JAMB UTME - Physics - 2023

Bayanin Amsa

The pinhole camera works on the principle of the rectilinear propagation of light. This principle states that light travels in straight lines. When light passes through the tiny hole in a pinhole camera, it forms an inverted image on the opposite side of the camera. The size of the image depends on the distance between the object and the pinhole.

Bayanin Amsa

Bayanin Amsa

The number of holes in an intrinsic semiconductor is equal to the number of free electrons.

In an intrinsic semiconductor, the valence band is completely filled with electrons. However, due to thermal energy, some of these electrons can gain enough energy to jump to the conduction band, leaving behind holes in the valence band.

For every electron that moves to the conduction band, a hole is created in the valence band. Since the number of electrons and holes is equal, the number of holes in an intrinsic semiconductor is equal to the number of free electrons.

Therefore, the correct option is: is equal to the number of free electrons.

Bayanin Amsa

W = 400 N; P = 100 N; θ = 30o; μ = ?

Frictional force (Fr) = μR (where R is the normal reaction)

The forces acting along the horizontal direction are Fr and Px

∴ Pcos 30° - Fr = ma (Pcos 30° is acting in the +ve x-axis while Fr in the -ve x-axis)

⇒ 100cos 30° - μR = ma

Since the box is moving at constant speed, its acceleration is zero

⇒ 100cos 30° - μR = 0

⇒ 100cos 30o = μR ----- (i)

The forces acting in the vertical direction are W, Py and R

∴ R - Psin 30° - W = 0 (R is acting upward (+ve) while Py and W are acting downward (-ve) and they are at equilibrium)

⇒ R - 100sin 30° - 400 = 0

⇒ R = 100sin 30° + 400

⇒ R = 50 + 400 = 450 N

From equation (i)

⇒ 100cos 30° = 450μ

⇒μ=100cos30°

  N = 100cos30°450 $\frac{\mathrm{<br>}}{}$

        = μ = 0.19

Bayanin Amsa

Bayanin Amsa

Bayanin Amsa

To find the effort E required to lift the load, we first need to understand the concept of mechanical efficiency in levers.
A lever is a simple machine that consists of a rigid beam (lever arm) that pivots around a fixed point called the fulcrum. In this case, the fulcrum is point P.
The mechanical efficiency of a lever is defined as the ratio of the output work done (load lifted) to the input work done (effort applied). Mathematically, it can be expressed as:
Efficiency = (Output Work / Input Work) * 100%
In this problem, the load is the output work and the effort is the input work.
Given: Load = 200 kg Length of lever (distance between fulcrum and load) = 10 m Efficiency = 80% Gravitational acceleration (g) = 10 m/s^2
To calculate the effort, let's first calculate the output work:
Output Work = Load * Distance lifted
The distance lifted is equal to the length of the lever arm, which is 10 m.
Output Work = 200 kg * 10 m = 2000 kg·m
Since 1 kg·m is equivalent to 10 J (1 Joule), we can convert the units:
Output Work = 2000 kg·m * 10 J/kg·m = 20000 J
Now, let's calculate the input work:
Input Work = Effort * Distance moved by the effort
The distance moved by the effort is the length of the lever arm, which is 110 m.
Input Work = Effort * 110 m
Using the formula for mechanical efficiency, we can rewrite it as:
Efficiency = (Output Work / Input Work) * 100%
Solving for the effort:
Effort = (Output Work / (Efficiency/100)) / Distance moved by the effort
Effort = (20000 J / (80/100)) / 110 m
Simplifying the equation:
Effort = (20000 J / 0.8) / 110 m
Effort = 250 J / m
Given that g = 10 m/s^2, we know that 1 N = 1 kg·m/s^2. Therefore, we can convert the units:
Effort = (250 J / m) / (1 kg·m/s^2 / 1 N)
Effort = 250 N
Therefore, the effort E required to lift the load is 250 N.

