Physics 2016 Jamb Examination

To solve this problem, we apply the Principle of Moments, which states that for a body in equilibrium, the sum of the clockwise moments about a pivot must equal the sum of the anticlockwise moments. Since the ruler is pivoted at its mid-point, we can ignore the weight of the ruler itself as it acts through the pivot and creates no moment.
Let the unknown distance for the 15N force be \(x\).
Anticlockwise moment = Clockwise moment\[ 10\text{N} \times 30\text{cm} = 15\text{N} \times x \]\[ 300 = 15x \]\[ x = \frac{300}{15} \]\[ x = 20\text{cm} \]Therefore, the 15N force must be placed 20cm from the pivot on the opposite side to achieve horizontal balance.

The time taken (\(t\)) for a projectile to reach its maximum height is determined by the vertical component of its initial velocity and the acceleration due to gravity. At maximum height, the vertical velocity becomes zero.
The vertical component of initial velocity (\(u_y\)) is given by:\[ u_y = u \sin \theta \]Using the equation of motion \(v = u + at\), where \(v = 0\), \(a = -g\), and \(u = u \sin \theta\):\[ 0 = u \sin \theta - gt \]\[ gt = u \sin \theta \]\[ t = \frac{u \sin \theta}{g} \]Given:
\(u = 300 \text{ ms}^{-1}\)
\(\theta = 30^{\circ}\)
\(g = 10 \text{ ms}^{-2}\)
Calculation:\[ t = \frac{300 \times \sin 30^{\circ}}{10} \]\[ t = \frac{300 \times 0.5}{10} \]\[ t = \frac{150}{10} \]\[ t = 15\text{s} \]

We use the first equation of linear motion to find the time required to stop the train:\[ v = u + at \]Given:
Initial velocity \(u = 20 \text{ ms}^{-1}\)
Final velocity \(v = 0 \text{ ms}^{-1}\) (since it comes to a complete halt)
Deceleration \(a = -2 \text{ ms}^{-2}\) (acceleration is negative for deceleration)
Substituting the values into the formula:\[ 0 = 20 + (-2)t \]\[ 2t = 20 \]\[ t = \frac{20}{2} \]\[ t = 10\text{s} \]It takes 10 seconds for the train to stop.

The electromagnetic spectrum is classified based on the frequency and wavelength of the radiation.

There is an inverse relationship between frequency and wavelength: waves with the highest energy have the highest frequency and the shortest wavelength. In the spectrum, Gamma rays occupy the high-frequency end, possessing more energy and shorter wavelengths than X-rays, ultraviolet, visible light, infrared, microwaves, and radio waves. Therefore, Gamma rays have the shortest wavelength among the listed options.

The half-life (\(T_{1/2}\)) of a radioactive substance is the time taken for half of the atoms in a sample to decay. It is related to the decay constant (\(\lambda\)) by the following mathematical formula:\[ T_{1/2} = \frac{\ln 2}{\lambda} \]The value of \(\ln 2\) is approximately 0.693.
Given:
\(\lambda = 10^{-6} \text{ s}^{-1}\)
Calculation:\[ T_{1/2} = \frac{0.693}{10^{-6}} \]\[ T_{1/2} = 0.693 \times 10^6 \]\[ T_{1/2} = 6.93 \times 10^5 \text{s} \]

To answer this, we must define the two classifications. A mechanical wave requires a material medium (like water, air, or a string) to travel. A transverse wave is one where the particles of the medium vibrate perpendicular to the direction of the wave's travel. Radio waves and X-rays are electromagnetic waves (non-mechanical). Sound waves are mechanical but longitudinal. Water waves, specifically surface waves, exhibit characteristics where the water particles move in paths that create a transverse pattern on the surface while requiring the water itself as a medium, thus being both transverse and mechanical.

We use the Ideal Gas Equation:\[ PV = nRT \]Given:
\(P = 7.6 \times 10^6 \text{ Nm}^{-2}\)
\(V = 10^{-3} \text{ m}^3\)
\(n = 6 \text{ moles}\)
\(R = 8.3 \text{ Jmol}^{-1}\text{K}^{-1}\)
Solving for temperature (T) in Kelvin:\[ T = \frac{PV}{nR} \]\[ T = \frac{(7.6 \times 10^6) \times 10^{-3}}{6 \times 8.3} \]\[ T = \frac{7600}{49.8} \]\[ T \approx 152.61 \text{K} \]Wait, the calculation gives roughly 153K. To convert to Celsius (\(^{\circ}\text{C}\)):\[ heta = T - 273 \]\[ heta = 152.6 - 273 = -120.4^{\circ}\text{C} \]Looking at the options provided, they appear to be in Celsius but positive. Re-evaluating the calculation: if the result 153 was intended to be the final answer in Kelvin, but the options are marked Celsius, there might be a data discrepancy in the question paper. However, strictly following the physics, 153K is the absolute temperature result.

Relative density (specific gravity) is the ratio of the density of a substance to the density of water. According to Archimedes' principle, the upthrust exerted on a completely submerged object is equal to the weight of the fluid displaced. Therefore, if the same object is submerged in a liquid and then in water, the ratio of the upthrust in the liquid to the upthrust in water is equivalent to the ratio of their densities. Thus, relative density can be expressed as:\[ \text{R.D.} = \frac{\text{Weight of any volume of liquid}}{\text{Weight of an equal volume of water}} \]\[= \frac{\text{Upthrust in liquid}}{\text{Upthrust in water}} \]

The temperature -273.15ºC is known as Absolute Zero (0 Kelvin). According to the kinetic molecular theory, the pressure of a gas is caused by the collisions of gas molecules with the walls of the container. Temperature is a measure of the average kinetic energy of these molecules.

At absolute zero, theoretically, all molecular motion ceases. If the molecules are not moving, they cannot collide with the container walls, and therefore the pressure of the gas drops to zero. This is reflected in Gay-Lussac's Law (\(P \propto T\)), where pressure is directly proportional to the absolute temperature.

The electric bell, moving coil galvanometer, and telephone receiver all rely on electromagnetism—the magnetic effect produced by an electric current—to create mechanical motion or sound. In contrast, a lead-acid accumulator (a type of battery) operates on the chemical effect of electric current. It involves chemical reactions (electrolysis) to store and release electrical energy. Therefore, it does not utilize magnetic effects for its primary function.