JAMB UTME - Physics - 2018

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F = 20cm
V = 100cm
U = ?
$\frac{1}{U}$ + $\frac{1}{V}$ = $\frac{1}{F}$
$\frac{1}{20}$ + $\frac{1}{100}$ = $\frac{1}{F}$
$\frac{5+1}{100}$ = $\frac{1}{F}$
F = $\frac{100}{6}$
= 16.7cm
= 17cm

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The speed of sound in air is approximately 343 meters per second at room temperature. The formula for the speed of sound is:

Speed of sound = Frequency × Wavelength

In this problem, we are given the frequency (260 Hz) and the wavelength (1.29 m) of the sound wave. We can use these values to calculate the speed of sound:

Speed of sound = 260 Hz × 1.29 m = 335.4 m/s

Next, we need to use the fact that the man hears his echo 2 seconds after he shouted. Since the sound wave traveled from the man to the hill and then back to the man, the total distance traveled by the sound wave is twice the distance from the man to the hill. We can use the formula:

Distance = Speed × Time

to calculate the distance from the man to the hill:

Distance = (335.4 m/s) × (2 s/2) = 335.4 m

Therefore, the hill is 335.4 meters away from the man. The answer is option (B), 335.4m.

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Formulae resistance in parallel
= 1/R = 1/R1 +1/R2
1/R = 1/2 +1/2 = 1
Resistance are now in series
R = 1 + 3 + 4
= 8 ohms

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Molecules cannot be given energy during the heating and the molecules of oil cannot force each other out

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The force required to pull a 20kg mass up a slope inclined at 300 can be calculated using the formula: force = mass * gravity * sin(angle) where mass is 20kg, gravity is 10 m/s^2 and angle is 300. The formula for efficiency is: efficiency = output force / input force where output force is the force required to pull the mass up the slope and input force is the force applied to the rope. Since the efficiency of the plane is 75%, the input force is 4 times the output force. So, the output force can be calculated as: output force = input force / 4 input force = mass * gravity * sin(angle) / efficiency input force = 20 * 10 * sin(300) / 0.75 input force = 533.2 N And the output force can be calculated as: output force = input force / 4 output force = 533.2 / 4 output force = 133.3 N So, the force required to pull the load up the plane is 133.3 N.

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The pitch of an acoustic device refers to the perceived highness or lowness of a sound, and is determined by the frequency of the sound wave. To increase the pitch of an acoustic device, you need to increase the frequency of the sound wave. This can be done by increasing the number of vibrations per second that the device produces. So, the correct answer is to "increase the frequency".

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The three 2uf capacitors are in parallel to each other so u add them like this
2uf+2uf+2uf=6uf
So u have three capacitors in series
6uf 2uf and 3uf
They are in series so
1/C= 1/6+1/3=1/2
C=2uf
Then the same thing with the last two capay
1/2+1/2=1uf
Thanks

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When an atom loses or gains a charge, it becomes an ion. An ion is a type of atom that has an unequal number of protons and electrons, giving it a net electrical charge. If an atom loses one or more electrons, it becomes positively charged and is called a cation. On the other hand, if an atom gains one or more electrons, it becomes negatively charged and is called an anion. So, in summary, an atom can lose or gain electrons to become an ion, which has a net electrical charge.

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Among the given options, the Accumulator has the lowest internal resistance when new. Internal resistance is the resistance that a battery or cell provides to the flow of electric current within itself. Lower internal resistance means that the battery can supply more current to an external circuit without losing much of its own energy as heat. An Accumulator, also known as a rechargeable battery, is designed to be charged and discharged multiple times. It has a relatively low internal resistance when new, meaning it can provide a higher current than the other cells listed while wasting less energy internally as heat. A Leclanche cell and Daniell cell are primary cells, meaning they are designed to be used once and discarded. They have higher internal resistance compared to the accumulator, which limits their ability to supply high currents. A Torch battery, also known as a dry cell, is also a primary cell and has a higher internal resistance than the accumulator. It is commonly used in small electronic devices and has a longer shelf life than Leclanche and Daniell cells. In summary, an Accumulator has the lowest internal resistance when new, which makes it an ideal choice for applications requiring high current delivery such as electric vehicles, power tools, and renewable energy systems.

