JAMB UTME - Physics - 2022

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The equation that establishes a relationship between the amount left undecayed, 

A, the initial amount, A0, and the number of half-lives that pass in a period of time t looks like this:

12n∗A0=A $\frac{\mathrm{<br>}}{}<br>$

12n∗120=15 $<br>$

12n $\frac{\mathrm{<br>}}{}$ = 15120 $\frac{\mathrm{<br>}}{}$

12n $\frac{\mathrm{<br>}}{}$ = 18 $\frac{\mathrm{<br>}}{}$

12n = 123 $\frac{\mathrm{<br>}}{}$

2n=23 ${\mathrm{<br>}}^{}<br>$

n = 3
:6days ÷ 3 = 2days

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The concentration of charge on the outside of a pear-shaped conductor is highest at the pointy end of the pear shape, which we will label as "X". This is because charges on a conductor will always distribute themselves as far away from each other as possible, in order to minimize their electrostatic potential energy. In the case of a pear-shaped conductor, the charges will distribute themselves so that they are as far away from each other as possible, while still remaining on the surface of the conductor. At point X, the curvature of the surface of the conductor is greatest, which means that the charges on the surface will be more tightly packed together than they would be at any other point on the surface. This results in a higher concentration of charge at point X compared to points Z, Y, and K. Therefore, the concentration of charge on the outside of a pear-shaped conductor is highest at point X.

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The lost voltage of the cell can be calculated using Ohm's Law, which states that voltage (V) is equal to the current (I) multiplied by the resistance (R) of the circuit, plus the voltage lost within the internal resistance (r) of the cell. So, we can use the formula V = IR + Ir to find the lost voltage of the cell, where I is the current (4 A), R is the external resistance (unknown), and r is the internal resistance of the cell (0.55 Ω). Rearranging the formula, we get V - IR = Ir. Substituting the values we know, we get: V - (4 A x R) = 4 A x 0.55 Ω Simplifying this equation, we get: V - 4R = 2.2 V So, the lost voltage of the cell is 2.2 volts. Therefore, the correct option is 2.20 V.

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The coefficient of friction is a number that represents the resistance to motion between two objects in contact. It is determined by the properties of the surfaces in contact and the force pressing them together. When an object just begins to slide on a surface inclined at 30º to the horizontal, the coefficient of friction can be calculated using the formula: friction = μ * normal force where μ is the coefficient of friction and normal force is the force perpendicular to the surface. In this case, the normal force is equal to the weight of the object, which is given by the formula: normal force = object weight * cos(30º) Combining these two formulas, we can calculate the coefficient of friction: friction = μ * object weight * cos(30º) Since the object is just beginning to slide, the friction force is equal to the force needed to start the slide, which is the gravitational force acting on the object down the incline. Therefore, we can set these two equal: friction = object weight * sin(30º) Solving for μ, we get: μ = friction / (object weight * cos(30º)) = sin(30º) / cos(30º) = 1/√3 So, the coefficient of friction for an object just beginning to slide on a surface inclined at 30º to the horizontal is 1/√3.

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Examples of scalar quantities are mass, energy, distance, charge, volume, time, speed, and the magnitude of physical vectors in general.

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The galvanometer is an instrument used to measure the current flowing in a circuit. When current flows through the solenoid, it creates a magnetic field around it. When a bar magnet is placed near the solenoid, the magnetic field of the magnet interacts with the magnetic field of the solenoid. The interaction between these magnetic fields can cause a current to flow through the solenoid and hence through the galvanometer. The direction and strength of the current flowing through the galvanometer depends on the relative motion between the magnet and the solenoid. In the given options, when the magnet is moved towards the stationary solenoid or when the solenoid is moved away from the stationary magnet, there will be a change in the relative motion between the two, and hence a current will flow through the galvanometer. However, when there is no relative motion between the magnet and the solenoid, the interaction between their magnetic fields remains constant and there will be no induced current flowing through the solenoid or the galvanometer. Therefore, the pointer of the galvanometer shows no deflection when there is no relative motion between the magnet and the solenoid. So, the correct option is "there is no relative motion."

