JAMB UTME - Physics - 2018

Antwoorddetails

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.

Antwoorddetails

The linear magnification of an image is given by the formula: magnification = height of image / height of object = -v/u where v is the image distance, u is the object distance, and the negative sign indicates that the image is inverted. In this problem, the object is placed 20cm from a concave mirror of focal length 10cm. Since the object is placed beyond the focal point, the image will be real and inverted. Using the mirror formula 1/f = 1/v + 1/u, we can find the image distance v: 1/10 = 1/v + 1/20 Solving for v, we get: v = -20 cm Now, we can use the magnification formula to find the linear magnification: magnification = -v/u = -(-20)/20 = 1 Therefore, the linear magnification of the image produced is 1, which means the image is the same size as the object and is also inverted. The answer is: 1.

Antwoorddetails

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".

Antwoorddetails

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.

Antwoorddetails

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

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

Resolve vertically, 40cos? = 20, ? = 60${}^o$
Resolve horizontally, f = 40sin? = 40sin60${}^o$
= 40($\frac{\sqrt{3}}{2}$)
= 20?3 N

Antwoorddetails

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.

Antwoorddetails

The force provided by the engine to keep a vehicle moving at a constant speed is proportional to the power (P) required from the engine. This power is proportional to the product of the speed (V) and force (P), so the relationship can be expressed as P = kV, where k is a proportionality constant.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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

Antwoorddetails

The critical angle is the angle of incidence at which light is just able to pass through the interface between two media and not reflect back. When light travels from a medium with a higher refractive index to a medium with a lower refractive index, it slows down and bends towards the normal. If the angle of incidence is increased, the light will eventually reach a point where it will not be able to escape the higher index medium and will be totally reflected back. This is the critical angle. The formula for the critical angle can be expressed as follows: sin(θc) = n2/n1 Where θc is the critical angle, n1 is the refractive index of the first medium, and n2 is the refractive index of the second medium. In this case, the first medium is the transparent medium and the second medium is air, which has a refractive index of approximately 1. By substituting the value of sin(θc) with the value of 340, and n2 with 1, we can solve for n1. sin(340) = n1/1 n1 = 1/sin(340) The value of n1 calculated using this formula is approximately 1.79, which means that the refractive index of the transparent medium is 1.79.

Antwoorddetails

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.

Antwoorddetails

Conduction: the flow of internal energy from a region of higher temperature to lower temperature
Convection: heat transfer due to bulk movement of molecules within fluids
Expansion: the action of becoming larger or more extensive

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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

Antwoorddetails

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.

Antwoorddetails

(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.

Antwoorddetails

Antwoorddetails

Antwoorddetails

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

Antwoorddetails

Antwoorddetails

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.

Antwoorddetails

Electrical appliances in homes are normally earthed so that a person touching the appliances is safe from electric shock. Earthing provides a safety mechanism by connecting the metal case of an electrical appliance to the earth through a conductor. In the event of a fault in the appliance, such as a short circuit, the current will flow through the earth wire instead of the person's body, preventing electric shock. By connecting the metal case of an appliance to the earth, the potential difference (PD) between the appliance and the earth is reduced to zero, ensuring that the appliance is maintained at a lower PD than the earth. Therefore, "the appliances are maintained at a lower pd than the earth" is the correct answer.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

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.

Antwoorddetails

I think the correct option is C ($\frac{m_2}{m_1}$). The coefficient of friction is a ratio of two forces and hence g will cancel out.

Antwoorddetails

Momentum = Mass x Velocity
Change in Momentum = Mass x (change in velocity)
Change in Momentum = Mass x (v - u)
Mass = 100g = 0.1kg
U = 2ms${}^{-1}$
V = 10ms${}^{-1}$
Change in momentum = m (v − u)
= 0.1 (10 − 2)
= 0.1 (8)
= 0.8Ns