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Convex mirrors are used as driving mirrors because the images formed by them are "erect, virtual, and diminished." Let me explain what these terms mean: - Erect: It means that the image appears upright, just like the actual object. This is important for a driving mirror because it allows the driver to perceive the correct orientation of the vehicles behind them. - Virtual: It means that the image appears to be behind the mirror, and not in front of it. This is also important for a driving mirror because it allows the driver to see a wider field of view without having to turn their head. - Diminished: It means that the image is smaller than the actual object. This is important for a driving mirror because it allows the driver to see a larger area behind them while still fitting it within the mirror's frame. Overall, these properties make convex mirrors ideal for use as driving mirrors as they provide the driver with an accurate view of the vehicles behind them without sacrificing their field of view.

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In case of small drops of mercury, the gravitational potential energy is negligible in comparison to the potential energy due to surface tension.Consequently, to keep the drop in equilibrium, the mercury drop’s surface tends to contract so that its surface area will be the least for a sphere and the drops will be spherical.
But in the case of bigger drops of mercury, the potential energy due to gravity is predominant over the potential energy due to surface tension.Consequently, to keep equilibrium , the mercury drop tends to assume minimum potential energy as possible, the drop becomes oval in shape and lower center of gravity.

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Angular velocity is a measure of how fast an object is rotating around a center point. It's usually measured in radians per second (rad/s). To calculate angular velocity, we use the formula: angular velocity = linear velocity / radius. In this case, the linear velocity is 1 m/s, and the radius is 0.5 m. So, the angular velocity would be: 1 m/s / 0.5 m = 2 rad/s Therefore, the answer is 2 rad/s or 2rads^-1

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Cathode rays are streams of electrons. They were first discovered by scientists experimenting with vacuum tubes, and they observed that a glowing beam of particles traveled from the negatively charged electrode (the cathode) to the positively charged electrode (the anode). These particles were found to have a negative charge, which was later identified as electrons. Cathode rays played an important role in the development of electronics and the understanding of atomic structure.

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The type of reaction represented by the given scheme is a nuclear fission reaction. Nuclear fission is a process where a heavy nucleus is split into smaller nuclei with the release of energy. In the given scheme, a heavy element X is split into two lighter elements, Y and Z, along with the release of energy and some neutrons (n). In a nuclear fission reaction, a neutron is usually absorbed by the nucleus of the heavy element, which then becomes unstable and splits into two smaller nuclei and some neutrons. These neutrons can then go on to split other heavy nuclei, resulting in a chain reaction. In the given scheme, the release of energy and the presence of neutrons suggest that it is a fission reaction. Moreover, the scheme depicts the process of splitting a heavy element into two lighter elements, which is a characteristic of a fission reaction. Therefore, the type of reaction represented by the given scheme is a nuclear fission reaction.

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Radioactive decay releases different types of energetic emissions. The three most common types of radioactive emissions are alpha particles, beta particles, and gamma rays.

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To calculate the voltage needed for a 40W instrument with a resistance of 90 Ohms, we can use the formula: Voltage = √(Power x Resistance) Plugging in the given values, we get: Voltage = √(40W x 90Ω) Voltage = √(3600) Voltage = 60V Therefore, the instrument should be operated at 60V to generate 40W of power with a resistance of 90 Ohms. The correct answer is, 60V.

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Different musical instruments playing the same note can be distinguished from one another due to the difference in their "timbre" or "tone color." Timbre refers to the unique character or quality of a sound that allows us to distinguish it from other sounds even when they have the same pitch and loudness. For example, a piano and a guitar playing the same note will sound different due to the differences in their timbre. This is why we can tell the difference between different instruments and why some instruments are better suited to certain styles of music than others.

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Ohm's law states that the current passing through a conductor is directly proportional to the voltage applied across it, given the temperature and other physical conditions remain constant. Among the given options, only "all metals" obey Ohm's law. This is because metals have a linear relationship between their resistance and the applied voltage, meaning that the resistance of a metal remains constant regardless of the voltage applied. As a result, the current passing through a metal is directly proportional to the voltage applied, following Ohm's law. On the other hand, a diode, all electrolytes, and glass do not obey Ohm's law. A diode is a semiconductor that has a non-linear current-voltage relationship, and its resistance is not constant. Similarly, electrolytes and glass are non-metallic substances that do not have a linear relationship between their resistance and the applied voltage. Their resistance can change significantly with the voltage applied, and hence they do not follow Ohm's law.

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The differences observed in solids, liquids, and gases can be accounted for by the spacing and forces acting between the molecules. In a solid, the molecules are packed closely together, so they have a fixed shape and volume. The intermolecular forces are strong enough to keep the molecules in a fixed position relative to one another. In a liquid, the molecules are still close together, but they are free to move around each other. The intermolecular forces are weaker than in a solid, so the molecules can slide past one another, giving the liquid its ability to flow and take the shape of its container. In a gas, the molecules are widely spaced and are in constant motion. The intermolecular forces are very weak, so the molecules are free to move around and fill any available space. Gases have no fixed shape or volume. So, the differences observed in solids, liquids, and gases can be explained by the spacing and forces acting between the molecules. It's not about their relative masses, melting points, or the different molecules in each of them.

