JAMB UTME - Physics - 2006

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The half-life of a radioactive substance is the amount of time it takes for half of the original radioactive nuclei to decay. If the half-life of the substance is 20 days, then after 20 days, half of the original radioactive nuclei will have decayed, and half will remain. After another 20 days (a total of 40 days), half of the remaining nuclei will have decayed, leaving a quarter of the original nuclei. After another 20 days (a total of 60 days), half of the remaining nuclei will have decayed again, leaving an eighth of the original nuclei. Finally, after another 20 days (a total of 80 days), half of the remaining nuclei will have decayed, leaving a sixteenth of the original nuclei. Therefore, after 80 days, 1/16 of the original radioactive nuclei will remain. So the answer is (14).

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The question asks which statements about machines are true. Let's evaluate each statement: I. Work done by load is always less than the work done by effort. This statement is generally true for all machines because some of the work done by the effort is used to overcome friction and other resistive forces in the machine. Therefore, the statement is true. II. All machines are made of levers, pulleys, screws and gear wheels. This statement is not true as machines can be made of a variety of components including electronic parts, hydraulic systems, etc. Therefore, the statement is false. III. A fishing rod is a machine. This statement is true as a fishing rod is a simple machine that uses a lever to catch fish. Therefore, the statement is true. IV. Effort is always larger than load. This statement is not true because machines can be designed to have a load larger than the effort, such as in a hydraulic press. Therefore, the statement is false. From the above evaluations, we can see that the true statements about machines are I and III. Therefore, the correct answer is "I and III".

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Non-luminous objects can be seen because they reflect light. When light falls on an object, it either gets absorbed or reflected by the object's surface. Non-luminous objects do not emit light of their own, but they can still be seen because they reflect light that falls on them. This reflected light then enters our eyes, and we can see the object as a result.

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Y = sin π(150t - x/4)
comparing the above with the standard wave equation:
Y = A sin π ((2vt)/λ - (2x)/λ)
=> the phase difference x/4 = 2x/λ
∴ 1/4 = 2/λ => λ = 8cm
∴ 2/8x = 45o
∴ x/4 = 0.7071 => x = 4 x 0.7071
= 2.82
= 3cm

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The motion of smoke particles from a chimney is typical of random motion. Smoke particles move in random directions and with random speeds due to the turbulent nature of the flow. This is in contrast to circular motion, which involves objects moving in a circular path, rotational motion, which involves objects rotating around an axis, or oscillatory motion, which involves objects oscillating back and forth around a central point. In the case of smoke particles, they are subjected to various forces, including air resistance, wind, and changes in temperature, causing them to move in unpredictable paths. Therefore, the motion of smoke particles from a chimney is a clear example of random motion.

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The half-life of a radioactive element is the time it takes for half of its atoms to decay. So if the half-life of an element is 4 days, it means that after 4 days, half of the atoms will decay, and after another 4 days, half of the remaining atoms will decay, and so on. To find the fraction that has decayed in 16 days, we need to determine how many half-lives have occurred. Since the half-life of the element is 4 days, there are 4 half-lives in 16 days. Each half-life reduces the amount of radioactive material by half. So after 1 half-life, half of the material is left. After 2 half-lives, only a quarter of the material remains. After 3 half-lives, there is only an eighth left. After 4 half-lives, only a sixteenth is left. Therefore, the fraction that has decayed in 16 days is 1 - 1/16 = 15/16. So the answer is (15)/16.

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The main purpose of the transformer in an a.c radio set is to "step up" or "step down" the voltage of the alternating current that comes from the power outlet to a voltage level suitable for the operation of the radio. The voltage level required by the radio is typically different from the voltage level of the power outlet, and this is where the transformer comes in. It consists of two coils of wire wound around a core, and when an alternating current flows through one of the coils, it induces an alternating current in the other coil, but with a different voltage level. This allows the radio to receive the appropriate voltage for its operation. Therefore, the correct option is "step up the voltage" or "step down the voltage," depending on the specific application.

