Physics 2019 Jamb Examination

J.J. Thomson discovered the electron in 1897 through his experiments with cathode ray tubes."
He demonstrated that cathode rays were composed of previously unknown negatively charged particles, which were later named electrons. Dalton proposed the atomic theory, Chadwick discovered the neutron, and Bohr developed the model of electron shells.

Rutherford's model had two major flaws based on classical physics. First, a revolving electron is accelerating and should continuously radiate energy (II). Second, as it loses energy, it should spiral into the nucleus, making the atom unstable (I). Classical physics also predicted a continuous spectrum, whereas atoms produce discrete line spectra. Statement III is more specifically a limitation of the Bohr model regarding complex atoms.

Inductive reactance (\(X_L\)) is the opposition that an inductor offers to alternating current. Similar to Ohm's law for resistance (\(R = V/I\)), reactance is defined as the ratio of the peak (amplitude) or RMS voltage to the peak or RMS current. The formula is \( X_L = \frac{V_0}{I_0} \).

Ripple is the residual periodic variation of the DC voltage within a power supply which has been derived from an AC source. While rectification converts AC to DC, the resulting wave is pulsating. Capacitors are used to smooth this, but under a heavy load, the capacitor discharges faster between peaks, leading to an increase in ripple voltage.

Surface tension is caused by cohesive forces between liquid molecules. As temperature increases, the kinetic energy of the molecules increases, which weakens these intermolecular forces. Consequently, the surface tension of the liquid decreases.

For a real image, the distance between object and image is \( L = u + v = 40 \; \text{cm} \).
Magnification \( M = \frac{v}{u} = 3 \), so \( v = 3u \).
Substituting into the distance equation:\[ u + 3u = 40 \Rightarrow 4u = 40 \Rightarrow u = 10 \; \text{cm} \]Then \( v = 3(10) = 30 \; \text{cm} \).
Using the lens formula:\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]\[ \frac{1}{f} = \frac{1}{10} + \frac{1}{30} = \frac{3 + 1}{30} = \frac{4}{30} \]\[ f = \frac{30}{4} = 7.5 \; \text{cm} \]

Any ray of light passing through the centre of curvature (C) of a spherical mirror hits the surface normally (at 90° to the tangent). According to the law of reflection, the angle of incidence is 0° relative to the normal. Therefore, the angle of reflection is also 0°, causing the ray to reflect back along its own path.

In a pin-hole camera, a smaller hole allows only a narrow beam of light from each point on the object to reach the screen, creating a sharp image. If the pin-hole is made larger, multiple beams of light from the same point on the object overlap on the screen, resulting in a blurred or less sharply defined image.

The magnetic force on a current-carrying wire is given by the formula:\[ F = BIl \sin \theta \]Given:
\( B = 0.40 \; \text{T} \)
\( I = 6.0 \; \text{A} \)
\( l = 15 \; \text{cm} = 0.15 \; \text{m} \)
\( \theta = 90^\circ \) (right angle, so \( \sin 90^\circ = 1 \))
\[ F = 0.40 \times 6.0 \times 0.15 \times 1 \]\[ F = 2.4 \times 0.15 = 0.36 \; \text{N} \]

First, find the Velocity Ratio (V.R.) of the screw jack:\[ V.R. = \frac{2\pi L}{p} \]where \( L = 60 \; \text{cm} \) and \( p = 0.45 \; \text{cm} \).\[ V.R. = \frac{2\pi \times 60}{0.45} = \frac{120\pi}{0.45} = \frac{12000\pi}{45} = \frac{800\pi}{3} \]Efficiency \( \eta = \frac{75}{\pi}\% = \frac{75}{100\pi} \).
Since \( M.A. = \eta \times V.R. \):\[ M.A. = \frac{75}{100\pi} \times \frac{800\pi}{3} \]\[ M.A. = \frac{75}{3} \times \frac{800}{100} = 25 \times 8 = 200 \]