Physics 2024 Jamb Examination

Stress is defined as the force applied per unit cross-sectional area.
 First, find the radius (\( r \)) of the wire:\[ r = \frac{\text{diameter}}{2} = \frac{y}{2\pi} \] Calculate the cross-sectional area (\( A \)):\[ A = \pi r^2 = \pi \left(\frac{y}{2\pi}\right)^2 = \pi \left(\frac{y^2}{4\pi^2}\right) = \frac{y^2}{4\pi} \] Calculate the stress (\( \sigma \)) using \( \text{Stress} = \frac{\text{Force}}{\text{Area}} \):\[ \sigma = \frac{y^2}{\frac{y^2}{4\pi}} \]\[ \sigma = y^2 \cdot \frac{4\pi}{y^2} = 4\pi \, \text{Nm}^{-2} \]

In physics, work is done only when a force causes a displacement in the direction of the force (\( W = Fs \cos \theta \)). [Image showing work done versus no work done]
In options A, B, and D, there is no displacement (the load, pot, and tanker remain stationary), so the work done is zero. When a boy climbs onto a table, he exerts a force to move his body weight through a vertical distance (height), fulfilling the requirement for work to be done against gravity.

Mechanical advantage of a machine = $\frac{\text{LOAD}}{\text{EFFORT}}$
In this case of a wedge, we can consider the dimensions given:
Load distance (height of the machine): 15cm
 Effort distance (movement of the effort): 0.5cm\[ \text{M.A.} = \frac{15}{0.5} = 30.0 \]

The formation of a rainbow is primarily due to the dispersion of sunlight.
When sunlight enters a raindrop, it is refracted, then undergoes total internal reflection at the back of the drop, and is refracted again as it leaves. During these refractions, the white light is separated into its component colours (ROYGBIV) because different wavelengths refract at slightly different angles. Dispersion is the specific term for this separation of white light into a spectrum.

Capacitance (\( C \)) is defined as the amount of charge (\( Q \)) stored per unit potential difference (\( V \)).
The formula is:\[ C = \frac{Q}{V} \]Given:
Charge \( Q = 30 \, \text{C} \)
Voltage \( V = 5 \, \text{V} \)
\[ C = \frac{30}{5} = 6 \, \text{F} \]The capacitance is 6 Farads.

Acceleration is defined as the rate of change of velocity with respect to time. Since velocity is a vector quantity (having both magnitude and direction), an object accelerates if its speed changes, its direction changes, or both change. While changing speed (A) or direction (D) are forms of acceleration, the most complete and technically accurate description is that the velocity is changing. Position (C) changes whenever an object is in motion, regardless of whether it is accelerating or moving at a constant velocity.

Air resistance, or drag, is a type of friction that occurs when an object moves through the atmosphere. To reduce this, objects are designed with a smooth, contoured shape known as 'streamlining'. Streamlining allows the air to flow smoothly around the object (laminar flow) rather than creating turbulent eddies that pull back on the object. Lubrication and polishing are used to reduce friction between solid surfaces, not air mass.

A dynamo (specifically a generator) works on the principle of electromagnetic induction, which is closely linked to the magnetic effect of electric current. It converts mechanical energy into electrical energy by rotating a conductor within a magnetic field. An electric heater uses the heating effect (Joule heating), and a photocell uses the photoelectric effect. While 'Dynamo' is the best fit among these options for magnetic interactions, many instruments like electric bells or galvanometers are more direct examples of the magnetic effect of current.

In electrostatics, an ebonite rod rubbed with fur acquires a negative charge, whereas a glass rod rubbed with silk acquires a positive charge. Since the rods have opposite types of charges (positive and negative), they will exert an attractive force on each other according to the law that unlike charges attract.

An aneroid barometer does not contain liquid (unlike a mercury barometer), making it compact, portable, and non-spillable. These qualities make it 'small and convenient' for use in the cockpit of an aircraft as an altimeter. Since atmospheric pressure decreases predictably with altitude, the barometer can be calibrated to show height above sea level.