JAMB UTME - Physics - 2005

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Marching soldiers crossing a suspension bridge are usually advised to break their steps to avoid damaging the bridge owing to resonance. The steps of the marching soldiers can set the bridge into vibration, and when the frequency of the bridge is equal to that of the steps of the soldiers, the resonance occurs,and at this resonance, the bridge vibrates violently with maximum amplitude, and can collapse.

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To determine the density of the mixture, we need to use the formula: density = mass/volume We can start by calculating the total mass of the two liquids, which is the sum of the masses of liquid W and liquid L: mass = density x volume For liquid W, mass = 200 kg/m^3 x 3 m^3 = 600 kg For liquid L, mass = 150 kg/m^3 x 7 m^3 = 1050 kg Total mass = 600 kg + 1050 kg = 1650 kg Next, we can find the total volume of the mixture by adding the volumes of the two liquids: total volume = 3 m^3 + 7 m^3 = 10 m^3 Now we can use the formula for density: density = mass/volume density of mixture = 1650 kg/10 m^3 = 165 kg/m^3 Therefore, the answer is option A: 165 kg/m^3.

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Normal reaction R = 3 kg x 10 = 30N
coefficient of friction , μ = 0.5
∴ acting frictional force = μR = 30 x 0.5
Pulling/sliding force F = 6kg x 10 = 60N.
∴ Net downward force = ma = 60 - 15.0
=> (3 + 6)a = 45
∴ 9a = 45
a = 5m/s2

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The thick glass tumbler cracks because of the uneven expansion of glass. When very hot water is poured into the glass tumbler, the inner layer of the glass heats up and expands faster than the outer layer. The thick glass tumbler has a larger volume than the thin glass tumbler, so the difference in expansion between the inner and outer layers is greater, which leads to uneven expansion and eventually causes the glass to crack. Glass is not a crystal, but it is a poor conductor of heat, which means it doesn't conduct heat as easily as metal, for example. However, this doesn't prevent the uneven expansion of glass when exposed to a sudden change in temperature.

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The sharpness of the boundary of the shadow of an object is determined by the rays of light passing through the object. The smaller the rays passing through , that is from a point source, the more sharp the shadow becomes, but the more the rays, that is rays from a large source, the more blurred the shadow becomes.

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The charges carriers in gasses are the ions

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According to Coulomb's law, the electrostatic force between two charges is inversely proportional to the square of the distance between them. Therefore, if the distance between two charges is increased by a factor of four, the force between them will decrease by a factor of 16 (4^2). Therefore, the answer is: 1/16 of its former value.

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In the circuit diagram of a transistor, the terminals P, Q, and R represent the emitter, base, and collector, respectively. The transistor is a three-layer semiconductor device that is used to amplify and switch electronic signals. The emitter is the terminal that emits current carriers, while the collector is the terminal that collects them. The base controls the flow of current carriers between the emitter and the collector by acting as a gate. When a small current flows into the base, it causes a much larger current to flow between the emitter and the collector, making the transistor useful for amplification and switching.

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The correct answer is "magnetic dipole". A magnetic dipole refers to a pair of poles of opposite sign, which are characteristic of all magnets. These poles cannot be separated from each other, as trying to do so would simply result in the creation of two smaller dipoles, each with its own north and south pole. This property is known as magnetic attraction and is what makes magnets so useful in many applications, such as in electric motors, generators, and MRI machines. The other options listed - magnetic octopole, magnetic monopole, and magnetic quadrupole - do not describe the property that explains why the north and south poles of a magnet cannot be separated.

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The half-life of a radioactive material is the amount of time it takes for half of the material to decay. In this question, the half-life is given as 50 days, which means that after 50 days, half of the material will have decayed. To find the time it takes for the material to reduce to 1/32 of its original number, we need to determine how many half-lives it will take to reach that point. 1/32 is equivalent to 2^(-5) since 2^5 = 32. So the material needs to decay 5 half-lives to reach 1/32 of its original number. Since the half-life is 50 days, it will take 50 x 5 = 250 days for the material to reduce to 1/32 of its original number. Therefore, the answer is 250 days.

