JAMB UTME - Physics - 2018

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The most suitable instrument for measuring the outside diameter of a narrow pipe in a few millimeters in diameter is a micrometer screw gauge. A micrometer screw gauge is a precision measuring instrument that can accurately measure small dimensions with high accuracy. It has a spindle that moves towards an anvil and a scale that indicates the measurement. The spindle moves in response to a small rotation of the thimble, allowing for precise and sensitive measurements. In contrast, a pair of calipers or a meter rule may not be accurate enough for measuring such small dimensions, and a tape rule may not be able to fit inside the narrow pipe. Therefore, a micrometer screw gauge is the most suitable option for measuring the outside diameter of a narrow pipe in a few millimeters in diameter.

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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 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.

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

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The resistance of a 40W car headlamp can be calculated using Ohm's Law, which states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points, and inversely proportional to the resistance (R) of the conductor. The equation can be written as V = IR. Since the power (P) of the headlamp is given as 40W and the voltage is 12V, we can calculate the current using the equation P = IV. Substituting I = P/V, we get I = 40/12 = 3.33A. Finally, using Ohm's Law, we can calculate the resistance as R = V/I = 12/3.33 = 3.6Ω. So, the resistance of the 40W car headlamp, drawing current from a 12V battery, is 3.6Ω.

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We can use the lens formula, 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance between the lens and the image, and u is the distance between the lens and the object. From the problem, we know that the focal length of the lens is 15 cm, and the image is erect and three times the size of the object. This means that the image distance v is positive and the object distance u is negative (since the object is in front of the lens). Let's assume that the object distance u is -x cm, where x is a positive number. Then, the image distance v is +3x cm, since the image is three times the size of the object. Substituting these values into the lens formula, we get: 1/15 = 1/(+3x) - 1/(-x) Simplifying the right-hand side, we get: 1/15 = (1 + 3)/3x Multiplying both sides by 3x, we get: 3x/15 = 4 Simplifying, we get: x = 20 Therefore, the distance between the object and the lens is -20 cm (since it is in front of the lens), and the distance between the image and the lens is +60 cm (since it is behind the lens). The distance between the object and the image is the sum of these distances, which is: (-20) + (+60) = 40 cm Therefore, the answer is 40cm.

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The energy changes that take place when a steam engine drives a generator which lights a lamp can be described as: Heat energy from burning fuel is used to create steam in the boiler of the steam engine. This steam is then used to drive the turbine, which generates kinetic energy as it spins. The kinetic energy is transferred to the generator, which converts it into electrical energy (electricity). The electricity then flows through the wires to the lamp, where it is converted back into light energy, which is what we see. Therefore, the correct option would be: Heat ----> Kinetic ----> Electricity ----> Light

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The fission process refers to the splitting of an atomic nucleus into two or more smaller nuclei. One of the key features of the fission process is that it can lead to a chain reaction, where the neutrons released during fission can go on to trigger additional fission reactions. This chain reaction can produce a large amount of energy, as is the case in nuclear power plants and nuclear weapons. Another feature of the fission process is that it typically produces radioactive products. These products can remain radioactive for a long time, which is why there are concerns about the safe disposal of nuclear waste. Additionally, the fission process typically releases neutrons, which can go on to cause further fission reactions. This neutron release is an important aspect of the chain reaction mentioned earlier. Finally, the fission process is accompanied by a small loss of mass, which is converted into energy according to Einstein's famous equation E=mc². This loss of mass is what allows the large amount of energy to be released during a fission reaction.

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The particle nature of matter refers to the idea that matter is made up of tiny particles that are constantly moving. Diffusion, Brownian motion, and crystallization are all examples of phenomena that can be explained by the particle nature of matter. However, diffraction is not an evidence of the particle nature of matter. Diffraction is a phenomenon that occurs when waves encounter an obstacle or a slit, causing them to spread out and interfere with each other. While particles can also exhibit diffraction, this is a property of waves and is not specific to particles. In summary, diffusion, Brownian motion, and crystallization are all evidences of the particle nature of matter, but diffraction is not.

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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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The density of a substance is defined as its mass per unit volume. Therefore, the mass of the palm oil before frying was: Mass = Density x Volume = 0.9 g/cm³ x 400 cm³ = 360 g After frying, the mass of the palm oil remains the same, but its density changes to 0.6 g/cm³. Therefore, the new volume of the palm oil can be calculated by rearranging the density formula: Volume = Mass / Density = 360 g / 0.6 g/cm³ = 600 cm³ So the new volume of the palm oil after frying is 600 cm³. is the correct answer.