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The graph of pressure (P) against the reciprocal of the volume (1/V) in Boyle's law is a straight line. Boyle's law states that at a constant temperature, the pressure of a gas is inversely proportional to its volume. This means that as the volume of a gas increases, its pressure decreases, and as the volume decreases, its pressure increases. When you plot these values on a graph, you will get a straight line, with pressure on the y-axis and 1/V on the x-axis. The slope of the line will be negative, indicating the inverse relationship between pressure and volume.

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A semiconductor is a type of material that can conduct electricity, but not as well as a metal. It is formed by covalent bonds, which are strong bonds between atoms that involve the sharing of electrons. In a semiconductor, the covalent bonds between the atoms are neither too strong nor too weak. This means that when energy is added to the material, some of the electrons can become "excited" and move around more freely. This makes the material conductive, but not as conductive as a metal where the electrons can move very freely. Semiconductors are used in a variety of electronic devices, such as transistors and diodes, and are essential components in the modern electronics industry.

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Secondary pigments are pigments that contribute to the color of an object or substance but are not essential for its function or survival. The answer to the question is magenta, yellow, and cyan. These three colors are called subtractive primary colors because when combined in equal amounts, they can create all other colors. Magenta is a reddish-purple color, yellow is a bright and warm color, and cyan is a blue-green color. When combined, magenta and yellow make red, magenta and cyan make blue, and yellow and cyan make green. These three colors are commonly used in printing and color reproduction, where they are mixed together to create a wide range of colors. In contrast, the primary colors of light are red, green, and blue, which are called additive primary colors because when combined, they produce white light. The secondary colors of light are cyan, magenta, and yellow, which are produced by combining two of the additive primary colors. So, to summarize, the secondary pigments consist of magenta, yellow, and cyan, which can be combined to create a wide range of colors.

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A helioscope is an instrument used for observing the sun and sunspots.

The helioscope was first used by Benedetto Castelli and refined by Galileo Galilei.

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The mercury column in the barometer at notational atmospheric pressure has a height of 76 cm at sea level. This means that the height of the column of mercury in a barometer, which is a device used to measure atmospheric pressure, is 76 cm when the barometer is placed at sea level and the atmospheric pressure is at its standard value. So, the correct answer is: "76 cm at sea level."

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Fiber optic couplers are used to split the input signals into two or more outputs, they are called splitters in this case.

On the other hand, some types of couplers can be used to combine two or more inputs into one single output, they are called combiners in this case.

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Water is not a good thermometric liquid because it expands unevenly between 0 ºC and 4 ºC. This means that its volume changes at a different rate for different temperature changes within this range. This makes it difficult to accurately measure temperature changes using water as the thermometric liquid. In contrast, good thermometric liquids have a more uniform expansion rate over a range of temperatures, making it easier to accurately measure temperature changes.

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The energy dispatched by an electrical device is given by the product of the power consumed by the device and the time it is operating. In this case, the device is a resistor, and its power consumption can be calculated using Ohm's Law, which states that the power (P) consumed by a resistor is equal to the product of its resistance (R) and the square of the current (I) passing through it: P = I^2 * R. The resistance of the resistor is not given, but we can calculate it using the information given in the problem. Ohm's Law can also be rearranged to find the resistance of a resistor: R = V / I, where V is the voltage applied across the resistor. In this case, the voltage is given as 40 V and the current is 0.5 A, so the resistance of the resistor is R = 40 V / 0.5 A = 80 Ω. Now that we know the resistance of the resistor, we can use Ohm's Law to find its power consumption: P = I^2 * R = 0.5 A^2 * 80 Ω = 20 W. The problem asks for the energy dispatched in 2 minutes. To find this, we need to convert the time from minutes to seconds, since power is measured in watts, which are joules per second. 2 minutes is equal to 120 seconds. The energy dispatched is the product of the power consumption and the time: E = P * t = 20 W * 120 s = 2400 J. Therefore, the answer is: 2400 J.