Bayanin Amsa

The correct statement about the angle of dip at various points on Earth is: The angle of dip is zero at the equator and 90 degrees at the magnetic poles.
The angle of dip, also known as the inclination, refers to the angle between the Earth's magnetic field lines and the horizontal plane at a specific location. It tells us how much the magnetic field lines of the Earth are inclined or tilted at that point.
At the equator, the angle of dip is zero. This means that the magnetic field lines are parallel to the horizontal plane. As we move closer to the magnetic poles, the angle of dip increases. At the magnetic poles, the angle of dip is 90 degrees, indicating that the magnetic field lines are perpendicular to the horizontal plane.
The second statement that the angle of dip is greater at higher altitudes than at lower altitudes is incorrect. The angle of dip is primarily affected by the latitude or distance from the equator and the proximity to the magnetic poles, rather than the altitude. So, the angle of dip remains consistent at a specific latitude regardless of the altitude above sea level.
The third statement that the angle of dip is positive in the northern hemisphere and negative in the southern hemisphere is also incorrect. The angle of dip is positive in the northern hemisphere and negative in the southern hemisphere. This means that the magnetic field lines are inclined downwards in the northern hemisphere and upwards in the southern hemisphere.
The fourth statement that the angle of dip is constant at all points on Earth is incorrect as well. The angle of dip varies depending on the latitude and the proximity to the magnetic poles, as explained earlier. So, it is not constant across all points on Earth.
To summarize, the correct statement is that the angle of dip is zero at the equator and 90 degrees at the magnetic poles. It is important to note that the angle of dip is not affected by altitude but is primarily determined by latitude and proximity to the magnetic poles.

Bayanin Amsa

A wave that is both mechanical and longitudinal is sound waves.

Sound waves are created by the vibration of an object, such as a speaker, which causes the air particles around it to vibrate. These vibrations then travel through the air in the form of a wave.

Sound waves are classified as mechanical waves because they require a medium, such as air, water, or solid objects, to travel through. Without a medium, sound waves cannot propagate.

Furthermore, sound waves are classified as longitudinal waves because the particles in the medium vibrate parallel to the direction of the wave. This means that as the sound wave travels, the particles in the medium move back and forth in the same direction as the wave itself.

In contrast, water waves and seismic waves are mechanical waves, but they are not longitudinal. Water waves are categorized as transverse waves because the particles in the water move up and down at right angles to the direction of the wave. Seismic waves, which include earthquake waves, can be both transverse and longitudinal, but typically the primary seismic waves are classified as transverse waves.

Lastly, light waves are not mechanical waves but rather electromagnetic waves. They do not require a medium to travel through and can propagate in a vacuum, unlike sound waves.

Bayanin Amsa

To determine the type of equilibrium for each position of the ball, we need to understand what each type of equilibrium means. 1. **Unstable equilibrium**: This occurs when a small disturbance or change in the system causes the object to move away from its equilibrium position. In other words, the system is "unstable" and will not return to its original position on its own. 2. **Neutral equilibrium**: This occurs when a small disturbance or change in the system does not cause the object to move away from its equilibrium position. The system remains in its new position without any tendency to return to its original position. 3. **Stable equilibrium**: This occurs when a small disturbance or change in the system causes the object to move away from its equilibrium position, but the system has a tendency to return to its original position on its own. Now, let's analyze each position of the ball: A - **Unstable equilibrium**: Suppose the ball is placed at position A. If the ball is slightly disturbed or moved from this position, it will roll away further from its original position and won't come back on its own. Hence, position A is an unstable equilibrium. B - **Stable equilibrium**: Suppose the ball is placed at position B. If the ball is slightly disturbed or moved from this position, it will oscillate back and forth but eventually come back to its original position. This indicates that position B is a stable equilibrium. C - **Neutral equilibrium**: Suppose the ball is placed at position C. If the ball is slightly disturbed or moved from this position, it will stay at the new position without any tendency to return to its original position. This identifies position C as a neutral equilibrium. Based on the explanations above, the correct answer is: A - unstable, B - stable, C - neutral.

