Physics 2017 Jamb Examination

The standard equations of linear motion for uniform acceleration are:
1. \( v = u + at \)
2. \( s = ut + \frac{1}{2}at^2 \)
3. \( v^2 = u^2 + 2as \)
Option B and D are different versions of the third equation. Option C is the second equation. Option A suggests \( a = \frac{v^2 - u^2}{2} \), which is missing the displacement factor (s). From the third equation, the correct expression for acceleration is \( a = \frac{v^2 - u^2}{2s} \).

Electromagnetic radiation consists of waves of the electromagnetic field, which propagate through space and carry electromagnetic radiant energy.
X-rays, radio waves, and sunlight (visible light) are all part of the electromagnetic spectrum and can travel through a vacuum. Sound waves, however, are mechanical waves; they require a physical medium (like air, water, or solids) to travel and are produced by physical vibrations.

The electric field intensity (E) between two parallel plates is given by the potential gradient formula:\[ E = \frac{V}{d} \]Given:
Potential difference \( V = 6.5 \text{ V} \)
Distance \( d = 35 \text{ cm} = 0.35 \text{ m} \)
Calculation:\[ E = \frac{6.5}{0.35} \approx 18.5714 \text{ NC}^{-1} \]The electric field intensity is approximately 18.57 NC\(^{-1}\).

Resonance occurs when the frequency of a periodic force matches the natural frequency of a system, causing large-amplitude oscillations. If soldiers march in step (rhythmically), the frequency of their footsteps might match the natural frequency of the bridge. This could lead to a massive increase in the bridge's vibration, potentially causing it to collapse. By marching 'out of step' (disorderly), they ensure their footsteps are random and do not sync with the bridge's natural frequency.

Upthrust is equal to the weight of the fluid displaced (Archimedes' Principle):\[ U = V \rho g \]Given:
Volume \( V = 50 \text{ cm}^3 = 50 \times 10^{-6} \text{ m}^3 \)
Density \( \rho = 10^3 \text{ kgm}^{-3} \)
Gravity \( g = 10 \text{ ms}^{-2} \)
Calculation:\[ U = (50 \times 10^{-6}) \times 10^3 \times 10 \]\[ U = 50 \times 10^{-2} = 0.5 \text{ N} \]

In a gas discharge tube, cathode rays (streams of electrons) are produced when the gas inside is at a very low pressure (usually around 0.01 mmHg) and a very high potential difference (voltage) is applied between the electrodes.

The low pressure reduces the number of gas molecules, allowing electrons to travel from the cathode to the anode without constant collisions, and the high voltage provides the energy needed to pull electrons from the cathode.

In physics, work is done only when a force causes a displacement in the direction of the force (\( W = Fd \cos \theta \)).
In options A, C (if the table doesn't move), and D, there is a force being applied, but no distance is covered by the object. When a boy climbs onto a table, he exerts a force to move his own mass against gravity over a vertical distance. Therefore, work is done against gravity.

The formula for latent heat is:\[ Q = mL \]Where:
\( Q = 1.13 \times 10^6 \text{ J} \)
\( m = 15 \text{ kg} \)
Solving for \( L \) (Specific Latent Heat):\[ L = \frac{Q}{m} \]\[ L = \frac{1.13 \times 10^6}{15} \]\[ L \approx 75,333.33 \text{ Jkg}^{-1} \]\[ L \approx 7.53 \times 10^4 \text{ Jkg}^{-1} \]

The efficiency (\( \eta \)) of a cell is the ratio of the power delivered to the external circuit (load) to the total power generated. It can be calculated using the resistance values:\[ \eta = \frac{R}{R + r} \times 100\% \]Given:
External resistance \( R = 6 \Omega \)
Internal resistance \( r = 2 \Omega \)
Calculation:\[ \eta = \frac{6}{6 + 2} \times 100\% = \frac{6}{8} \times 100\% = 0.75 \times 100\% = 75\% \]

According to the kinetic molecular theory, molecules in all states of matter (solid, liquid, and gas) are in a state of constant motion. In a liquid, the molecules are close together but have enough energy to slide past one another. They are certainly not stationary. Therefore, statement A is incorrect.