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The amount of energy required to change a kilogram of ice block into water without a change in temperature is called the "specific latent heat of fusion of ice." Specific latent heat is the amount of energy required per unit mass to change the state of a substance without a change in temperature. In the case of ice, it takes a specific amount of energy to melt a kilogram of ice at 0 degrees Celsius into water at the same temperature without raising the temperature of the water. This energy is known as the specific latent heat of fusion of ice. The specific heat capacity of ice, on the other hand, is the amount of energy required to raise the temperature of a unit mass of ice by one degree Celsius. Heat capacity, on the other hand, is the amount of energy required to raise the temperature of a substance by one degree Celsius, regardless of its mass. The specific heat of vaporization of ice, on the other hand, is the amount of energy required per unit mass to change the state of a substance from a liquid to a gas at a constant temperature. Therefore, to change a kilogram of ice block into water without a change in temperature, we need to use the specific latent heat of fusion of ice.

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Examples of first class levers are pliers, scissors, a crow bar, a claw hammer, a see-saw and a weighing balance.

A wheelbarrow, a bottle opener, and an oar are examples of second class levers

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When a bar magnet is divided into two pieces, two new magnets are created. The magnetic field of each separate piece will be weaker than the original bar magnet, but not necessarily weaker than each other. The magnetic field of a bar magnet depends on several factors, including the size and shape of the magnet, and the magnetic material it is made of. When a bar magnet is divided into two smaller pieces, each piece will have a smaller magnetic field than the original bar magnet. There is no electric field created as a result of dividing a bar magnet into two pieces.

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The pressure at a depth "h" in a liquid of density "ρ" can be calculated using the formula: P = ρ * g * h where "g" is the acceleration due to gravity (9.8 m/s^2). So, we can rearrange the formula to find the depth "h" at which the pressure will be 9100 N/m^2: h = P / (ρ * g) Plugging in the given values, we get: h = 9100 N/m^2 / (2000 kg/m^3 * 9.8 m/s^2) = 0.455 m So, the pressure in the liquid will be equal to 9100 N/m^2 at a depth of 0.455 m.

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The main factor that affects the speed of sound waves is the properties of the medium. The speed of sound is a measure of how fast sound waves travel through a particular medium, such as air, water, or solid objects. The speed of sound in air, for example, is approximately 343 meters per second at room temperature and normal atmospheric pressure. The properties of the medium affect the speed of sound waves because sound waves travel by compressing and expanding the particles in the medium through which they are propagating. The speed of sound waves is determined by the density, compressibility, and temperature of the medium. In general, sound waves travel faster through denser and less compressible media, and at higher temperatures. Therefore, the correct answer to the question is "properties of the medium." The amplitude, intensity, and loudness of the sound wave do not directly affect the speed of sound, although they can influence the perception of the sound by the human ear. Amplitude is a measure of the maximum displacement of the particles in the medium, intensity is a measure of the power of the sound wave per unit area, and loudness is a subjective measure of how loud the sound is perceived to be by an observer.

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A magnet relay is a device used for controlling another circuit carrying a larger current. It works by using a small current to switch on or off a larger current in another circuit. This is done by using an electromagnet to move a switch or contact, which then controls the flow of current in the larger circuit. Magnet relays are commonly used in electrical systems to control motors, lights, and other devices, and are an important part of automation and control systems.

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A person standing waist-deep in a swimming pool appears to have short legs because of refraction. Refraction is the bending of light as it passes through a medium with a different density, such as air and water. Light travels slower in water than in air, so when it enters the water, it bends and changes direction. As a result, the person's legs appear shorter because the light is bending and distorting the image of their legs. This is why objects appear distorted when viewed through the surface of water, a phenomenon known as the "bent-stick" effect.