Bayanin Amsa

An AC generator uses slip rings to transfer the induced current smoothly to the circuit. A DC generator uses split rings to transfer the induced current to the circuit and also convert the induced AC into pulsating DC. So, to convert an AC generator into a DC generator, the slip rings needs to be replaced with split rings.

Bayanin Amsa

In an AC circuit, resonance occurs when the impedance of the circuit is minimum.

Impedance is the total opposition to the flow of alternating current in a circuit, and it consists of two components: resistance (R) and reactance (X).

Reactance can be further divided into two types: inductive reactance (XL) and capacitive reactance (XC).

At resonance, the inductive reactance and the capacitive reactance are equal in magnitude and opposite in sign. This means that their effects cancel each other out, resulting in a minimum total reactance.

Since impedance is the combination of resistance and reactance, when the reactance is at its minimum, the impedance of the circuit is also at its minimum.

So, in summary, resonance occurs in an AC circuit when the impedance is minimum. At resonance, the inductive reactance and the capacitive reactance cancel each other out, resulting in a minimum total reactance and minimum impedance.

Bayanin Amsa

Bayanin Amsa

To calculate the force acting on the charge in an electric field, we can use the formula: F = q * E Where: F is the force acting on the charge, q is the charge of the particle, and E is the electric field intensity. In this case, the charge is given as 4.6 × 10^(-5) C and the electric field intensity is given as 3.2 × 10^4 V/m. Substituting these values into the formula: F = (4.6 × 10^(-5) C) * (3.2 × 10^4 V/m) To multiply numbers in scientific notation, we multiply the coefficients and add the exponents: F = (4.6 * 3.2) * (10^(-5 + 4)) C * V/m F = 14.72 * 10^(-1) C * V/m To simplify, we can convert the result to standard form: F = 1.472 C * V/m Therefore, the force acting on the charge is **1.472 N**.

Bayanin Amsa

T=800N; I=50cm=0.5m,

m=10g=0.01kg

fundamental freq: fo ${\mathrm{<br>}}_{}$ =?

fo ${\mathrm{<br>}}_{}$ = 121√Tμ $\frac{1}{21}<br>$

μ =m1 $\frac{\mathrm{<br>}}{}$=0.010.5 $\frac{0.01}{0.5}$

⇒ fo ${\mathrm{<br>}}_{}$ =12×0.5 $\frac{1}{2\times 0.5}$√8000.02 $\frac{800}{0.02}$

                  fo ${\mathrm{<br>}}_{}$  ⇒√ 40,000

⇒1st overtone = 2fo ${\mathrm{<br>}}_{}$ =2×200 = 400Hz

⇒2nd overtone =3fo ${\mathrm{<br>}}_{}$ =3×200=600Hz

∴3rd over tone= 4fo ${\mathrm{<br>}}_{}$  =4×200=800Hz

Bayanin Amsa

Bayanin Amsa

As light ray enters a drop of water the light is refracted at the surface and at the end of the drop, it is totally internally reflected in which the reflected light returns to the front surface, where it again undergoes refraction as it moves from water to air. The result of this is a dispersed light of colours of different wavelengths.

Bayanin Amsa

Bayanin Amsa

Bayanin Amsa

The working of the beam balance is based on the principle of moments.

Moments, also known as torques, are a measure of the turning effect of a force. In the case of the beam balance, it is the moments that help determine the equilibrium or balance of the system.

The beam balance consists of a beam or lever that is supported at a pivot point called the fulcrum. On either end of the beam, there are pans where the objects to be weighed are placed.

When objects of different weights are placed on the pans, the beam becomes unbalanced. This causes the beam to tilt towards the side with the heavier object. However, in order to achieve equilibrium or balance, the moments on both sides of the beam must be equal.

