JAMB UTME - Physics - 2013

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Total internal reflection occurs when a light ray travels from a medium with a higher refractive index to a medium with a lower refractive index at an angle greater than the critical angle. At the interface between the two media, the light ray is refracted in a way that it bends away from the normal. If the angle of incidence is increased to a critical angle, the refracted angle becomes 90 degrees, and the light ray is reflected back into the first medium at the same angle. In the case of the options given, total internal reflection will not occur when light travels from water to air or glass to air because air has a lower refractive index than both water and glass, so the angle of incidence would never be greater than the critical angle. However, total internal reflection can occur when light travels from water into glass or glass into water because glass has a higher refractive index than water. Therefore, if the angle of incidence is greater than the critical angle, total internal reflection will occur.

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The angular magnification of a microscope is given by the product of the linear magnifications of the objective and the eyepiece lenses. In this case, the linear magnification of the objective lens is 4 and that of the eyepiece lens is 7. Therefore, the angular magnification of the microscope is: Angular magnification = Linear magnification of objective lens × Linear magnification of eyepiece lens = 4 × 7 = 28 Hence, the angular magnification of the microscope is 28. This means that the microscope magnifies the image 28 times more than the original size.

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The pressure at a given depth below the sea level can be calculated using the equation of hydrostatic pressure, which states that the pressure at a point in a fluid is equal to the weight of the fluid above it. In this case, the density of sea water is given as 1013 kg/m^3, and the acceleration due to gravity is given as 10 m/s^2. The pressure at a depth of h below the sea level can be calculated as: P = ρ * g * h where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth below the sea level. We are looking for the depth at which the pressure changes by one atmosphere, which is equal to 0.01 x 10^5 N/m^2. So, we can set up an equation to solve for h: 0.01 x 10^5 N/m^2 = ρ * g * h Solving for h, we get: h = 0.01 x 10^5 N/m^2 / (ρ * g) = 0.01 x 10^5 N/m^2 / (1013 kg/m^3 * 10 m/s^2) = 10.0 m So, the depth below the sea level at which the pressure changes by one atmosphere is 10.0 m.

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The question is asking about the ratio of specific heat capacities of two liquids, X and Y, which have the same mass and are supplied with the same amount of heat. If the temperature rise in X is twice that of Y, then we can use the formula: Q = mcΔT where Q is the amount of heat supplied, m is the mass of the liquid, c is the specific heat capacity, and ΔT is the change in temperature. Since both liquids have the same mass and are supplied with the same amount of heat, we can write: mcΔTx = mcΔTy where ΔTx is the temperature rise in X and ΔTy is the temperature rise in Y. We are given that ΔTx = 2ΔTy, so we can substitute this into the equation to get: mc(2ΔTy) = mcΔTy Simplifying this equation gives: 2cX = cY where cX is the specific heat capacity of liquid X and cY is the specific heat capacity of liquid Y. Therefore, the ratio of specific heat capacity of X to that of Y is 2:1, which means the correct option is: 2:1

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The coefficient of friction between two perfectly smooth surfaces is zero. This is because friction is the force that opposes motion between two surfaces in contact, and it arises due to irregularities in the surfaces that create interlocking between them. In the case of perfectly smooth surfaces, there are no irregularities or interlocking, so there is no friction. Therefore, the correct option is "zero".

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To solve this problem, we need to use the conservation of mechanical energy principle, which states that the total mechanical energy of a system (the sum of potential and kinetic energy) remains constant if there are no external forces acting on the system. Let's first calculate the kinetic energy of the moving object. The kinetic energy formula is KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity. Since we are not given the mass of the object, we can assume it to be 1 kg (since the mass does not affect the height at which the other object must be situated). Therefore, the kinetic energy of the moving object is: KE = 0.5 * 1 * (5)^2 = 12.5 Joules Now, we need to find the height at which the other object must be situated to have the same amount of potential energy as the kinetic energy of the moving object. The potential energy of an object is given by the formula PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height at which the object is situated. We want to find the height h at which PE = KE, so we can equate the two formulas: m * g * h = 0.5 * m * v^2 Canceling out the mass on both sides, we get: g * h = 0.5 * v^2 Plugging in the values, we get: h = (0.5 * v^2) / g h = (0.5 * 5^2) / 9.8 h = 1.275 m Therefore, the height at which the other object must be situated to have the same amount of potential energy as the kinetic energy of the moving object is 1.275 meters. The closest option to this answer is 1.3m, so the correct answer is (C) 1.3m.

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When a charge moves through an electric circuit in the direction of an electric force, it gains kinetic energy and loses potential energy.
Electric potential energy is the energy stored in a system due to the arrangement of charges, while kinetic energy is the energy of motion. When a charge moves in the direction of an electric force, it loses potential energy because it moves from a higher potential energy to a lower potential energy. At the same time, it gains kinetic energy because it accelerates due to the electric force acting on it.
Therefore, the correct option is "gains kinetic energy and loses potential energy."