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R.D = (density of the subs)/density of water
19.2 =(P)/103; ∴P = 19.2 X 103
But Vol. = (Mass)/density = (2.4)/19.2 x 103
= 1.25 x 10-4 M3

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Gamma rays are neutral, meaning they have no electrical charge.

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The apparent depth of an object in water is the depth at which it appears to be when viewed from above the water's surface. The apparent depth of an object is affected by the refractive index of water, which is a measure of how much light is bent as it passes from one medium to another. When a submarine rises from a real depth of 80 m to 60 m, its apparent depth changes because the light rays from the submarine bend as they pass from water to air, causing the submarine to appear to be at a different depth than it actually is. To calculate the change in apparent depth, we need to use the formula: Change in apparent depth = real depth x (refractive index of water - 1) Plugging in the values, we get: Change in apparent depth = 80m x (4/3 - 1) = 80m x (1/3) = 26.67m Therefore, the change in apparent depth is 26.67 meters, which is closest to the option labeled "15m".

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The root mean square (rms) value of an alternating current (AC) is the equivalent steady or direct current (DC) value that gives the same energy to a resistor as does the AC. When an AC supply is connected to a lamp, the brightness of the lamp depends on the power being delivered to the lamp. If the lamp lights with the same brightness as it does with a 12 V DC battery, it means that the power being delivered to the lamp in both cases is the same. Therefore, the rms value of the AC supply must be the same as the DC voltage of the battery, which is 12.0 V. Thus, the answer is 12.0 V.

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When a charge moves through an electric field, the work done on the charge is given by the formula W = QV, where Q is the charge and V is the potential difference across which the charge moves. In this case, the potential difference across the charged plates is 3 kV, and the charge that is moved across the field is 600 µC (or 6.0 × 10^-4 C). Therefore, the work done is: W = QV = (6.0 × 10^-4 C)(3 × 10^3 V) = 1.8 J So the correct answer is 1.8J.

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IF the volume of gas is plotted against the reciprocal of pressure, the slope will be given as
Slope = V/1/P = P x V
thus the unit of the slope will be;

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Horizontal range = 3 x maxi. height
=> (U2Sin2θ) / g = (3 x U2sin2θ) / 2g

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The ammeter has a resistance of 5Ω and reads full scale when a current of 50 mA flows through it. To measure a current of 5A, a shunt resistor is required to be connected in parallel with the ammeter. We can use the formula I(total) = I(ammeter) + I(shunt), where I(total) is the total current, I(ammeter) is the current passing through the ammeter, and I(shunt) is the current passing through the shunt resistor. Since the ammeter reads full scale at 50 mA, it means that 50 mA will flow through the ammeter when a total current of 5 A is passing through the circuit. Therefore, we can substitute the values in the formula: 5A = 50mA + I(shunt) Solving for I(shunt), we get: I(shunt) = 5A - 50mA I(shunt) = 4.95A To find the value of the shunt resistor, we can use Ohm's Law: V = IR Where V is the voltage drop across the shunt resistor, I is the current passing through the shunt resistor, and R is the resistance of the shunt resistor. We know that the total current passing through the shunt and ammeter is 5A, and the current passing through the shunt is 4.95A. Therefore, the current passing through the ammeter is: I(ammeter) = 5A - 4.95A I(ammeter) = 0.05A We also know that the resistance of the ammeter is 5Ω. Therefore, the voltage drop across the ammeter is: V(ammeter) = I(ammeter) x R(ammeter) V(ammeter) = 0.05A x 5Ω V(ammeter) = 0.25V Since the shunt resistor is connected in parallel with the ammeter, the voltage drop across the shunt resistor will also be 0.25V. Therefore, we can use Ohm's Law to find the resistance of the shunt resistor: R(shunt) = V(shunt) / I(shunt) R(shunt) = 0.25V / 4.95A R(shunt) = 0.0505Ω Therefore, the value of the resistor required to adapt the ammeter to measure a current of 5 A is 0.0505Ω, which is closest to the option 0.05Ω.