The moment of a force is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of rotation (the fulcrum) to the line of action of the force.

By adjusting the position of the counterweights or by moving the objects on the pans, the moment on each side of the beam can be balanced, resulting in the beam becoming level or horizontal. This indicates that the weights on both sides are equal.

Therefore, the beam balance operates on the principle of moments, where the balance is achieved by equalizing the moments on both sides of the fulcrum.

Bayanin Amsa

To calculate the relative humidity, we need to understand the concept of saturation and how much water vapor the air can hold at a given temperature.
Saturation is the point at which the air is holding the maximum amount of water vapor it can hold at a particular temperature. Once the air reaches saturation, any additional moisture will start to condense into liquid water.
The amount of water vapor that the air can hold increases with temperature. Warmer air can hold more water vapor, while cooler air can hold less.
Now, let's calculate the relative humidity using the given information:
1. Find the saturation vapor pressure at 40°C: - The saturation vapor pressure is the maximum amount of water vapor the air can hold at a specific temperature. - At 40°C, the saturation vapor pressure is approximately 55.3 mmHg.
2. Calculate the relative humidity: - Relative humidity is the ratio of the current partial pressure of water vapor to the saturation vapor pressure, expressed as a percentage. - Relative Humidity = (Partial pressure of water vapor / Saturation vapor pressure) * 100 - In this case, the partial pressure of water vapor is 38.8 mmHg and the saturation vapor pressure at 40°C is 55.3 mmHg. - Plugging in these values into the formula, we get: Relative Humidity = (38.8 mmHg / 55.3 mmHg) * 100 = 70.2%
Therefore, the relative humidity on this particular hot day is approximately 70%.
Answer: The correct option is 70.

Bayanin Amsa

Instrument resolution is not a limitation of experimental measurements. It is the smallest change in a measured quantity that can be detected by an instrument. While instrument resolution limits the accuracy of a measurement, it is not a limitation of experimental measurements itself.

Bayanin Amsa

When a negatively charged rod is brought close to a metal sphere, the free electrons in the sphere are repelled from the rod and move to the other end of the sphere. This creates a region of positive charge on the side of the sphere closest to the rod, and a region of negative charge on the opposite side. The process of charge distribution stops when the net force on the free electrons inside the metal is equal to zero.

If the sphere is then earthed, the free electrons will flow from the sphere to the ground, leaving the sphere with a net positive charge.

Bayanin Amsa

Bayanin Amsa

The polarities at X and Y would be north and north.

Bayanin Amsa

The electrolyte used in the Nickel-Iron (NiFe) accumulator is **potassium hydroxide solution**.

In a Nickel-Iron accumulator, the electrolyte is the substance that allows the flow of electric current between the electrodes. It is essential for the proper functioning of the accumulator.

Potassium hydroxide solution is the ideal electrolyte for the NiFe accumulator due to its properties. It has good electrical conductivity, which means it allows the movement of ions between the positive and negative electrodes, enabling the flow of electrons and facilitating the charging and discharging process.

In addition to good conductivity, potassium hydroxide solution also has other beneficial properties for the NiFe accumulator. It is stable, ensuring a longer lifespan for the accumulator. It is also less prone to self-discharge, meaning the accumulator can retain its charge for a longer period without significant loss.

Therefore, the electrolyte used in the Nickel-Iron (NiFe) accumulator is potassium hydroxide solution.

Bayanin Amsa

Bayanin Amsa

A couple is a pair of forces that are equal in magnitude but opposite in direction, and that are applied to a body at different points. The forces of a couple do not produce any translation, but they do produce a rotation.

Bayanin Amsa

The penetrating power of alpha rays, beta rays, and gamma rays varies greatly. Alpha particles can be blocked by a few pieces of paper. Beta particles pass through paper but are stopped by aluminum foil. Gamma rays are the most difficult to stop and require concrete, lead, or other heavy shielding to block them.

