JAMB UTME - Physics - 2010

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The efficiency of a machine is the ratio of the output work to the input work. In this case, the output work is the work done on the load and the input work is the work done by the effort. Given that the velocity ratio of the machine is 6, this means that for every 6 meters of rope pulled by the machine, the load is raised by 1 meter. Therefore, the distance moved by the effort is 6 times the distance moved by the load. Hence, the input work done by the effort is: Input work = effort × distance moved by effort Input work = 400 N × 6 m Input work = 2400 J The work done on the load is the output work. Since the load is raised through a height of 1 m, the output work done on the load is: Output work = load × distance moved by load Output work = 800 N × 1 m Output work = 800 J Therefore, the efficiency of the machine is: Efficiency = output work / input work Efficiency = 800 J / 2400 J Efficiency = 1/3 Efficiency = 0.333 Converting to a percentage, we get: Efficiency = 0.333 × 100% Efficiency = 33.3% Therefore, the answer is 33.3%.

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C = C1 + C2 + C3
= 2 + 4 + 8 = 14μF
V = 6V
Energy = 1/2CV21/2 x 14 x 10-6 x 62
= 2.52 x 10-4 J

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The hydraulic press works on the principle of Pascal's law, which states that the pressure applied at any point in an enclosed fluid is transmitted uniformly in all directions. In this case, the pump piston exerts a pressure of 100 Pa on the liquid. This pressure is transmitted through the liquid and acts equally in all directions, including on the second piston. The force exerted on the second piston can be calculated using the formula: Force = Pressure x Area where pressure is the pressure applied by the pump piston, and area is the cross-sectional area of the second piston. Substituting the values given in the question, we get: Force = 100 Pa x 3 m^2 Simplifying the equation, we get: Force = 300 N Therefore, the force exerted on the second piston is 300 N.

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T = 27 + 273 = 300 K, volume, V = 10-2 m3 molar gass constant, R = 8.3 Jmol- 1k - 1 number of mole, n = 1
PV = NRT
i.e P = (NRT)/V = (1 x 8.3 x 300)/10-2
= 2.49 x 105 Nm-1

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When a thunderstorm happens, lightning produces a sudden shockwave that moves through the air as sound waves. Sometimes, these sound waves can bounce off of surfaces such as buildings or mountains and reflect back to the listener, which creates a prolonged sound called reverberation. Diffraction is the bending of sound waves around obstacles, and refraction is the change in direction of sound waves as they pass through materials of different densities. Superposition is the phenomenon that occurs when two or more waves meet and their amplitudes combine, creating a new wave. Therefore, the correct answer to the question is "reverberation."

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1/R = 1/8 + 1/8 = 2/8
∴ R = 4Ω
l/l1 = R/R1
(x)/(100-x) = 4/8
4(100-x) = 8x
400-4x = 8x
400 = 8x + 4x = 12x
x = 400/12 = 33.3cm

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To accurately measure the relative density of a substance in its powdered form, a density bottle is used. A density bottle is a specialized glass bottle designed to hold a specific volume of liquid at a specific temperature. By measuring the mass of an empty density bottle, then filling it with the powdered substance and measuring the mass again, the mass of the substance can be determined. The volume of the substance can then be determined by filling the density bottle with a liquid of known density, such as water, and measuring the mass again. The relative density can then be calculated as the mass of the substance divided by the mass of an equal volume of water.

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Energy stored in a stretched wire (strain energy)
= average force x extension
= (1)/2 Fe
= (1)/2 x 300 N (30.5 - 30.0) x 10-2 m
= (300)/2 x 0.5 x 10-2 = 0.75J

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When light travels from one medium to another medium of different optical density, its path gets bent at the interface between the two media. This phenomenon is called refraction. The bending occurs because the speed of light is different in each medium. The speed of light is slower in a denser medium than in a less dense one. When an object is placed in a denser medium like ice, the apparent depth of the object appears to be higher than its actual depth. The amount of apparent depth increase depends on the refractive index of the medium. The formula for the apparent depth is given by: Apparent depth = Actual depth / Refractive index Here, the actual depth is given as 10 cm, and the refractive index of ice is 1.50. By substituting these values in the formula, we get: Apparent depth = 10 / 1.50 = 6.67 cm Therefore, the answer is 6.67 cm.