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The electrolyte in the Nickel-Iron (NiFe) accumulator is potassium hydroxide solution. A NiFe battery is a rechargeable battery that is used for energy storage in renewable energy systems. It consists of a positive electrode of nickel hydroxide and a negative electrode of iron. Potassium hydroxide is used as an electrolyte in this battery. The electrolyte facilitates the movement of ions between the electrodes during the charge and discharge cycles. It allows the battery to store and release electrical energy as needed.

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The behavior of a solid cube of material when submerged in water depends on its density relative to that of water. If the cube is denser than water, it will sink. If it is less dense than water, it will float. If the density of the cube is equal to that of water, it will rest at an equilibrium position in water. Since the mass of the cube is 700g and its volume is 1000 cubic centimeters (since it is a 10cm cube), we can calculate its density as 0.7 g/cm^3. This is less than the density of water (which is approximately 1 g/cm^3), so the cube will float in water. Therefore, the answer is "the cube will float".

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To calculate the frequency of the photon, we can use the formula E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon. Rearranging the formula to solve for f, we get f = E/h. Given that the energy associated with the emitted photon when a mercury atom changes from one state to another is 3.3 eV, we first need to convert this to joules. We know that 1 eV is equal to 1.6 x 10^-19 J, so 3.3 eV is equal to 3.3 x 1.6 x 10^-19 J, which is 5.28 x 10^-19 J. We also know that Planck's constant, h, is 6.6 x 10^-34 J s. Plugging these values into the formula f = E/h, we get: f = (5.28 x 10^-19 J)/(6.6 x 10^-34 J s) = 8.0 x 10^14 Hz Therefore, the frequency of the photon is 8.0 x 10^14 Hz. Answer: 8.0 x 10^14 Hz

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In terms of dimension: power , P, = ML2T3
Force F1 = MLT-2; Vel, V, LT-1
From the above, => P = F x V
i.e, ML2T-3 = MLT-2 x LT-1
ML2T-3
=> 80,000 = F x 32

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The formula for resistivity is given by ρ = RA/l, where R is the resistance, A is the cross-sectional area of the conductor, and l is the length of the conductor. In this case, the diameter of the conductor is given as 1.00mm, so the radius is 0.5mm or 0.0005m. The cross-sectional area A of the conductor is given by A = πr^2 = π(0.0005m)^2 = 7.85 x 10^-7 m^2. The length of the conductor is given as 2.00m, and the resistance is given as 0.1Ω. Substituting these values into the formula for resistivity, we get: ρ = RA/l = (7.85 x 10^-7 m^2 x 0.1Ω) / 2.00m Simplifying this expression, we get: ρ = 3.925 x 10^-9 Ωm Therefore, the answer is option (D) 3.93 * 10^-8 Ωm.

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The question is asking for the focal length of a lens that will enable a person to focus on objects at a closer distance than they currently can. The given information is that the person's least distance of distinct vision (or near point) is 75 cm, which means that they can focus on objects only if they are beyond 75 cm from their eyes. To be able to focus on objects that are closer, the person needs a lens with a focal length such that the image of an object at a distance of 25 cm from the eye is formed at the person's least distance of distinct vision, which is 75 cm. This means that the lens should form a virtual image of the object at 25 cm on the other side of the lens, which then acts as the object for the eye. Using the lens formula, 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance (25 cm), and u is the object distance (the distance at which the virtual image is formed), we can find the value of u. 1/f = 1/v - 1/u 1/f = 1/25 - 1/u 1/f = (u - 25)/25u 25u/f = u - 25 25u = uf - 25f u = (25f)/(f + 25) Now, we know that the person's least distance of distinct vision is 75 cm, so the object distance u should be 75 cm. Substituting this in the above equation, we get: 75 = (25f)/(f + 25) Multiplying both sides by (f + 25), we get: 75f + 1875 = 25f Simplifying and solving for f, we get: f = 37.5 cm Therefore, the focal length of the lens required to reduce the person's least distance of distinct vision to 25 cm is 37.5 cm.