Therefore, X = γ-ray; Y = α-particle; Z = β-particle

Bayanin Amsa

Bayanin Amsa

Night vision goggles use infrared waves to enable the user to see in the dark.

Infrared waves are a type of electromagnetic radiation that have longer wavelengths than visible light. They fall between the visible and microwave regions on the electromagnetic spectrum. Unlike visible light, which is visible to the human eye, infrared waves cannot be seen without the use of specialized devices such as night vision goggles.

When it is dark, objects do not emit visible light that can be detected by the human eye. However, they do emit heat in the form of infrared radiation. Night vision goggles work by detecting and amplifying this infrared radiation, which is then converted into visible light that can be seen by the user.

The goggles contain an image intensifier tube that is sensitive to infrared radiation. This tube amplifies the incoming infrared light and converts it into an image that can be seen through the goggles. The resulting image appears green because the human eye is more sensitive to green light.

Therefore, to see in the dark, night vision goggles use infrared waves to detect and amplify the infrared radiation emitted by objects. This enables the user to have enhanced vision in low-light conditions or complete darkness.

Bayanin Amsa

To determine the number of turns on the primary winding of a step-down transformer, we need to understand how a transformer works and how the voltage is transformed from the primary to the secondary winding.

A transformer operates on the principle of electromagnetic induction. When an alternating current flows through the primary winding, it creates a changing magnetic field that induces a voltage in the secondary winding.

The voltage ratio between the primary and secondary windings is determined by the ratio of the number of turns in each winding. This means that if we decrease the number of turns in the secondary winding compared to the primary winding, we can reduce the voltage output.

In this case, we are given that the secondary winding has 25 turns and we want to deliver 110 V. The primary winding has a higher voltage, which is 2.2 kV (kilovolts) or 2200 V.

To determine the number of turns on the primary winding, we can set up a simple equation using the voltage ratios:

Primary voltage / Secondary voltage = Primary winding turns / Secondary winding turns

Plugging in the values we have:

2200 V / 110 V = Primary winding turns / 25 turns

Simplifying the equation:

20 = Primary winding turns / 25

To solve for the number of turns on the primary winding, we can cross multiply:

20 x 25 = Primary winding turns

Therefore, the number of turns on the primary winding is 500.

So, the correct answer is 500.

Bayanin Amsa

Electrical conduction of gas is applied in:
(i) The identification of gases
(ii) Lighting/fluorescent tubes
(iii) Advertising industry/Neon signs
(iv) Cathode ray oscilloscope/T.V. tubes

Bayanin Amsa

The Tungsten filament lamp is a type of incandescent light source.

An incandescent light source works by using electricity to heat a filament inside the bulb until it becomes so hot that it emits light. In a tungsten filament lamp, the filament is made of tungsten, which is a metal that has a very high melting point. This allows the filament to get extremely hot without melting.

When an electric current passes through the filament, it heats up and starts to glow, producing visible light. The light emitted by a tungsten filament lamp is actually a result of the high temperature, which causes the atoms in the filament to vibrate and release energy in the form of light.

Incandescent light sources like tungsten filament lamps have been widely used for many years because they produce a warm, yellowish light that is similar to natural sunlight. However, they are not very energy-efficient, as a significant amount of the electrical energy is converted into heat rather than light.

In recent years, there has been a shift towards more energy-efficient alternatives like LED lamps and fluorescent lamps. LED lamps use a different mechanism to produce light, using a semiconductor that emits light when electric current passes through it. Fluorescent lamps use a gas-filled tube that emits ultraviolet light when electric current flows through it, and this ultraviolet light is then converted into visible light by a phosphor coating inside the tube.

So, in summary, the tungsten filament lamp is the type of incandescent light source among the options given. It works by heating a tungsten filament to a very high temperature, causing it to emit light. However, it is less energy-efficient compared to LED and fluorescent lamps.