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When impurities are added to semiconductors, a process called doping, the conductivity of the semiconductor increases. This is because impurities such as boron and phosphorus can either create additional positive or negative charge carriers in the material, thereby increasing the number of charge carriers available for conduction. The added impurities can also change the electronic properties of the material, making it easier for electrons to move through the crystal lattice. This increased conductivity allows the semiconductor to be used in electronic devices, such as transistors and diodes, where its electrical properties can be carefully controlled to perform specific functions. Therefore, the correct option is: increases.

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The effective capacitance in the circuit is given by:
1/C = 1/2 + 1/3 + 1/6 = 6/6
therefore C = 1μF or
1.0 x 10-6F.
Since C = Q/V, its implies that the charges Q, flowing in the circuit is given by Q = CV
= 1.0 x 10-6 x 12
= 12.0 x 10-6 Coulomb.
∴ P.d across the 6μF,

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For anybody falling through a viscous liquid, at its terminal velocity. the resultant force acting on its is zero. from the equation: Mg - v - u = 0. where v = viscous drag
U = upthrust Mg = weight of the body.
∴ 36 x 10 - 260 - U = 0
∴ U = 360 - 260 = 100N
Upthrust on the body = 100N.

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When a junction is reverse biased, a potential barrier is formed at the junction. This potential barrier prevents majority carriers from crossing the junction, so the current in a reverse-biased junction is due to minority carriers. The minority carriers (electrons in a p-type material and holes in an n-type material) can be thermally generated or arise from impurities. Therefore, the correct option is: minority carriers.

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The electric field intensity can be calculated using the formula: E = F/Q, where E is the electric field intensity, F is the force experienced by the charge Q. Substituting the values given in the question, we have: E = F/Q = (0.4N)/(10^-10C) Simplifying this expression, we get: E = 4.0 x 10^9 NC^-1 Therefore, the electric field intensity in the given place is 4.0 x 10^9 NC^-1, which is option D.

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for a real image 3 times the size of the object, it implies that the magnification 3 = v/u, 3 = 24/u, therefore 3u = 24, u = 8cm thus we have from the relation:m = (f)/(u)-f; that 3 = (f)/(8) - f. therefore f = 3(8-f) f = 24 - 3f ∴4f = 24; f = 6cm OR: (1)/(u) + (1)/(v) = (1)/(f).
(1)/(8) + (1)/(24) = (1)/(f)
therefore (3+1)/(24) = (1)/(f)
4/24=1/f;therefore 4f = 24
f = 6cm

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In general, the velocity of sound in air varies directly as the square root of temperature measured in kelvin.

That V$\propto \sqrt{T}⟹V^2\propto T.\text{Therefore}\frac{V_1^2}{T_1}=\frac{V_2^2}{T_2}\text{Thus Let}{V}_1=4m/s{T}_1=10K\text{Therefore}{V}_2=2V_1=8m/s⟹\frac{4^2}{10}=\frac{8^2}{T_2}{T}_2=\frac{64\times 10}{16}=40K{T}_2=4T_1$

Thus when the velocity of sound in air is doubled, it's absolute temperature will be quadrupled.

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The ray which causes gas molecules to fluoresce or glow is the cathode rays

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When a silicon material is doped with an element from group III of the periodic table, it creates a p-type semiconductor because group III elements have three valence electrons, and when they replace a silicon atom, they create a "hole" or vacancy in the crystal lattice, which behaves like a positively charged particle. On the other hand, when a silicon material is doped with an element from group V, it creates an n-type semiconductor because group V elements have five valence electrons, and when they replace a silicon atom, the extra electron creates a negatively charged particle called an "electron." Therefore, the most likely group of the element that was used to dope the silicon and form an n-type semiconductor is group V. Hence, the correct answer is option (I).

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The ray which causes gas molecules to fluoresce or glow is the cathode rays

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for a body projected at an angle θ to the horizontal, the time of the flight is given by T = (2u sin θ)/g =(2x 40)x sin (30)/10 =(2 x 40) x (0.5)/10 = 4.0secs.

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In an AC circuit with only a capacitor, the voltage lags behind the current by 90 degrees. In other words, the voltage reaches its maximum value a quarter of a cycle (90 degrees) after the current reaches its maximum value. This is because the capacitor stores energy in the form of an electric field, which takes time to build up as the current passes through it. As a result, the voltage across the capacitor lags behind the current flowing through it.