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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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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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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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The process by which protons are converted into helium atoms with a tremendous release of energy is called "thermonuclear fusion". In this process, two light atomic nuclei combine to form a heavier nucleus, releasing a huge amount of energy in the form of light and heat. This is the same process that powers the sun and other stars. The high temperatures and pressures required for fusion to occur can only be achieved in stars or in controlled environments such as fusion reactors. Thermonuclear fusion is different from nuclear fission, which is the process of splitting a heavy nucleus into lighter nuclei with the release of energy. Thermionic emission and photoelectric emission are different processes that involve the emission of electrons from a material due to heating or exposure to light, respectively.

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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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To determine the final temperature of the water, we can use the formula: Q = mcΔT where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. We know that the power of the electric heating coil is 1KW, which means it transfers 1000 Joules of energy per second. In 2 minutes, or 120 seconds, it transfers 120,000 Joules of energy to the water. The mass of the water is given as 2kg and the specific heat capacity of water is 4000 J/kg°C. We can assume that the initial temperature of the water is 30°C. Using the formula, we can solve for the change in temperature: 120,000 J = (2 kg)(4000 J/kg°C)(ΔT) ΔT = 15°C Therefore, the final temperature of the water is 30°C + 15°C = 45°C. So, the final water temperature is 45.0oC.

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Temperature is proportional to the average kinetic energy of the molecules in a body. This means that as the average kinetic energy of the molecules increases, so does the temperature. Think about it like this: the hotter an object, the more energy its molecules have. This energy is what makes the molecules move faster, and therefore, the temperature of the object increases. The average kinetic energy of the molecules is a better measure of temperature than the maximum speed of the molecules because temperature is a measure of the overall energy distribution, not just the energy of a single molecule.

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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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Weight of water displaced = upthrust = 30 - 21 = 9N
Mass of water displaced = $\frac{9}{10}$ = 0.9kg
Volume of object = 9 × 10${}^{-4}$m${}^3$
= (9 × 10${}^{-4}$) (1.4 ×103)

 = 1.26kg = 12N
30 - 12.6 = 17.4N

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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 man first walks 1 km due east, which means he has moved 1 km horizontally to the right of his starting point. Then, he walks 1 km due north, which means he has moved 1 km vertically upwards from his previous position. To find his displacement, we need to draw a straight line from his starting point to his final position, which represents the shortest distance between the two points. This line is called the displacement vector. We can use the Pythagorean theorem to calculate the length of the displacement vector. The horizontal and vertical distances are the two legs of a right-angled triangle, and the hypotenuse is the length of the displacement vector. Using the Pythagorean theorem, we get: displacement = √((1 km)^2 + (1 km)^2) = √2 km The direction of the displacement vector is the angle between the displacement vector and the due north direction. We can find this angle using trigonometry. The tangent of the angle is the ratio of the horizontal distance to the vertical distance: tan(θ) = (1 km) / (1 km) = 1 Using a calculator, we can find that the angle is 45°. Therefore, the man's displacement is √2 km in the direction N 45° E. So, the correct answer is √2km N 45°E.

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The correct answer is "difference in temperature between the body and its surroundings." When a body is at a higher temperature than its surroundings, it will lose heat to the surroundings until it reaches thermal equilibrium, i.e., until the temperatures of the body and its surroundings are equal. The rate at which the body loses heat is proportional to the temperature difference between the body and its surroundings. This is known as Newton's law of cooling. The law of cooling applies to a wide range of situations, from the cooling of hot beverages to the cooling of electronic devices. It is important to understand this law because it allows us to predict how long it will take for a body to cool down to a certain temperature, and to design systems that can regulate the temperature of a body, such as heaters or refrigerators.

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X = $\frac{4}{3}$ r = ?
Shell?s law:. 7 = $\frac{Sin{2}^0}{Sin{r}^0}$
$\frac{V}{g}$ = $\frac{Sin{30}^0}{Sin{r}^0}$
Sin$r^0$ = $\frac{3Sin{30}^0}{4}$
Sin $r^0$ = 0.375
R ${}^o$ = Sin-1 (0.375)
R ${}^o$ = 22.02 ${}^o$
R ${}^o$ = 22 ${}^o$

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The correct answer is "I and III only". Isotopes of an element have the same number of protons in their nuclei, meaning they have the same atomic number and are therefore the same element. Because of this, they have the same chemical properties. However, isotopes of an element have different numbers of neutrons in their nuclei, which means they have different atomic masses. This is why isotopes can be separated using physical properties such as their mass or other characteristics related to their mass.