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A drop of petrol makes a finger colder than a drop of water would because petrol takes its latent heat of vaporization from the finger. When a liquid evaporates, it needs heat to convert from a liquid to a gas. This heat is called the latent heat of vaporization. When a drop of petrol evaporates from a finger, it takes heat from the finger to convert into a gas, thus making the finger feel colder. Water, on the other hand, also evaporates and takes heat from the finger, but it has a lower rate of evaporation than petrol and requires more time to evaporate, resulting in a slower cooling effect.

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Power, P = (V^2)/R, where V is the voltage and R is the resistance. Given that the p.d of the electric heater is 240 V and the total resistance is 960Ω, we can calculate the power rating of the heater as follows: P = (240^2)/960 P = 57600/960 P = 60 W Therefore, the power rating of the electric heater is 60 W. Answer option (D) is correct.

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In the stress - strain graph shown above, X represents the breaking point of the wire

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The process through which free electrons leave the surface of a hot metal is known as thermionic emission. When a metal is heated to a high temperature, some of its electrons gain enough energy to escape the metal's surface and become free electrons. This phenomenon is called thermionic emission, and it is used in devices such as vacuum tubes and cathode ray tubes. The other options, photon emission, photoemission, and electron emission, are different processes that involve the emission of electrons or photons but not specifically related to the process of free electrons leaving the surface of a hot metal.

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A p-n junction is formed by the junction of a p-type semiconductor and an n-type semiconductor. In order for current to flow across a p-n junction, it must be connected to a power source, such as a battery. The battery connection that allows current to flow across a p-n junction is called a "bias." There are two types of bias connections: forward bias and reverse bias. Forward bias occurs when the positive terminal of the battery is connected to the p-type semiconductor and the negative terminal is connected to the n-type semiconductor. This configuration allows current to flow across the junction easily. Reverse bias occurs when the positive terminal of the battery is connected to the n-type semiconductor and the negative terminal is connected to the p-type semiconductor. This configuration does not allow current to flow across the junction easily, and only a small leakage current is allowed. Therefore, the correct answer to the question is "forward biased."

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A thermos flask is a type of container that is designed to keep the temperature of its contents constant for as long as possible. It does this by preventing heat loss or gain through three different mechanisms: conduction, convection, and radiation. The flask consists of two walls with a vacuum between them, which minimizes heat transfer by conduction or convection. Additionally, the walls are coated with a reflective material to minimize heat transfer by radiation. Therefore, the correct answer is: "prevent heat loss or gain by conduction, convection, and radiation."

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M = Itz; z = (M)/It = (2)/0.5 x 3 x 60 x 60
= 3.703 x 10-4 gc-1
∴ M = Itz = 1.5 x 1 x 60 x 60 x 3.703 x 10-4
= 1.99962g.
=2.0g

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When a cell is connected to an external resistor, the power delivered to the resistor is maximum when the resistance of the external resistor matches the internal resistance of the cell. This is known as the maximum power transfer theorem. In this case, the internal resistance of the cell is given as "r" and the external resistance is "R". Therefore, the conductor for maximum power transfer would be when R = r, i.e., when the external resistor has the same value as the internal resistance of the cell. So the answer is: R = r.

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The theory of electronic conduction in solids that explains the properties of conductors, insulators, and semiconductors is known as the "band theory." This theory explains how electrons in a solid material are distributed in energy levels, or bands, which determine whether the material conducts electricity. Conductors have partially filled energy bands that allow electrons to move freely, while insulators have completely filled bands that prevent electrons from moving. Semiconductors have partially filled bands that can be easily manipulated to allow or prevent electron flow, making them useful in electronic devices. Therefore, the correct option is "band theory."

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At low humidity in an environment, the human skin usually becomes dry and rough. When there is low humidity, the air is dry and tends to absorb moisture from the skin, leaving it dry and rough. In contrast, high humidity conditions prevent moisture loss from the skin, resulting in a damp and smooth feel.