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Short-sightedness, also known as myopia, is a condition where a person is able to see nearby objects clearly but distant objects appear blurry. It is caused by an elongated eyeball or a misshapen cornea, which causes the light entering the eye to focus in front of the retina instead of on it. To correct myopia, a concave lens is used. A concave lens is thinner at the center than at the edges, which causes the light entering the eye to diverge before it reaches the cornea, allowing the image to focus correctly on the retina. Therefore, the correct answer is concave lens.

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P: $\frac{\alpha h\theta }{\alpha h\theta }$

$\frac{2\times 3\times \theta }{3\times 4\times \theta }$

$\frac{1}{2}$

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The formula for the speed of a wave is given by v = λ/T, where v is the velocity, λ is the wavelength, and T is the period. We are given that the velocity is 420 m/s and the wavelength is 42 m. We can use these values to solve for the period. Rearranging the formula, we get: T = λ/v Substituting the given values, we get: T = 42 m / 420 m/s Simplifying, we get: T = 0.1 s Therefore, the period of the wave is 0.1 seconds. Answer: 0.1 s

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To calculate the acceleration of the car, we can use the formula: acceleration = (final velocity - initial velocity) / time In this case, the final velocity is 45 m/s, the initial velocity is 25 m/s, and the time is 10 seconds. Plugging these values into the formula, we get: acceleration = (45 m/s - 25 m/s) / 10 s acceleration = 20 m/s / 10 s acceleration = 2 m/s^2 Therefore, the acceleration of the car is 2 m/s^2. Answer: 2 ms-2

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A discharge tube is a device that consists of a partially evacuated tube containing a gas at low pressure, and electrodes at each end. When a high voltage is applied across the electrodes, the gas inside the tube becomes ionized and conducts electricity, producing a glowing plasma. In order for this to happen, most of the gas inside the tube needs to be pumped out, leaving only a small amount of gas at low pressure. Therefore, the correct answer is low pressure.

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When an electron drops from a higher energy level to a lower energy level, energy is released in the form of electromagnetic radiation (photons). The frequency of the radiation can be calculated using the formula: E = hf where E is the energy of the photon, h is Planck's constant, and f is the frequency of the radiation. In this question, the energy of the photon is equal to the difference between the initial energy level (zero) and the final energy level (5.44 x 10^-19 J): E = 5.44 x 10^-19 J Planck's constant is given as h = 6.6 x 10^-34 Js. Substituting these values into the formula, we get: 5.44 x 10^-19 J = (6.6 x 10^-34 Js) x f Solving for f, we get: f = (5.44 x 10^-19 J) / (6.6 x 10^-34 Js) f ≈ 8.24 x 10^14 Hz Therefore, the frequency of the emitted radiation is approximately 8.24 x 10^14 Hz, which is not one of the given options.

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When white light passes through a glass prism, it gets separated into its constituent colours, forming a rainbow-like spectrum. This is because different colours of light travel at different speeds through the glass due to the phenomenon of refraction. The amount of bending of the different colours of light is different because each colour has a different wavelength and thus travels at a different speed. Therefore, the dispersion occurs due to the different speeds of the colours in the glass.

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The current flow can be found using Ohm's Law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. First, we can find the total resistance of the circuit by adding the external resistor to the internal resistance of the cell: total resistance = external resistance + internal resistance = 2Ω + 4Ω = 6Ω Next, we can use Ohm's Law to find the current flow: current = voltage / resistance current = 12V / 6Ω = 2A Therefore, the current flow in the circuit is 2A. Answer: 2 A

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R = (Vg)/lg = G, where lg = current through galvanometer
R = resistance of the multiplier
G = resistance of the galvanometer
∴ G = (vg-R)/lg 5(1000/10) - 490 = 500 -490 = 10Ω

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When a container is filled with ice to the brim, some portion of the ice stays above the water level, and some portion of the ice stays below the water level. The portion of ice that is above the water level will melt and occupy the same amount of space as it did in its solid state. However, the portion of ice that is below the water level will melt and the resulting water will occupy less space than the ice did in its solid state because ice has a lower density than water. Therefore, when all the ice melts, the water level in the container will actually decrease slightly. Thus, the correct answer is: "the level of water drops."