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The product of force and time is known as impulse. Impulse can be defined as the change in momentum that an object experiences as a result of a force being applied to it over a period of time. In simpler terms, impulse is the "push" that an object receives from a force acting on it for a certain amount of time. The more force applied, or the longer the time the force is applied, the greater the impulse and the greater the change in momentum of the object. It's important to note that impulse is a vector quantity, meaning it has both magnitude and direction. Impulse is a measure of the ability of a force to cause an object to change its velocity, and can be used to explain many phenomena in physics, such as why a heavy object is harder to stop than a lighter one, or why a soccer ball changes direction when it is kicked.

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To calculate the energy dispatched in the resistor, we need to use the formula: Energy = Power x Time Where Power is the amount of electrical power consumed by the resistor, and is equal to the product of the voltage across the resistor and the current flowing through it: Power = Voltage x Current In this case, the voltage across the resistor is 12V, and the current flowing through it is 2A. Therefore, the power consumed by the resistor is: Power = 12V x 2A = 24W Now, we can substitute this value of power along with the given time of 5 minutes into the formula for energy: Energy = 24W x 5min x 60s/min = 7,200J Therefore, the energy dispatched in the resistor in 5 minutes is 7,200J. is the correct answer.

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When a conductor is connected to the earth, electrons flow to the earth. Electrons are negatively charged particles that are present in all conductors. When a conductor is connected to the earth, it creates a path for electrons to flow from the conductor to the earth, which helps to balance the electric potential and prevent the buildup of electric charge. This flow of electrons is known as grounding and is an important safety measure in electrical systems.

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(ii) Adhesion : The force of attraction between unlike molecules, i.e. between the molecules of different liquids or between the molecules of a liquid and those of a solid body when they are in contact with each other, is known as the force of adhesion. This force enables two different liquids to adhere to each other or a liquid to adhere to a solid body or surface.

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Efficiency = $\frac{\text{useful energy output from machine}}{\text{energy input into machine}}$
= $\frac{E3}{E2}$

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The half-life of a radioactive material is the time it takes for half of the atoms in a sample to decay. The fraction of atoms left after a certain number of half-lives can be calculated using the formula: fraction left = (1/2)^(number of half-lives) Let's use this formula to solve the problem. We know that the fraction of atoms left after 120 years is 1/64, which means that: (1/2)^(number of half-lives) = 1/64 To solve for the number of half-lives, we can take the logarithm of both sides: log[(1/2)^(number of half-lives)] = log(1/64) Using the rule that log(a^b) = b*log(a), we can simplify the left side of the equation: number of half-lives * log(1/2) = log(1/64) Dividing both sides by log(1/2), we get: number of half-lives = log(1/64) / log(1/2) Using a calculator or the change of base formula, we can evaluate this expression: number of half-lives = 6 Therefore, the half-life of the material is 120/6 = 20 years.

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The correct explanation for why a narrow beam of white light can be split up into different colors by a glass prism is that different colors of white light travel with different speeds in glass. White light is made up of different colors with different wavelengths, ranging from violet to red. When a narrow beam of white light passes through a glass prism, the different colors refract at slightly different angles due to the fact that their wavelengths are different. This causes the different colors to spread out and form a spectrum. The amount of refraction that occurs depends on the speed of light in the medium. Different colors of light have different speeds in glass due to the fact that their wavelengths are different. This means that they will refract at different angles as they pass through the glass prism, causing them to spread out. So, the correct explanation for why a narrow beam of white light can be split up into different colors by a glass prism is that different colors of white light travel with different speeds in glass. Therefore, is the correct explanation. is incorrect because it describes what white light is made up of, but does not explain how it is split up into colors by a prism. is incorrect because a prism does not have all the colors of white light, but rather it separates the colors that are already present in white light. is incorrect because total internal reflection occurs when light is completely reflected back into the same medium, which is not what happens when white light is split up by a prism.