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V esc = √2Rg. =√2 x 6.4 x 106 x 10 = 1.13 x 104 ms-1

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Generally, period T = 1/f(reciprocal of frequency).
=> f = 1/T
And from the diagram, period T = 4s
∴ frequency, f = 1/T = 1/4 = 0.25 Hz

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An n- type semi conductor is usually formed by dopping the semi conductor(a four valent element)with a five valent
element.(arsenic and antimony)

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A constant volume thermometer is a type of thermometer that measures temperature by keeping the volume of the gas inside the thermometer constant. The thermometric property in this case would be the property that changes with temperature and is responsible for indicating the temperature on the thermometer. In the case of a constant volume thermometer, the thermometric property is the pressure of the gas. As the temperature increases, the average kinetic energy of the gas molecules increases, which in turn causes them to collide with the walls of the thermometer more frequently and with greater force. This results in an increase in the pressure of the gas, which is measured by the thermometer and used to indicate the temperature. Therefore, the correct option is "change in pressure."

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The equation for the energy required to heat a substance can be written as: Q = mcΔT where Q is the energy required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. Using the given information, we can solve for the energy required to heat the water from 52°C to 100°C: ΔT = 100°C - 52°C = 48°C Q = (2.5 kg)(4.2 x 10^3 J/kg°C)(48°C) = 5.04 x 10^5 J The power of the immersion heater is given as 2.0A at 240V, so the power output can be calculated as: P = IV = (2.0A)(240V) = 480W The time required to provide the energy needed to heat the water can be found using the formula: t = Q/P t = (5.04 x 10^5 J) / (480W) = 1.05 x 10^3 s Therefore, the time taken to boil the water is 1.05 x 10^3 seconds, which is equivalent to 17.5 minutes (since there are 60 seconds in a minute). The answer closest to this value is "1.05 x 10^3 s".

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Pressure of the Gas, P = A + h
= 76 + 10
86 cm Hg

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When an object is hung by a cord, the cord exerts a force on the object known as tension. In this case, the mirror is hung by a cord from a hook on the wall, and the cord makes an angle of 30 degrees with the horizontal. The weight of the mirror acts downwards, and the tension in the cord acts upwards to balance the weight. To find the tension in the cord, we need to use trigonometry. We can resolve the weight of the mirror into its horizontal and vertical components. The horizontal component is given by Wcosθ, where W is the weight of the mirror and θ is the angle between the cord and the horizontal. The vertical component is given by Wsinθ. In this case, the weight of the mirror is 75N, and the angle θ is 30 degrees. Therefore, the horizontal component is: Wcosθ = 75N x cos 30 = 64.95N The vertical component is: Wsinθ = 75N x sin 30 = 37.5N Since the mirror is in equilibrium, the tension in the cord must be equal to the vertical component of the weight: Tension = Wsinθ = 37.5N Therefore, the tension in the cord is 37.5N. The correct option is: 150N.

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When an AC (alternating current) voltage is applied to a capacitor, the current lags behind the voltage by 90 degrees. This means that when the voltage reaches its maximum value, the current is at its minimum value, and when the voltage is at its minimum value, the current is at its maximum value. However, even though the current is constantly changing, the net power consumed by the capacitor is zero. This is because the capacitor stores energy in its electric field when the voltage is increasing, and releases this stored energy when the voltage is decreasing. Therefore, over one complete cycle of the AC voltage, the energy stored in the capacitor is equal to the energy released, resulting in no net power consumption.

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When a thermometer is heated, both the glass and the liquid inside it will expand. However, if the glass expands more than the liquid, then the volume of the glass will increase more than that of the liquid. This will result in a decrease in the pressure inside the thermometer. As a result, the liquid will rise up in the stem of the thermometer to fill the partial vacuum created. Therefore, the correct option is "the liquid will rise up in the stem".

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In a closed tube, the fundamental note occurs when the length of the tube l = (λ)/4,
the first over tone occurs when the length of the tube l = (3)/4λ.
λ = (4)/3 l = (4)/3 x (33)/T = 44 cm

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A p-n junction diode is used as a rectifier in a circuit, either in a DC circuit or an AC circuit. A rectifier is a device that converts AC to DC by allowing the flow of current in one direction and blocking it in the other direction. This is achieved by the p-n junction diode, which has a unique property of allowing current to flow in only one direction. Therefore, the p-n junction diode is widely used as a rectifier in various electronic circuits.