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Energy consumed = power x time
= 200W x 24hr = 4800wh
= 4.8 kwh
But 1 kwh cost N40
∴ 4.8kwh costs 4.8 x 40
= N192

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When resistors are connected in parallel, the voltage across each resistor is the same, while the total current through the circuit is the sum of the current through each resistor. In this case, we have three 4Ω resistors connected in parallel, with a potential difference of 16 V applied across them. Using Ohm's Law, we can calculate the current through one resistor as I = V/R, where V is the voltage across the resistor, and R is the resistance of the resistor. For each of the three resistors, the current through them would be I = 16 V / 4 Ω = 4 A. Since the resistors are connected in parallel, the total current through the circuit is the sum of the current through each resistor, which is 4 A + 4 A + 4 A = 12 A. Therefore, the total current in the circuit is 12 A. Answer is correct.

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When an object is weighed at different locations on the Earth, its weight changes but its mass remains constant. Mass is the amount of matter present in an object, while weight is the force exerted on an object due to gravity. The weight of an object depends on the acceleration due to gravity, which varies depending on the location on the Earth. Therefore, is correct: the mass is constant while the weight varies.

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A vapor is said to be saturated when a dynamic equilibrium exists between liquid molecules and the vapor molecules. This means that the rate of evaporation of liquid is equal to the rate of condensation of vapor at a given temperature and pressure. In other words, the vapor is holding as much moisture as it can at that temperature and pressure. If the temperature or pressure changes, the saturation point will also change.

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Sound wave requires a material medium for its propagation. so when air is being pumped out the density of the medium is being reduced and the sound dies down. when all the air has been pumped out of the glass, no sound will be heard, as sound sound cannot travel through vacuum

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The surfaces of conveyor belts are made rough to prevent the loads from slipping. The rough surface provides more friction between the belt and the load, thereby preventing it from sliding off the conveyor belt. This is important for the safety of workers and to ensure that products are transported effectively without any damage or loss.

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Length of the string
L = y + x = 0.5m
∴ x = L - y
= distance moved in the direction of force (which is the weight) when the body is released But cos 60o = y/0.5
∴ y = 0.5cos60 = 0.5 x 1/2 = 0.25
∴ x = l - y = 0.5 - 0.25 = 0.25m
Work done = force x distance moved in the direction of force.
= 0.1 x 0.25 = 0.0252J

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The correct answer is "dew." Dew is formed when the temperature of the surface, such as grass or leaves, falls below the dew point temperature of the surrounding air. Water vapor in the air then condenses into small droplets on the surface. Dew is commonly seen in the early morning hours when the temperature is coolest and the humidity is highest. Hail, fog, and mist are different forms of precipitation or atmospheric moisture that form under different conditions.

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When a positively charged rod is brought near the cap of a positively charged electroscope, the leaves divergence will increase or become more pronounced. This is because the electroscope becomes more positively charged, which leads to increased repulsion between the leaves, causing them to move further apart. Therefore, the correct answer is "diverge".

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Looking at the velocity-time graph, we can see that the slope of the graph represents the acceleration of the car. When the slope is horizontal, the car has no acceleration (zero acceleration). Between points F and G, the slope is horizontal, which means the car has no acceleration during this time. Therefore, the correct statement is that the car has no acceleration between points F and G.

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IN magnetisation by stroking, the last touched has a pole opposite to that of the magnet used. Therefore, the poles T and V are N and N respectively

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Total inductance,L = L1 + L2 = m
15 + 5 = 20mH = (20)H/1000
1 = 5A
Energy of inductor, (1)/2 L I2
= (1)/2 X (20)/1000 X 5-2
= 0.25 J

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Radiation depends on nature of the surface area and temperature. It is independent of density.

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Transistors are electronic components that are commonly used for amplifying signals. They are capable of amplifying weak signals to higher levels and are therefore used in a variety of electronic devices such as radios, televisions, and computers. While transistors can be used for rectification of signals or conversion of a.c to d.c or d.c to a.c, their most common use is for signal amplification.

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The acceleration of free fall due to gravity is independent of mass of the body. Therefore, ignoring air resistance, which affects feather more than the stone, the stone and the feather will both reach the ground at the same time

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The velocity of sound in air, V∝√T, where T is absolute temperature
Thus V = K√T or K = V/T
V is independent of pressure and density at a fixed temperature.
∴ V1/√T1 = V2/√T2
T1 = 16 + 273 = 289K, V1 = 340ms-1
T2 = 127 + 273 = 400K, V2 = ?

