Physics 2014 Jamb Examination

Convection occurs because heating a fluid (liquid or gas) causes it to expand and become less dense. This less dense, warmer portion of the fluid rises, while the cooler, denser portions sink to take its place. This continuous cycle, known as a convection current, is driven by the variation in density within the liquid.

The distance between two successive crests is the wavelength (\(\lambda\)).
Given:
\(\lambda = 15\text{cm} = 0.15\text{m}\)
\(v = 300\text{ms}^{-1}\)
Using the wave equation:
\\[ v = f\lambda \\]\\[ f = \frac{v}{\lambda} = \frac{300}{0.15} = 2000\text{Hz} \\]In scientific notation, this is \(2.0 \times 10^3\text{Hz}\).

For an echo, the sound travels to the hill and back, covering the distance (\(d\)) twice. The total distance is \(2d = v \times t\).
Given:
\(v = 340\text{ms}^{-1}\)
\(t = 0.8\text{s}\)
\\[ 2d = 340 \times 0.8 \\]\\[ 2d = 272 \\]\\[ d = \frac{272}{2} = 136\text{m} \\]

Magnification (\(M\)) is the ratio of image distance (\(v\)) to object distance (\(u\)).
Given:
\(u = 10\text{m}\)
\(v = 25\text{cm} = 0.25\text{m}\)
\\[ M = \frac{v}{u} = \frac{0.25}{10} = 0.025 \\]In scientific notation, this is \(2.5 \times 10^{-2}\).

Using the mirror formula:
\\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \\]Given \(f = 2.0\text{cm}\) and \(u = 8.0\text{cm}\):
\\[ \frac{1}{2} = \frac{1}{8} + \frac{1}{v} \\]\\[ \frac{1}{v} = \frac{1}{2} - \frac{1}{8} = \frac{4 - 1}{8} = \frac{3}{8} \\]\\[ v = \frac{8}{3} \approx 2.67\text{cm} \\]Note: The options in the prompt use 'm' instead of 'cm', but based on the calculation, 2.7cm is the intended answer.

A compound microscope is designed to produce high magnification of very small objects. To achieve this, both the objective lens and the eyepiece have very short focal lengths. The objective lens forms a real, enlarged image, which is then further magnified by the eyepiece acting as a simple magnifying glass.

An astronomical telescope is in 'normal adjustment' when the final image is formed at infinity. This allows the observer to view the image with a relaxed eye (no accommodation), which is comfortable for long periods of observation.

The electroscope is initially positive, meaning the leaves are diverged due to mutual repulsion. When a negatively charged rod is brought near the cap, it attracts positive charges from the leaves up to the cap. This reduction in positive charge density in the leaves reduces the repulsive force between them, causing the leaves to collapse.

The charge (\(Q\)) stored in a capacitor is the product of its capacitance (\(C\)) and the potential difference (\(V\)) across it.
\\[ Q = CV \\]Given:
\(C = 0.1\text{F}\)
\(V = 10\text{V}\)
\\[ Q = 0.1 \times 10 = 1\text{C} \\]

The Maximum Power Transfer Theorem states that for a power source with a fixed internal resistance, the maximum power is delivered to an external load when the resistance of the load (\(R\)) is exactly equal to the internal resistance (\(r\)) of the source.