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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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To calculate the distance between point A and point B, we can use the formula: Distance = Speed x Time where the speed is given as 100 km/h and the time is given as 15 minutes, which we need to convert to hours. 1 hour = 60 minutes, so 15 minutes = 15/60 hours = 0.25 hours. Now, we can substitute these values into the formula: Distance = 100 km/h x 0.25 h = 25 km Therefore, the distance between point A and point B is 25 km. is the correct answer.

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The speed of sound in air is given as 3.40 m/s. The echo of the clap is heard 0.8 seconds after it was produced, which means it traveled to the hill and back. The time taken for sound to travel to the hill is half of the time taken for it to travel to and from the hill. Therefore, the time taken for sound to travel to the hill is 0.8/2 = 0.4 seconds. We can use the formula: distance = speed x time to calculate the distance between the boy and the hill. distance = speed of sound x time taken for sound to travel to the hill distance = 3.40 m/s x 0.4 s distance = 1.36 m Therefore, the distance between the boy and the hill is 1.36 meters. However, the answer options provided are in meters and are significantly larger than 1.36 meters. It is possible that the speed of sound provided in the question is incorrect or the answer options are incorrect.

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The linear expansivity of brass is given as 2 x 10^-5 /°C. This means that for every 1°C increase in temperature, the brass expands by 2 x 10^-5 of its original size. To find the new volume of the brass at 100°C, we need to take into account the expansion in all three dimensions (length, width, and height). Since the expansivity given is for length only, we need to find the expansivity in all three dimensions by multiplying it by 3. The expansivity in all three dimensions is: 3 x (2 x 10^-5 /°C) = 6 x 10^-5 /°C To find the new volume, we can use the formula: Vf = Vi (1 + αΔT) where Vf is the final volume, Vi is the initial volume, α is the expansivity in all three dimensions, and ΔT is the change in temperature. Plugging in the values, we get: Vf = 15.00 cm3 (1 + (6 x 10^-5 /°C) x (100°C - 0°C)) Vf = 15.09 cm3 Therefore, the volume of the brass at 100°C is 15.09 cm3.

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The correct answer is "Viscosity". Viscosity is the property of a fluid that describes its resistance to flow. When two layers of liquid are in relative motion, the viscosity of the liquid causes friction between the layers. This friction creates a resistance to the movement of one layer past the other. The greater the viscosity of the liquid, the greater the friction and the more difficult it is for the layers to move past each other. This property is important in many industrial and natural processes, such as the flow of oil in pipelines or the movement of blood through the human body.

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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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Let the total number of pulleys used in both the blocks be $n$.
In a block-and-tackle pulley system, the velocity ratio is equal to n.
Efficiency = $\frac{\text{MA}}{\text{VR}}\times 100\%$
$\text{MA}=\frac{\text{L}}{\text{E}},\text{VR}=n$
Efficiency = $\frac{\text{L}}{\text{E}}\times \frac{1}{\text{n}}\times 100\%$
$\text{E}=\frac{\text{L}}{\text{Eff.}\times n}\times 100\%$
$\text{E}=\frac{120\text{N}}{40\%\times 6}\times 100\%$
$\text{E}=50\text{N}$

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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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To solve this problem, we can use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, the energy transferred is in the form of heat. We can use the formula: Q = m*c*(ΔT) where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. First, we can calculate the heat transferred from the hot water to the cold water: Q1 = 150g * 4.18 J/(g°C) * (60°C - T) Q1 = 627 * (60 - T) where T is the temperature of the mixture. Next, we can calculate the heat transferred from the cold water to reach the final temperature of the mixture: Q2 = 300g * 4.18 J/(g°C) * (T - 20°C) Q2 = 1254 * (T - 20) Since the heat transferred between the two water samples must be equal, we can set Q1 equal to Q2 and solve for T: 627 * (60 - T) = 1254 * (T - 20) 37620 - 627T = 1254T - 25080 1881T = 62760 T = 33.4°C Therefore, the temperature of the mixture is approximately 33°C. Answer: 33°C

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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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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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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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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.