Physics 2018 Jamb Examination

The provided nuclear equation shows two light nuclei (isotopes of Hydrogen, such as Deuterium) combining to form a heavier nucleus (an isotope of Helium) with the release of a neutron and a significant amount of energy.
This process is known as nuclear fusion. Unlike fission, where a heavy nucleus splits into smaller fragments, fusion involves the joining of light nuclei under extremely high temperature and pressure. It is the process that powers the sun and other stars.

Heat capacity (also known as thermal capacity) is defined as the amount of heat energy required to raise the temperature of a given mass of a substance by one unit of temperature (1 K or 1 °C).

While 'specific heat capacity' refers to the heat required per unit mass (exactly 1 kg), 'heat capacity' refers to the object as a whole, in this case, the entire 10 kg of Copper. Mathematically, Heat Capacity \( C \) is related to specific heat capacity \( c \) by the formula:\[ C = mc \]Since the question specifies a particular mass (10 kg), the energy required to raise that specific mass by 1 K is the heat capacity of that 10 kg copper block.

According to Faraday's first law of electrolysis, the mass \( m \) of a substance deposited is proportional to the quantity of electricity \( Q \) passed through the electrolyte. The formula is:\[ m = zIt \]Where:
\( m = 36.0 \; \text{g} \) (mass deposited)
\( z = 0.0012 \; \text{g/C} \) (electrochemical equivalent)
\( t = 5 \; \text{mins} = 5 \times 60 = 300 \; \text{s} \) (time in seconds)
\( I \) is the current in Amperes.

Rearranging the formula to solve for current \( I \):\[ I = \frac{m}{zt} \]\[ I = \frac{36.0}{0.0012 \times 300} \]\[ I = \frac{36.0}{0.36} \]\[ I = 100 \; \text{A} \]

Rectilinear propagation of light refers to the tendency of light to travel in straight lines. When an opaque object is placed in the path of light, it blocks the straight-travelling rays, creating a dark region behind it known as a shadow. An eclipse is a large-scale natural version of this phenomenon, where one celestial body moves into the shadow of another. If light could bend easily around objects (significant diffraction), distinct shadows and eclipses would not form as they do.

Ohm's law states that the current flowing through a conductor is directly proportional to the potential difference across it, provided physical conditions like temperature remain constant. Metals are 'Ohmic' conductors because they show this linear relationship under constant conditions. Diodes and electrolytes are 'non-Ohmic' because their current-voltage relationship is non-linear. Glass is an insulator and does not conduct electricity under normal conditions.

Isotopes are atoms of the same element that have the same number of protons (atomic number) but different numbers of neutrons (mass number).
1. Since they have the same number of protons, neutral isotopes also have the same number of electrons, which determines their chemical behavior. Thus, they have identical chemical properties.
2. Because they have different masses, isotopes differ in physical properties like density and boiling point, which are used in processes like mass spectrometry or diffusion to separate them.
3. By definition, isotopes of the same element must have the same number of protons. Therefore, all three statements are correct.

When the mass \( m_1 \) is on the verge of sliding, the system is in limiting equilibrium. The tension \( T \) in the string is equal to the weight of the hanging mass \( m_2 \), and this tension is also equal to the limiting frictional force \( F_s \) acting on \( m_1 \).
From the hanging mass \( m_2 \):\[ T = m_2 g \]From the mass \( m_1 \) on the table:\[ F_s = T = m_2 g \]The normal reaction \( R \) on \( m_1 \) is:\[ R = m_1 g \]The coefficient of static friction \( \mu_s \) is defined as the ratio of the limiting frictional force to the normal reaction:\[ \mu_s = \frac{F_s}{R} \]\[ \mu_s = \frac{m_2 g}{m_1 g} \]\[ \mu_s = \frac{m_2}{m_1} \]

A mirage is an optical illusion caused by the refraction and total internal reflection of light in the atmosphere.
Statement I is correct: On a hot day, the air near the ground is hotter and less dense than the air above it, creating a gradient of refractive indices.
Statement III is correct: Light rays from the sky travelling downwards towards the hot ground are bent (refracted) progressively until they undergo total internal reflection and travel upwards to the observer's eye. This makes the sky appear as if it is reflected on the ground (looking like water).
Statement II is incorrect: The road surface does not become invisible; rather, an image of the sky is superimposed over it.

In a U-tube manometer, the pressure in the chamber \( P_G \) is balanced by the atmospheric pressure \( P_{atm} \) and the pressure due to the height difference \( h \) of the liquid column. Looking at the diagram provided (where the liquid level in the arm open to the atmosphere is higher than the level in the arm connected to G), it indicates that the pressure in G is greater than atmospheric pressure.\[ P_G = P_{atm} + h \]Assuming the height difference \( h \) shown in the standard diagram for this problem is 70mm:\[ P_G = 760 \; \text{mm} + 70 \; \text{mm} = 830 \; \text{mm} \]Note: If the level in the chamber side was higher, we would subtract the height from atmospheric pressure.

Internal resistance is the opposition to the flow of current within the cell itself. Secondary cells, such as the lead-acid accumulator, are specifically designed to have a very low internal resistance (often less than 0.01 Ohms). This allows them to deliver the very high currents required to start motor engines. Primary cells like the Leclanche cell, Daniell cell, and standard torch batteries (zinc-carbon) have significantly higher internal resistances which limit their maximum current output.