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The capacitance of a capacitor is proportional to the surface area of its plates. So, when the plate area of a capacitor increases, the capacitance also increases. Capacitance is the ability of a capacitor to store electrical charge. It's measured in Farads (F). A larger surface area of the plates means that the capacitor can store more electrical charge, resulting in an increase in its capacitance. In simple terms, the bigger the plates, the more charge a capacitor can store, resulting in a higher capacitance.

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A person would weigh six times less on the moon than they do on Earth.

OR

A person would weigh six times more on the earth than they do on moon.

16ofx $\frac{\mathrm{<br>}}{}$= 6.0N on the moon

x = 6 * 6 = 36 

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The expression that gives magnetic flux is: - Φ = BA cosθ where Φ is the magnetic flux, B is the magnetic field, A is the area of the surface, and θ is the angle between the magnetic field and the surface normal. This expression tells us the amount of magnetic field that passes through a surface, and is measured in units of webers (Wb) or tesla meters squared (T m²). It is important in understanding the behavior of magnetic fields in various physical systems, including electric motors, generators, transformers, and many others.

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In the formation of a sea breeze, wind blows from the sea towards the land. This happens because during the day, the land heats up faster than the sea. The warm air above the land rises and cooler air from the sea moves in to replace it. As the cooler air moves over the warmer land, it heats up and rises, creating a cycle of air movement. This movement of air from the sea towards the land is known as a sea breeze. Sea breezes are common in coastal areas, especially during the summer months when the temperature difference between the land and sea is greatest.

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The velocity of sound is given by the formula: velocity = frequency × wavelength We are given the frequency of the tuning fork, which is 312 Hz, and the wavelength of the sound wave, which is 1.10 m. Plugging these values into the formula, we get: velocity = 312 Hz × 1.10 m velocity = 343.2 m/s Therefore, the velocity of sound in this scenario is 343.2 m/s. This is the speed at which sound waves are travelling through the medium (which could be air, water, etc.).

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S = ut + 12 $\frac{1}{2}$at2 ${}^2$

40 = 0 x 10 + 12 $\frac{1}{2}$a x 102 ${}^2$

50a = 40

a = 4050 $\frac{40}{50}$

= 0.8m/s2

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The correct answer is: ½KX2. When an elastic string is stretched or compressed, it stores potential energy, which can be calculated using the formula for elastic potential energy: Elastic potential energy = ½ * force constant * (extension)^2 In this case, the force constant is given as k, and the extension is given as X. So, the potential energy in the elastic string is: Elastic potential energy = ½ * k * X^2 Therefore, ½KX2, is the correct answer.

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The wave number is a measure of how many waves fit into a unit distance. In the given wave equation, the wave number is 1 cm^(-1). This can be seen from the argument of the sine function, which is 1 x - 60 t. The units of x and t are cm and s, respectively, so the units of the argument are cm^(-1) s^(-1). The wave number is therefore equal to the coefficient of x in the argument, which is 1 cm^(-1).

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Tyres are treaded to increase friction and provide better grip on the road surface. The treads on a tyre help to channel water, mud, and other debris away from the contact patch of the tyre, which helps to maintain traction and prevent hydroplaning. Treads also help to increase the longevity of the tyre by reducing wear and tear on the rubber. While the appearance of a tyre may be improved with a tread pattern, this is not the main purpose of treading. Increasing the weight of a tyre through treading is also not a desired outcome, as heavier tyres can negatively affect fuel efficiency and vehicle performance.

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Distilled water is a poor conductor of electricity. This is because distilled water is pure water that has gone through a process of distillation, which removes all minerals and impurities from the water. In order for a liquid to conduct electricity, it needs to contain ions or charged particles that can move around freely in the liquid. These ions or charged particles allow the electric current to flow through the liquid. Distilled water, being pure water, does not contain many ions or charged particles that can conduct electricity, so it is a poor conductor of electricity. On the other hand, tap water, sea water, and drinking water all contain varying amounts of minerals and impurities that can act as ions or charged particles and conduct electricity to some extent. Therefore, these liquids are better conductors of electricity than distilled water.