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The option that does NOT describe the image formed by a plane mirror is "Magnified". When an object is placed in front of a plane mirror, the image formed is: 1. Erect: The orientation of the object in the mirror is the same as the orientation of the object in real life. For example, if you raise your right hand in front of a plane mirror, the image in the mirror will also show your right hand raised. 2. Laterally inverted: The image formed in the mirror is flipped horizontally, which means that the left side of the object appears on the right side of the image and vice versa. For example, if you wear a shirt with the letter "H" on it and look at it in a plane mirror, the image will show the letter "H" flipped horizontally. 3. Same distance from the mirror as object: The image formed in the mirror is located behind the mirror at the same distance as the object is located in front of the mirror. For example, if you stand 1 meter away from a plane mirror, the image of yourself will also be located 1 meter away from the mirror, behind the mirror. 4. NOT magnified: The image formed in the plane mirror is of the same size as the object, which means that there is no magnification or reduction in the size of the image. For example, if you stand in front of a plane mirror with a height of 1 meter, the image of yourself in the mirror will also have a height of 1 meter. Therefore, the correct answer is "Magnified", as the image formed by a plane mirror is not magnified.

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Neutron is not a product of nuclear fusion. Nuclear fusion is the process by which two or more atomic nuclei come together to form a heavier nucleus, releasing a large amount of energy in the process. In most fusion reactions, the resulting products are alpha particles (helium nuclei) and energy in the form of gamma rays. X-rays and gamma rays are both forms of high-energy electromagnetic radiation that can be produced by nuclear reactions, including nuclear fusion. Alpha particles are also a common product of nuclear fusion, especially in the fusion reactions that power the sun. However, neutrons are not typically produced in fusion reactions. In fact, one of the major challenges in developing fusion as a practical energy source is finding ways to produce and control the high-energy neutrons that are generated in the process. Neutrons can be produced in some types of fusion reactions, but they are not a primary product. In summary, neutron is not a product of nuclear fusion, while X-rays, Y-rays (assuming this is a valid form of radiation), and alpha particles are common products of this process.

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The phenomenon of a mirage can be explained by options I and III. A mirage is an optical illusion that occurs when light rays passing through a medium with varying refractive indices create a false image of distant objects or even the sky. In hot weather, the air near the road surface becomes hotter and less dense than the air above, causing the light passing through it to bend and create a reflection of the sky or objects in the distance. This effect is known as a temperature inversion. Additionally, light from the sky can be reflected upwards after coming close to the road surface, adding to the illusion of a reflected object or the sky. Option II, which suggests that road surfaces become good reflectors in hot weather, is not a valid explanation for a mirage. Therefore, the correct answer is: I and III only.

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Volume of liquid displaced
= $\frac{2}{3}$(0.5)${}^3$
Mass of liquid displaced = mass of floating cube = 75kg
Density of liquid = $\frac{mass}{volume}$
= $\frac{75}{\left(\frac{7}{3\left(0.5\right)}\right)}$ × 3
= 0.9 × 103kgm${}^{-3}$
R.D of liquid = $\frac{\left(0.9\right)}{\left(1.0\right)}$ × 103
= 0.9

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A meter bridge is an instrument used to measure the unknown resistance of a conductor. The meter bridge consists of a long resistance wire AB of uniform cross-sectional area and a battery of known voltage connected across its ends. A galvanometer is connected across a point C on the wire, which is called the null point or balance point.
When a known standard resistor of 2.0 ohms is connected to the 0.0cm end of the meter bridge wire, the balance point is found to be at 55.0cm. This means that the resistance of the unknown resistor is equal to the resistance of a portion of the meter bridge wire between the 0.0cm and the 55.0cm point.
To find the value of the unknown resistor, we can use the principle of the Wheatstone bridge, which states that the ratio of the resistances in the two arms of a balanced bridge is equal.
Let R be the resistance of the unknown resistor, then we have:
R/2.0 = (100 - 55.0)/55.0
Simplifying this expression, we get:
R = 2.0 x (100 - 55.0)/55.0
R = 1.64 ohms
Therefore, the value of the unknown resistor is 1.64 ohms.

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The electrochemical equivalent of silver is a measure of the amount of silver that is deposited on a surface per unit of charge. In this case, the electrochemical equivalent of silver is 0.0012 grams per Coulomb of charge. To deposit 36.0 grams of silver by electrolysis, we need to know the amount of charge that must be passed through the solution. The amount of charge is given by: Q = m/z where m is the mass of silver to be deposited, 0.0012 is the electrochemical equivalent of silver, and z is the charge on one mole of electrons (z = 1 for a single electron). So, the amount of charge required is: Q = 36.0 g / 0.0012 g/C = 30000 C The current, I, is given by: I = Q / t where t is the time for which the current is flowing. In this case, t = 5 minutes. So, the current required is: I = 30000 C / (5 x 60 s) = 100 A Therefore, the current must be 100 Amperes.