Physics 2011 Jamb Examination

According to Boyle’s Law, at constant temperature, the volume of a gas is inversely proportional to its pressure. However, in this question, the pressure is constant while the volume changes with temperature. Charles’ Law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. Hence, when temperature decreases, the volume decreases as well. Since the question mentions that volume increases as temperature decreases, this is contrary to Charles’ Law and inconsistent with any of the stated gas laws. Therefore, no given option accurately describes such behaviour, as it violates the normal gas laws.

In household circuits, appliances are connected in parallel so that each device receives the full supply voltage and can operate independently. If connected in series, switching off one device would interrupt current flow to others. Parallel connections also allow each appliance to draw the current it needs without affecting others. Hence, the main reason for using parallel connection is that each appliance gets the same voltage as the supply, not less.

For a sinusoidal alternating current, the r.m.s (root mean square) value is related to the peak value by the expression \( I_{rms} = \dfrac{I_{0}}{\sqrt{2}} \). Hence, the ratio of the r.m.s value to the peak value is \( \dfrac{1}{\sqrt{2}} \), which is approximately 0.707. This ratio is standard for all sinusoidal AC quantities such as current and voltage.

For the series connection:\[R_s = 5 + 10 = 15\;\Omega\]Power dissipated, \(P_s = \dfrac{V^2}{R_s} = \dfrac{24^2}{15} = 38.4\;W\)

For the parallel connection:\[\dfrac{1}{R_p} = \dfrac{1}{5} + \dfrac{1}{10} = \dfrac{3}{10} \Rightarrow R_p = 3.33\;\Omega\]Power dissipated, \(P_p = \dfrac{V^2}{R_p} = \dfrac{24^2}{3.33} = 172.8\;W\)

Therefore, the ratio of power in series to parallel arrangement is:\[P_s : P_p = 38.4 : 172.8 = 1 : 4.5\]None of the provided options correctly matches this ratio.

Silicon and germanium are both group IV elements with similar electronegativities. They share electrons equally to form a covalent bond, typical of elements with four valence electrons. The bond is neither ionic nor dative because there is no transfer of electrons or lone pair donation; instead, they share electrons to achieve a stable configuration.

For an upright and magnified image formed by a convex lens, the image is virtual and the object lies within the focal length. Using the magnification formula:\[m = \dfrac{v}{u}\] and the lens formula:\[\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\]Given \(m = 3\) and \(f = 15\;cm\), so \(v = 3u\). Substituting:\[\dfrac{1}{15} = \dfrac{1}{3u} - \dfrac{1}{u}\]\[\dfrac{1}{15} = \dfrac{1 - 3}{3u} = -\dfrac{2}{3u}\]\[u = -10\;cm\]Hence, the object distance is 10 cm (the negative sign indicates the object is on the same side as the incident light).

The frequency of a vibrating string is given by:\[f \propto \sqrt{T}\]Therefore:\[\dfrac{f_2}{f_1} = \sqrt{\dfrac{T_2}{T_1}}\]\[f_2 = 255 \times \sqrt{\dfrac{324}{225}} = 255 \times \sqrt{1.44} = 255 \times 1.2 = 306\;Hz\]Hence, the new frequency is 306 Hz.

In a parallel connection, the voltage across each resistor is the same as the source voltage. Using Ohm’s law:\[I = \dfrac{V}{R}\]For the 12Ω resistor:\[I = \dfrac{12}{12} = 1.0\;A\]Hence, the current through the 12Ω resistor is 1.0 A.

When two vectors act at right angles, their resultant is given by Pythagoras’ theorem:\[R = \sqrt{P^2 + Q^2}\] If the perpendicular components are 6 N and 8 N (as is standard for such vector diagrams), then:\[R = \sqrt{6^2 + 8^2} = \sqrt{100} = 10\;N\] Therefore, the resultant vector is 10.0 N.

A body is in neutral equilibrium when its centre of gravity remains at the same height after slight displacement. For a cone lying on its side (position Z), any small movement does not change the height of its centre of gravity, so it neither tends to return nor move further away from its original position. Hence, Z represents neutral equilibrium.