Physics 2019 Jamb Examination

We use the general gas law: \[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \] Given: \( P_1 = 114 \, \text{cmHg}, V_1 = 2667 \, \text{cm}^3, T_1 = 273 + 273 = 546 \, \text{K} \) At STP: \( P_2 = 76 \, \text{cmHg}, T_2 = 273 \, \text{K} \) \[ \frac{114 \times 2667}{546} = \frac{76 \times V_2}{273} \] \[ V_2 = \frac{114 \times 2667 \times 273}{546 \times 76} \] \[ V_2 = \frac{114 \times 2667}{2 \times 76} = \frac{114 \times 2667}{152} \approx 2000.25 \, \text{cm}^3 \]

Gas conduction requires high voltage and low pressure. If air is at normal atmospheric pressure, it acts as an insulator. Pumping air out *without lowering the pressure* (essentially keeping the pressure high) prevents the electrons from gaining enough kinetic energy between collisions to ionize the gas molecules. Therefore, conduction does not occur.

The depth of the sea is measured using SONAR (Sound Navigation and Ranging). This technique involves sending a sound wave (ultrasound) to the seabed and timing how long it takes for the signal to bounce back. This 'bouncing back' of the wave is the phenomenon of reflection.

Newton's First Law (Law of Inertia) states that an object will continue in its state of rest or uniform motion in a straight line unless acted upon by an external force. The Sun's gravity provides the centripetal force that keeps Earth in orbit. If that force vanishes, inertia causes the Earth to continue in a straight line at its current velocity, which is tangential to its orbit.

Conduction and convection require a material medium (solid, liquid, or gas) to transfer thermal energy. Radiation, however, travels in the form of electromagnetic waves. [Image showing conduction, convection, and radiation mechanisms] Because electromagnetic waves do not require particles to move, radiation is the only method that can transfer heat through a vacuum (like the space between the Sun and Earth).

In a camera, the diaphragm adjusts the size of the aperture to control the amount of light entering. [Image comparing camera diaphragm to human iris] In the human eye, the iris is the muscular structure that changes the size of the pupil (the opening) to regulate light entry based on brightness.

Gravitational Potential Energy (P.E.) is calculated using the formula: \[ P.E. = mgh \] Given \( m = 4 \, \text{kg}, g = 10 \, \text{ms}^{-2}, h = 40 \, \text{m} \): \[ P.E. = 4 \times 10 \times 40 = 1600 \, \text{J} \]

The tip of the seconds hand moves in a circle. The time taken for one complete revolution (period \( T \)) is 60 seconds. \[ \text{Speed} (v) = \frac{2\pi r}{T} \] Given \( r = 0.1 \, \text{m} \) and \( T = 60 \, \text{s} \): \[ v = \frac{2 \times 3.14159 \times 0.1}{60} \approx \frac{0.6283}{60} \approx 0.01047 \, \text{ms}^{-1} \] In scientific notation, this is \( 1.05 \times 10^{-2} \, \text{ms}^{-1} \).

Potential energy is the energy stored in an object due to its position or state. When work is done against a field (like gravity or an electric field) to move an object to a specific point, that work is stored as potential energy.

The change in length (\( \Delta L \)) is proportional to the original length (\( L_1 \)) and the change in temperature (\( \Delta T \)): \[ \Delta L = \alpha L_1 \Delta T \] For the first rod: \[ 1 \, \text{mm} = \alpha (5 \, \text{m}) (10 ^\circ\text{C}) \implies \alpha = \frac{1}{50} \] For the second rod: \[ \Delta L_2 = \alpha (2.5 \, \text{m}) (5 ^\circ\text{C}) \] Substitute \( \alpha \): \[ \Delta L_2 = \left( \frac{1}{50} \right) \times 2.5 \times 5 = \frac{12.5}{50} = 0.25 \, \text{mm} \]