JAMB UTME - Physics - 2018

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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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The relative density of a substance is defined as the ratio of its density to the density of a reference substance, usually water at 4 degrees Celsius. In this problem, we can use the principle of buoyancy to determine the density of the solid. When an object is submerged in a fluid, it experiences an upward force called the buoyant force, which is equal to the weight of the fluid displaced by the object. If the object is less dense than the fluid, it will float, and if it is more dense, it will sink. We are given that the solid weighs 15 N in water, which means it displaces 15 N of water. The weight of the water displaced is equal to the buoyant force on the solid, which is equal to the weight of the solid when it is completely submerged in water. Therefore, the weight of the solid when it is completely submerged in water is 15 N. We are also given that the weight of the solid in air is 45 N. The difference between the weight of the solid in air and water is equal to the weight of the water displaced, which is 30 N. This means that the volume of water displaced by the solid is 30/9.8 = 3.06 L (since the density of water is 1000 kg/m^3 or 9.8 N/L). The relative density of the solid is equal to its density divided by the density of water. We can find the density of the solid by dividing its weight in air by its volume: Density of solid = Weight of solid in air / Volume of solid Density of solid = 45 N / (45 N - 15 N) [since weight of displaced water is 15N] Density of solid = 45 N / 30 N Density of solid = 1.5 N/L Therefore, the relative density of the solid is: Relative density = Density of solid / Density of water Relative density = 1.5 N/L / 1000 N/L Relative density = 0.0015 So the answer is 0.33 (rounded to two decimal places).

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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 photocell works on the principle of the emission of electrons by incident radiation. In simple terms, a photocell is a device that converts light energy into electrical energy. It does this by using a material (such as silicon) that releases electrons when it is exposed to light. These electrons can then be collected and used to produce a current, which can be used to power an electrical device. The more light that hits the photocell, the more electrons are released and the greater the electrical current.

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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 magnitude of the resulting impulse can be calculated using the formula impulse = change in momentum. In this scenario, the ball experiences a change in velocity (speed) as it hits the wall. The ball's initial momentum is equal to its mass times its velocity, and its final momentum is zero since it comes to a stop after hitting the wall. The change in momentum is equal to the final momentum minus the initial momentum, which is equal to the negative of the initial momentum. Since the ball has a mass of 5.0 kg and a velocity of 2 m/s, its initial momentum is 5.0 kg * 2 m/s = 10.0 kg m/s. Therefore, the change in momentum is -10.0 kg m/s and the magnitude of the resulting impulse is 10.0 kg m/s, which is equal to 10.0 Ns. So, the correct answer is 10.0kgms−1.

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Brownian motion is the practical evidence for the existence of the continual motion of molecules. This phenomenon is observed as the random movement of particles suspended in a fluid, such as a liquid or a gas, due to the constant bombardment of the fluid molecules. It was first described by the Scottish botanist Robert Brown in 1827 and provides strong evidence for the kinetic theory of matter, which states that all matter is made up of constantly moving particles. The random movement of the suspended particles can be observed through a microscope and is a direct result of the continual motion of the fluid molecules.

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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 correct answer is option D: "All of the above." An electrical charge refers to the presence of an excess or deficit of electrons in an atom or molecule. In this context, positive charge means a deficit of electrons, whereas negative charge means an excess of electrons. Electric current refers to the flow of charged particles, typically electrons, through a conductor. Therefore, an electric current means the movement of electrons. In summary, all of the given options are true of an electrical charge, and they all relate to the behavior of electrons in an electrically charged system.

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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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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 process whereby a liquid turns spontaneously into vapor is called evaporation. Evaporation is the process by which a liquid changes into a gas at a temperature below its boiling point. This happens when the molecules of the liquid gain enough energy to escape from the surface of the liquid into the air as a gas. The rate of evaporation depends on factors such as the temperature, the humidity of the air, and the surface area of the liquid. For example, a shallow pool of water will evaporate faster than a deep one because it has a larger surface area. Boiling, on the other hand, is the process by which a liquid changes into a gas at its boiling point. This happens when the pressure of the gas generated by the boiling liquid is equal to the atmospheric pressure. The temperature remains constant during boiling. Regelation and sublimation are different processes altogether. Regelation is the process by which a solid changes into a liquid when it is subjected to pressure. Sublimation is the process by which a solid changes directly into a gas, bypassing the liquid state.

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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 rectilinear propagation of light means that light travels in straight lines as a wave. This can be observed in the well-defined shadows formed when an object blocks a light source and through the use of a pinhole camera.
According to Sudipa Sarkar, the formation of shadows with sharp edges demonstrates the rectilinear propagation of light, i.e. The fact that light travels in straight line. When an opaque obstacle is placed between a source of light and a screen, a shadow of the obstacle is formed on the screen. The kind of shadow depends on the size of the source of light. If it is a point source (light from a small hole), the shadow obtained is a region of total darkness, called umbra.
If an extended source of light, e.g. a bulb, is used, the umbra is surrounded by a region of partial darkness, called penumbra. The moon is seen because it reflects the sun's light. An eclipse of the moon (lunar eclipse) occurs when the earth comes between the sun and the moon and prevents some of the light from the sun from reaching the moon. In other words, the earth casts its shadow on the moon. The solar eclipse occurs when the moon comes between the sun and the earth.