Bayanin Amsa

Bayanin Amsa

The correct answer is The electric force is directed from the positive particle to the negative particle.

When a positively charged particle is placed near a negatively charged particle, they exert an attractive force on each other. This force is called the electric force.

According to Coulomb's Law, the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In this case, the positively charged particle has a positive charge and the negatively charged particle has a negative charge. Since opposite charges attract each other, the electric force between them is attractive.

Therefore, the electric force is directed from the positive particle to the negative particle.

Bayanin Amsa

When light of a certain frequency is incident on a metal surface, no photoelectrons are emitted. This is because the energy of the photons in the light is not enough to overcome the work function of the metal, which is the minimum amount of energy required to remove an electron from the metal surface.
If the frequency of the light is increased, it means that the energy of the photons increases. This increase in energy means that there is now enough energy to overcome the work function of the metal. As a result, photoelectrons are now emitted from the metal surface.
Now, let's consider the stopping potential. The stopping potential is the minimum potential difference that needs to be applied across a pair of electrodes in order to stop the flow of photoelectrons from reaching the other electrode.
When the frequency of the light is increased, the energy of the photons also increases. This means that the photoelectrons have more kinetic energy when they are emitted from the metal surface. As a result, a higher stopping potential is required to stop the more energetic photoelectrons from reaching the other electrode.
Therefore, the stopping potential increases when the frequency of the light is increased.

Bayanin Amsa

A good insulator is a material that does not easily allow heat or electricity to pass through it. It acts as a barrier, preventing the flow of heat or electricity. Out of the given options, rubber is a good insulator.

Rubber is made up of long chains of molecules that are closely packed together. These chains do not allow the easy movement of heat or electricity. This means that when heat or electricity tries to pass through rubber, it encounters resistance, making it difficult for it to flow.

In contrast, materials like silver, water, and copper are good conductors rather than insulators.

Silver is an excellent conductor of electricity and heat because its atoms have loosely bound electrons that are free to move. This allows for the easy transfer of heat or electricity throughout the material.

Water is also a good conductor of both heat and electricity. It contains charged particles called ions that can carry electric current. Additionally, water molecules are able to transfer heat through convection.

Copper is widely used in electrical wiring because it is an excellent conductor of electricity. Like silver, its atoms have free electrons that can move easily and transfer electrical energy.

Therefore, rubber is the material that serves as a good insulator, while silver, water, and copper are good conductors of heat and electricity.

Bayanin Amsa

The frequency of a sound wave is proportional to the tension of the string. If two instruments have the same frequency, but one has a tighter string, then the instrument with the tighter string will have a higher pitch.

The other factors listed, such as the size of the instrument, the material of the instrument, and the shape of the instrument, will also affect the pitch of the instrument, but they will have a smaller effect than the tension of the string.

Bayanin Amsa

For the combination in series;

⇒R1 = 35kΩ + 40kΩ = 75kΩ

R is combined with 75kΩ in parallel to give 25kΩ

=  1Req $\frac{\mathrm{<br>}}{}$ = 1R $\frac{\mathrm{<br>}}{}$ + 1R $\frac{\mathrm{<br>}}{}$ 

=   125 $\frac{\mathrm{<br>}}{}$     = 1R $\frac{\mathrm{<br>}}{}$ + 175 $\frac{\mathrm{<br>}}{}$ 

=  125 $\frac{\mathrm{<br>}}{}$     - 175 $\frac{\mathrm{<br>}}{}$ + 1R $\frac{\mathrm{<br>}}{}$ 

=   3−175 $\frac{\mathrm{<br>}}{}$ = 1R $\frac{\mathrm{<br>}}{}$ 

=   275 $\frac{\mathrm{<br>}}{}$   = 1R $\frac{\mathrm{<br>}}{}$ 

=   752 $\frac{\mathrm{<br>}}{}$  = R

;      R = 37.5k Ω