Physics 2022 Jamb Examination

Fundamental units are basic units that are independent of others, such as the Kilogram (mass), Metre (length), and Second (time). A derived unit is one obtained by combining these fundamental units through multiplication or division. The Newton is the SI unit of force, and it is derived from the formula \( F = ma \). In terms of fundamental units, 1 Newton is equal to 1 \( \text{kg} \cdot \text{m/s}^2 \).

Magnetism is a property of the alignment of atomic dipoles within a material. When a bar magnet is cut in half, the alignment of these dipoles is preserved. Consequently, each piece will still have a North pole and a South pole. Instead of having one magnet, you now have two separate, complete magnets. It is impossible to isolate a single magnetic pole (monopole) by cutting a magnet.

The general equation for a progressive wave is given by: \[ y = A \sin(kx - \omega t) \] In this form, \( k \) represents the wave number (also known as the propagation constant). By comparing the given equation \( y = 5\text{mm} \sin(1\text{cm}^{-1}x - 60\text{s}^{-1}t) \) to the general form, we can see that the coefficient of \( x \) is the wave number \( k \). Therefore, \( k = 1.0 \, \text{cm}^{-1} \).

The magnification (\( M \)) of a pinhole camera is the ratio of the image height (\( h_i \)) to the object height (\( h_o \)), which is also equal to the ratio of the image distance (\( v \)) to the object distance (\( u \)). \[ \frac{h_i}{h_o} = \frac{v}{u} \] Given: \( h_o = 40 \, \text{cm} \) \( u = 30 \, \text{cm} \) \( h_i = 20 \, \text{cm} \) \[ \frac{20}{40} = \frac{v}{30} \] \[ 0.5 = \frac{v}{30} \] \[ v = 30 \times 0.5 = 15 \, \text{cm} \] The image is formed 15 cm from the pinhole.

According to Faraday's Law of Electromagnetic Induction, an electromotive force (EMF) and subsequently a current are induced in a conductor only when there is a change in the magnetic flux linkage. This change in flux occurs whenever there is relative motion between the magnet and the solenoid. If the magnet and solenoid are both stationary (no relative motion), the magnetic flux remains constant, no EMF is induced, and the galvanometer pointer remains at zero.

Treads are the patterns of grooves on the surface of a tyre. Their primary purpose is to increase the friction (grip) between the tyre and the road surface, especially in wet or slippery conditions. The grooves allow water to be expelled from beneath the tyre, preventing aquaplaning and ensuring the vehicle can accelerate, brake, and turn effectively.

We can use the equations of linear motion to solve for acceleration (\( a \)). Since the car starts from rest, its initial velocity (\( u \)) is 0. Given: \( u = 0 \) \( s = 40 \, \text{m} \) \( t = 10 \, \text{s} \) Using the formula: \[ s = ut + \frac{1}{2}at^2 \] \[ 40 = (0 \times 10) + \frac{1}{2}a(10)^2 \] \[ 40 = 0 + \frac{1}{2}a(100) \] \[ 40 = 50a \] \[ a = \frac{40}{50} = 0.80 \, \text{ms}^{-2} \] The magnitude of the acceleration is 0.80 ms\(^{-2}\).

For isotropic solids (solids that expand uniformly in all directions), the coefficient of area expansion (\( \beta \)) is approximately twice the linear expansion (\( 2\alpha \)), and the coefficient of volume expansion (\( \gamma \)) is approximately three times the linear expansion (\( 3\alpha \)). This is because volume is a three-dimensional quantity (Length × Width × Height).

The accumulation of hydrogen bubbles on the copper (positive) electrode of a primary cell is known as polarization. This layer of bubbles increases the internal resistance of the cell and produces a back EMF, which reduces the current. Local action, on the other hand, is a different defect caused by impurities in the zinc (negative) electrode, leading to the formation of tiny local cells that waste the zinc. Therefore, local action is not a consequence of hydrogen bubbles on the copper plate.

Lost voltage (also known as the voltage drop across the internal resistance) is the portion of the electromotive force (EMF) that is used to drive the current through the cell's own internal resistance. It is calculated using Ohm's Law: \[ V_{\text{lost}} = I \times r \] Given: \( I = 4 \, \text{A} \) \( r = 0.55 \, \Omega \) \[ V_{\text{lost}} = 4 \times 0.55 = 2.20 \, \text{V} \] The lost voltage of the cell is 2.20 V.