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The eclipse of the moon occurs when the Earth comes exactly between the moon and the sun. During a lunar eclipse, the Earth blocks the sunlight from reaching the moon, and the Earth's shadow falls on the moon, causing it to darken. This can only happen during a full moon, when the moon is on the opposite side of the Earth from the sun.

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To convert ice at 0 ºC to water at the same temperature, we need to supply heat energy to the ice to break its intermolecular bonds and change its state from solid to liquid. The amount of heat energy required for this process is known as the specific latent heat of fusion. The specific latent heat of fusion of ice is given as 336 Jg⁻¹. This means that 336 Joules of heat energy are required to melt 1 gram of ice at 0 ºC. In this question, we are given 20 g of ice, so the amount of heat energy required to convert it to water at the same temperature can be calculated as follows: Heat energy required = specific latent heat of fusion x mass of ice = 336 Jg⁻¹ x 20 g = 6,720 J Therefore, the amount of heat energy required to convert 20 g of ice at 0 ºC to water at the same temperature is 6,720 J. Therefore, the correct option is 6.72 x 10³ J.

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According to the kinetic molecular model in gases, the particles are very far apart and occupy all the spaces made available to them. In this model, gases are made up of large numbers of small particles (such as atoms or molecules) in constant random motion. These particles are separated by large distances, and they occupy all of the space made available to them. They collide with one another and with the walls of their container, but they do not form any long-range order or structured arrangements. This behavior is in contrast to liquids and solids, where the particles are closer together and are often held together by intermolecular bonds.

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The derived unit is the Newton. A derived unit is a unit of measurement that is derived from one or more base units. Base units are the fundamental units of measurement that are used to define all other units. In the International System of Units (SI), there are seven base units: meter, kilogram, second, ampere, kelvin, mole, and candela. The Newton is a derived unit because it is defined as the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared. In other words, it is derived from the base units of kilogram, meter, and second. In contrast, the kilogram, meter, and second are all base units, which means they are not derived from any other units of measurement. The kilogram is the base unit for mass, the meter is the base unit for length or distance, and the second is the base unit for time.

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If the zinc used in the simple cell is of the impure commercial variety bubbles of hydrogen will be seen coming off the zinc. This is called local action.

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The vapor pressure of any substance increases non-linearly with temperature, often described by the Clausius–Clapeyron relation.

As the temperature of a liquid or solid increases its vapor pressure also increases.

Conversely, vapor pressure decreases as the temperature decreases. 

i.e. vapor pressure is directly proportional to temperature

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The relationship between the coefficient of linear expansion (?) and volumetric expansion (?) is that the volumetric expansion is equal to 3 times the coefficient of linear expansion. In other words, ? = 3?. This relationship can be understood by considering the fact that volumetric expansion involves a change in all three dimensions of an object (length, width, and height), whereas linear expansion involves a change in only one dimension (length). Since a change in volume involves a change in all three dimensions, it makes sense that the coefficient of volumetric expansion would be larger than the coefficient of linear expansion. Specifically, since there are three dimensions involved in volumetric expansion, the coefficient of linear expansion is multiplied by 3 to obtain the coefficient of volumetric expansion. Hence, the relationship between the two coefficients is ? = 3?.

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M → HiHo $\frac{\mathrm{<br>}}{}$ = DiDo

where M is the magnification, Hi is the height of the image, Ho is the height of the object, Di is the distance from the lens to the in-focus projected image, and Do is the distance from the object to the lens.

But Di = Hi∗DoHo $\frac{\mathrm{<br>}}{}$ → 20∗3040 $\frac{20\ast 30}{40}$

Image distance(Di) = 15cm