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Generally, from Hares Experiment, density is inversely proportional to height
i.e h ∝1/d; → h1d1 = h2d2
∴ 8 x 103 = h2 x 800

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The angle of minimum deviation in a prism occurs when the angle of incidence and angle of refraction are equal. This means that the light passes symmetrically through the prism, and the deviation is at its minimum. Looking at the graph, we can see that the angle of incidence where the deviation is at a minimum is approximately 25 degrees. Therefore, the answer is: 25o

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To calculate the time required to fully charge a battery, we need to use the formula: Time (in hours) = (Battery capacity in Ah) / (Charger rating in A) In this case, the battery capacity is given as 45 Ah, and the charger rating is 2.5 A. Substituting the values in the formula, we get: Time (in hours) = 45 Ah / 2.5 A Time (in hours) = 18 hours Therefore, it will take 18 hours to fully charge the battery using a 2.5 A charger. Hence, the correct option is: 18 hrs.

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Among the given options, only Sodium is a conductor. Conductors are materials that allow electric current to flow through them easily. They have low resistance to the flow of electric current. Sodium is a metal and metals are generally good conductors of electricity. Glass, wax, and plastic are insulators and do not allow electric current to flow through them easily. They have high resistance to the flow of electric current.

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F = $\frac{17}{sin60}=\frac{17}{0.866}$

= 20N

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A hygrometer measures the relative humidity, which is the amount of water vapor present in the air compared to the maximum amount that the air can hold at that temperature. The wet-bulb and dry-bulb thermometer are two types of hygrometers used to measure relative humidity. When the temperature difference between the wet and dry bulbs of a hygrometer is high, it means that the air is dry and has a low relative humidity. This is because when the air is dry, water evaporates faster from the wet bulb, causing a greater temperature difference between the two bulbs. So, the correct option is "the relative humidity is low."

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since resistance R = p (l)/a
= (4 x 10-7 x 20)/8.0 x 10-6
R = 1.0 Ω

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When inductors are arranged in series, their individual inductances add up to give the total inductance. Therefore, the total inductance of two inductors of inductances 3H and 6H arranged in series can be found by simply adding their inductances. Total inductance = 3H + 6H = 9H Therefore, the total inductance of the two inductors is 9H. Hence, the correct option is: - 9.0H

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To calculate the work done, we need to use the formula: Work = Force x Distance x Cosine(angle) In this case, the force is 100N, the distance is 8m, and the angle is 60 degrees. We can convert the angle to radians by multiplying it by pi/180: 60 degrees x pi/180 = pi/3 radians Now we can plug in the values and solve for work: Work = 100N x 8m x Cosine(pi/3) Work = 100N x 8m x 0.5 Work = 400J Therefore, the work done by the force of 100N inclined at an angle of 60 degrees to the object dragged horizontally to a distance of 8m is 400J. The answer is option D: 400J.

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The answer is displacement and torque. This is because both displacement and torque are vector quantities, meaning they have a magnitude and direction associated with them. Momentum, power, velocity, distance, acceleration, and speed are all examples of physical quantities that can be scalar or vector, but in this question, it is specified that the quantities must be vectors only.

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When a charged particle moves through a magnetic field perpendicular to its velocity, it experiences a force that is perpendicular to both its velocity and the magnetic field. The direction of the force is given by the right-hand rule, where the thumb points in the direction of the velocity, the fingers point in the direction of the magnetic field, and the palm shows the direction of the force. If two charged particles are projected into such a magnetic field and are deflected in opposite directions, this means that they experience forces in opposite directions. This can only happen if the particles have opposite charges, since opposite charges attract and like charges repel. Therefore, the statement that is true of the charge is: "the charge must be of opposite sign."

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For Hooke's law F = Ke

$⟹F/e=Kf1/e1=f2/e2\text{Let the original length}=t_0\text{therefore}e1=(36-t_0)cm;e2=(46-t_0)cm\text{if f1}=40N\text{f2}=60N\text{Then}\frac{40}{36-t_0}=\frac{60}{45-t_0}⟹40(45-t_0)=60(36-t_0)\text{therefore}1800-40t_{0}2160-60t_{0}60t_0-40t_0=2160-180020t_0=360t_0=18cm$

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To find the correct fuse rating, we can use the formula: Fuse rating = Power/Voltage Plugging in the given values, we get: Fuse rating = 2000 W / 250 V = 8 A Therefore, the correct fuse rating of the device is 8 A. Answer: 8 A

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The voltage ratio in a transformer is proportional to the number of turns in the primary coil and the number of turns in the secondary coil. Therefore, we can use this proportionality to find the number of turns in the secondary coil. The voltage ratio is 240V (primary) to 12V (secondary), which is equal to 20. So, the ratio of the number of turns in the primary coil to the number of turns in the secondary coil is also 20. We are given the number of turns in the primary coil as 4000, so we can find the number of turns in the secondary coil as follows: Number of turns in the secondary coil = (Number of turns in the primary coil) / (Voltage ratio) Number of turns in the secondary coil = 4000 / 20 = 200 Therefore, the number of turns in the secondary coil is 200.

