = (5 \times 10^{-3}) \times L_v\]\[L_v = \frac{4000}{5 \times 10^{-3}} = \frac{4000}{0.005}\]\[L_v = 800,000 = 8.0 \times 10^5\,\text{Jkg}^{-1}\]

Relative Humidity (R.H.) is calculated by comparing the partial pressure of water vapour present in the air to the Saturated Vapour Pressure (S.V.P.) at the same temperature. [Image illustrating relative humidity and dew point] The partial pressure of the actual water vapour present is equal to the S.V.P. at the dew point temperature.\[\text{R.H.} = \frac{\text{S.V.P. at dew point}}{\text{S.V.P. at air temperature}} \times 100\%\]Given:
S.V.P. at 33ºC (air temperature) = 13.5 mmHg
S.V.P. at 7ºC (dew point) = 7.3 mmHg
\[\text{R.H.} = \frac{7.3}{13.5} \times 100\% \approx 0.5407 \times 100\% \approx 54\%\]

Electrolysis is the process of chemical decomposition produced by passing an electric current through a liquid or solution containing ions. The apparatus used to carry out and study this process is called a voltameter (or electrolytic cell). It is important not to confuse this with a 'voltmeter', which is an instrument used to measure electrical potential difference.

To find the horizontal component (\( F_x \)) of a force (\( F \)) acting at an angle (\( \theta \)) to the horizontal, we use the trigonometric relationship for the adjacent side of a right-angled triangle.\[ F_x = F \cos \theta \]Given:
\( F = 150 \\text{N} \)
\( \theta = 60^\circ \)\[ F_x = 150 \times \cos 60^\circ \]\[ F_x = 150 \times 0.5 = 75 \\text{N} \]

A concave mirror (also known as a converging mirror) has the property of reflecting parallel rays of light through a single focal point. In solar energy applications, concave mirrors are used to concentrate sunlight onto a specific area to increase energy intensity.

Rectification is the process of converting alternating current (A.C.) to direct current (D.C.). This is typically achieved using diodes.

Young's modulus (\( E \)) is defined as stress divided by strain. Stress has dimensions \( \text{ML}^{-1}\text{T}^{-2} \) while strain is dimensionless. Hence, Young's modulus has dimensions \( \text{ML}^{-1}\text{T}^{-2} \).