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In the given diagram, the balls are in positions where they are influenced by gravity and potential energy. In order for a position to be considered a stable equilibrium position, the ball must return to that position when displaced slightly from it. Looking at the diagram, we can see that positions III, VI, and IX are at the bottom of valleys, where the balls would naturally come to rest and be in a stable equilibrium. Therefore, the correct answer is option III, VI, and IX.

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The pure semiconductor among the options given is "silicon". A semiconductor is a material that has an electrical conductivity between that of a conductor and an insulator. Silicon is a widely used semiconductor material in electronics due to its abundance and desirable electrical properties. Carbon is not a semiconductor, and transistors are electronic devices made using semiconductor materials, but they are not semiconductors themselves. Phosphorus is also not a pure semiconductor, but it can be used as a dopant to modify the electrical properties of a semiconductor material such as silicon.

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The film of a camera functions like the retina of the human eye. The retina is a layer of tissue at the back of the eye that contains photoreceptor cells, which detect light and convert it into neural signals that are sent to the brain for processing. Similarly, the film in a camera records the light that enters the camera and captures the image that is being taken. Both the retina and the camera film are critical in creating a visual representation of the world around us.

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The low freezing point of alcohol, -115°c enable low temperatures to be measured. mercury freezes at 39°c, and cannot be used in countries like Russia where winter temperatures of -40°c are common

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H eat generated in a wire carrying current, H = 12 Rt.
so, when voltage is high and current is low heat generated in the wire will be minimal.
Therefore, high voltage and low current prevent overheating of the coil.

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The density of an object is equal to its mass divided by its volume. In this case, the density of the oil after frying is 0.4 kg/m³ and its volume is 20 m³. Therefore, we can calculate the mass of the oil as: mass = density x volume = 0.4 kg/m³ x 20 m³ = 8 kg Now we can use the formula for density to find the initial volume of the oil, assuming no loss of oil due to spillage. If the initial density of the oil was 0.8 kg/m³, then we can find the initial volume as: initial volume = mass / initial density = 8 kg / 0.8 kg/m³ = 10 m³ Therefore, the initial volume of the oil was 10 m³. The correct answer is "10 kgm-3".

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When two different materials are heated through the same temperature difference, the length of the materials changes. This change in length due to temperature is called thermal expansion. The amount of thermal expansion depends on the material's coefficient of linear expansion, which is denoted by alpha (α). From the problem, we know that the ratio of the linear expansivities of P to Q is 2:3, which means that alpha of P is (2/3) times alpha of Q. Also, the ratio of the lengths of P to Q is 3:4. Let's assume the original lengths of P and Q are 3x and 4x respectively. When heated, the increase in length of P will be α_P × l₁ = (2/3)α_Q × l₁ = (2/3)α_Q × (3x), since length of P is 3x and the ratio of linear expansivities is 2:3. Similarly, the increase in length of Q will be α_Q × l₂ = α_Q × (4x), since length of Q is 4x. Now, to find the ratio of increase in length of P to Q, we divide the increase in length of P by the increase in length of Q: [(2/3)α_Q × (3x)] / [α_Q × (4x)] = (2/3) × (3/4) = 1/2 Therefore, the ratio of increase in length of P to Q is 1:2. Hence, the answer is (C) 1:2.

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The instrument used in measuring relative density is hydrometer

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The slope of the graph of the mass deposited against the quantity of electricity in Faraday's law of electrolysis gives the electrochemical equivalent. The electrochemical equivalent is a measure of the amount of substance produced by the passage of one coulomb of electricity through an electrolyte. In other words, it represents the amount of substance that is deposited or liberated at an electrode per unit charge passed through the electrolyte during electrolysis. Therefore, the correct option is "the electrochemical equivalent."

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The velocity of the faster car as measured by an observer in the slower car can be found by taking the difference between the velocities of the two cars. Since both cars are moving in the same direction, the relative velocity of the faster car with respect to the slower car is given by: 130 km/h - 100 km/h = 30 km/h Therefore, the answer is: 30 kmh-1

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Heat is a type of energy that is generated by the movement of atoms and molecules within an object. When an object is hot, it radiates this heat energy outwards in the form of electromagnetic waves. These waves are known as infrared rays. Therefore, the correct option is "infrared rays."