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When a charged particle moves through a magnetic field, it experiences a magnetic force perpendicular to both the velocity of the particle and the direction of the magnetic field. The magnitude of the magnetic force is given by the equation F = qvB sin(theta), where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field, and theta is the angle between the velocity of the particle and the magnetic field. In this problem, a proton with a speed of 1.0 x 10^6 m/s is moving through a magnetic field of 1.0 T and experiences a magnetic force of magnitude 8.0 x 10^-14 N. We can use the equation F = qvB sin(theta) to solve for the angle between the proton's velocity and the field. Rearranging the equation, we get sin(theta) = F / (qvB). Substituting the given values, we get sin(theta) = (8.0 x 10^-14 N) / [(1.6 x 10^-19 C) x (1.0 x 10^6 m/s) x (1.0 T)] = 0.005. Taking the inverse sine of both sides, we get theta = sin^-1(0.005) = 0.29°. Therefore, the angle between the proton's velocity and the magnetic field is approximately 0.29° or very close to 0°, which is almost parallel to the field. Thus, the correct answer is option (C) 30°.

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If the string is in equilibrium, the the tension in the string Q = 4N + 5N = 9N

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The latent heat of vaporization of a substance is the amount of heat energy required to completely vaporize a unit mass of the substance at constant temperature and pressure, without a change in temperature. In this case, 10^6 J of heat energy is required to completely vaporize 2 kg of the liquid. We can find the latent heat of vaporization using the formula: Latent heat of vaporization = Heat energy required / Mass of substance Therefore, the latent heat of vaporization of the liquid is: 10^6 J / 2 kg = 5 x 10^5 J/kg So, the correct option is "5.0 x 10^5 J/kg".

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The question is asking about the mechanical advantage in an ideal wheel and axle system where R is the radius of the wheel and r is the radius of the axle. The mechanical advantage in this system is given by the ratio of the radius of the wheel to the radius of the axle, which is R/r. Therefore, the answer is (D) R/r.

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235U + 1n → 144Ba + 90Kr + 2x9205636
In the reaction above, balancing the left with the right, show that X is neutron

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The process described in the sentence is called "diffusion." Diffusion refers to the movement of molecules from a region of higher concentration to a region of lower concentration due to their random motion.

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Satellite communication network makes use of radio waves. Radio waves are a type of electromagnetic radiation, which are transmitted through the atmosphere and space. These waves have a longer wavelength and lower frequency than visible light, making them suitable for long-range communication. Radio waves can be transmitted from an Earth-based station to a satellite in orbit, which then relays the signal to another location on the ground. This technology is used for various communication purposes, such as television broadcasts, telephone calls, and internet services.

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According to the inverse square law, when the distance between two objects is halved, the force between them becomes four times stronger. Therefore, if a force of 200N acts between two objects at a certain distance apart and the distance is halved, the value of the force will be 4 times the original force, which is 800N. So the correct answer is option D: 800N.

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the power of a lens is defined as the reciprocal of the focal length ,expressed in metre.Mathematically, the power of a lens in dioptres is given by:(100)/f(in cm).
thus for lens of power of 4.0 dioptres we have that: (100)/(f) = +4.0
f= (100)/(4.0) = 25cm
= 0.25cm

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The process whereby a liquid turns spontaneously into vapor is called evaporation. This process occurs when the molecules at the surface of a liquid gain enough energy to break away from the liquid and become vapor. Evaporation is different from boiling, which occurs when a liquid is heated to its boiling point and the entire liquid turns into vapor. In evaporation, the liquid can turn into vapor even at temperatures below its boiling point, as long as the molecules at the surface of the liquid gain enough energy to break away and become vapor. Examples of evaporation include the drying of clothes on a clothesline, the formation of dew on grass in the morning, and the evaporation of sweat from our skin.