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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 energy needed to move a unit positive charge around a complete electric circuit is called the "electromotive force", also known as "emf". This is because the emf is what drives the flow of electric charge, or current, around the circuit. Think of it like a battery in a flashlight. The battery provides the emf that drives the flow of electric current through the wires and the light bulb. Without the emf from the battery, the electric charges wouldn't be able to flow and the light wouldn't turn on. The other answer options, such as electric potential difference and electric energy, are related to the emf but don't specifically refer to the energy needed to move a unit positive charge around a circuit. Kinetic energy, on the other hand, is not related to the movement of electric charges around a circuit at all.

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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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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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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 main way that the occupants of a room standing away from a charcoal fire are warmed is by radiation. Radiation is the transfer of heat energy through electromagnetic waves, and it can travel through empty space. In this scenario, the charcoal fire emits radiation in the form of infrared waves, which travel through the air and warm up the objects (including the occupants) in the room. Convection, on the other hand, is the transfer of heat through the movement of fluids (such as air), but in this case, the air in the room is not being actively circulated by a fan or other mechanism. Conduction involves the transfer of heat through direct contact between two objects, but the occupants are not in direct contact with the fire. Reflection refers to the bouncing of radiation off a surface, but it is not a significant factor in this scenario as most of the radiation is absorbed by the objects in the room.

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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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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 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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The dimension of pressure is ML^-1T^-2 Pressure is defined as the force per unit area. This means that pressure is dependent on the force applied and the area over which it is applied. The unit of force is measured in Newtons (N), and the unit of area is measured in square meters (m²). Therefore, the unit of pressure is N/m², which is also known as Pascals (Pa). To determine the dimension of pressure, we need to break down the units into their fundamental dimensions of mass (M), length (L), and time (T). Force is measured in N, which is kg m/s². Area is measured in m², which is L². Therefore, the dimension of pressure can be calculated as (kg m/s²)/(L²), which simplifies to ML^-1T^-2.

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The primary reason that power is transmitted at high voltages is to increase efficiency. As electricity is transmitted over long distances, there are inherent energy losses along the way. High voltage transmission minimizes the amount of power lost as electricity flows from one location to the next. How? The higher the voltage, the lower the current. The lower the current, the lower the resistance losses in the conductors. And when resistance losses are low, energy losses are low also. Electrical engineers consider factors such as the power being transmitted and the distance required for transmission when determining the optimal transmission voltage

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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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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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The impulse experienced by the ball can be calculated using the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, the momentum of the ball before the collision is: p1 = m * v1 where m is the mass of the ball and v1 is its velocity before the collision. Substituting the values given in the problem, we get: p1 = 0.8 kg * 5 m/s = 4 kg m/s After the collision, the ball rebounds with the same speed but in the opposite direction, so its velocity after the collision is: v2 = -5 m/s The momentum of the ball after the collision is: p2 = m * v2 Substituting the values, we get: p2 = 0.8 kg * (-5 m/s) = -4 kg m/s The negative sign indicates that the direction of the momentum is opposite to that before the collision. The change in momentum of the ball is given by: Δp = p2 - p1 Substituting the values, we get: Δp = (-4 kg m/s) - (4 kg m/s) = -8 kg m/s The negative sign indicates that the impulse experienced by the ball is in the opposite direction to its initial momentum, which is the direction of the wall. Therefore, the impulse experienced by the ball is 8 kg m/s. Therefore, the correct option is: 8kgm/s.

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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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To find the moment of the force about point X, we need to first understand what moment is. Moment is the turning effect of a force around a pivot point. It is calculated by multiplying the force by the perpendicular distance between the pivot point and the line of action of the force. In this case, the force of 5N is acting on the rod at point Y. To find the moment of this force about point X, we need to find the perpendicular distance between point X and the line of action of the force. From the diagram, we can see that the perpendicular distance between point X and the line of action of the force is 2m (the length of the rod). So, the moment of the force about point X is: Moment = force x perpendicular distance = 5N x 2m = 10Nm Therefore, the correct answer is: 10Nm.

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

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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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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 answer is "specific heat capacity." Specific heat capacity is a measure of how much heat energy is required to raise the temperature of a certain amount of a substance by 1 degree Celsius (or 1 Kelvin, which is the same size as 1 degree Celsius). In this case, we are dealing with 10kg of copper, so we need to know the specific heat capacity of copper. The specific heat capacity of copper is 0.385 J/g°C (joules per gram per degree Celsius). To calculate the amount of heat needed to raise the temperature of 10kg of copper by 1K, we need to know the total mass of copper (10kg) and the specific heat capacity of copper (0.385 J/g°C). The formula for calculating the amount of heat energy required is: Heat energy = mass x specific heat capacity x change in temperature Since we want to raise the temperature by 1K, the change in temperature is 1K. So, the amount of heat energy required to raise the temperature of 10kg of copper by 1K is: Heat energy = 10kg x 0.385 J/g°C x 1K = 3.85 kJ Therefore, it takes 3.85 kilojoules (kJ) of heat energy to raise the temperature of 10kg of copper by 1K.

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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.