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We can use the formula: mass = density × volume to solve this problem. We need to find the volume of alcohol that has the same mass as 4.2 m³ of petrol. First, let's calculate the mass of 4.2 m³ of petrol: mass of petrol = density of petrol × volume of petrol = (7.2 × 10³ kg/m³) × (4.2 m³) = 30,240 kg Next, let's find the volume of alcohol that has the same mass as the petrol: mass of alcohol = mass of petrol density of alcohol × volume of alcohol = density of petrol × volume of petrol volume of alcohol = (density of petrol / density of alcohol) × volume of petrol = (7.2 × 10³ kg/m³) / (8.4 × 10² kg/m³) × (4.2 m³) = 3.6 m³ Therefore, the volume of alcohol that has the same mass as 4.2 m³ of petrol is 3.6 m³, which is option C.

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The maximum current that an electric device can take can be calculated using Ohm's law, which states that the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance. In this case, the electric device is rated 2000W and 250V, so we can calculate the resistance using the power formula: P = IV where P is the power in watts, I is the current in amperes, and V is the voltage in volts. Rearranging the equation to solve for I, we get: I = P/V = 2000W / 250V = 8 A So, the maximum current that the electric device can take is 8 A.

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The energy of a photon can be calculated using the formula: Energy = Planck's constant × frequency where frequency = speed of light / wavelength. In this question, the wavelength of the photon is given as 10^-10 m, and the values of Planck's constant (h) and the speed of light (c) are also given. So, we can calculate the frequency of the photon as: frequency = c / wavelength = (3.0 x 10^8 m/s) / (10^-10 m) = 3.0 x 10^18 Hz Now, we can use the above formula to calculate the energy of the photon as: Energy = h × frequency = (6.63 x 10^-34 J s) × (3.0 x 10^18 Hz) = 1.89 x 10^-15 J Therefore, the energy of the photon is 1.89 x 10^-15 J, which is closest to option A: 2.0 x 10^-15 J.

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T2 = $\sqrt{\frac{L^2\times T_1^2}{L_1}}$

= $\sqrt{\frac{0.8\times 2^2}{0.4}}$

= 2$\sqrt{2}s$

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M.A. = $\frac{Eff\times V.R.}{100}$

M.A. = $\frac{90\times 2}{100}$

M.A. = 1.8

E = $\frac{L}{M.A.}$

E = $\frac{180}{1.8}$

E = 100N

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Scalar physical quantities are those that can be described only by their magnitude, without specifying any direction. For example, mass, temperature, and speed are scalar quantities. Out of the given options, the pair of physical quantities that are scalar only are volume and area. Both of these quantities can be described only by their magnitude, without any reference to direction. On the other hand, moment and momentum, length and displacement, and impulse and time are all vector quantities. These physical quantities have both magnitude and direction. Moment is the product of a force and its perpendicular distance from a reference point. Momentum is the product of an object's mass and velocity. Both of these physical quantities have direction and magnitude. Length and displacement are also vector quantities. Displacement is the change in position of an object from one point to another, and it has both magnitude and direction. Length, on the other hand, is the distance between two points, and it too has both magnitude and direction. Impulse and time are also not scalar quantities. Impulse is the product of force and time, and it has both magnitude and direction. Time, although it is a one-dimensional quantity, does not have direction but it has magnitude. Therefore, the correct answer is "volume and area". These are the only scalar physical quantities out of the given options.

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Wt loss = mg - m (g - a)

= 70 x 10 - 70 (10 - 1.5) = 105N

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The question is asking about the factor(s) that determine the number of photo-electrons ejected per second in photo-emission. In photo-emission, electrons are emitted from a metal surface when light is shone on it. The energy of the photons in the light must be greater than the work function of the metal for this to occur. So, the answer to the question is that the number of photo-electrons ejected per second depends on the work function of the metal. The other options given are also related to photo-emission, but do not directly affect the number of photo-electrons ejected per second. The frequency of the beam and the threshold frequency of the metal are related to the minimum energy required for photo-emission to occur, while the intensity of the beam affects the number of photons hitting the metal surface, but not the number of electrons ejected per second.

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The problem can be solved using the equation: v^2 = u^2 + 2as Where: v = final velocity (0 m/s) u = initial velocity (20 m/s) a = acceleration (-2 m/s^2) s = distance traveled (unknown) Rearranging the equation to solve for s: s = (v^2 - u^2) / 2a Substituting the given values: s = (0^2 - 20^2) / 2(-2) s = 200 m Now, we can use the equation: v = u + at Where: v = final velocity (0 m/s) u = initial velocity (20 m/s) a = acceleration (-2 m/s^2) t = time (unknown) Solving for t: 0 = 20 - 2t t = 10 s Therefore, the time required to bring the train to a complete halt is 10 seconds. The correct option is 10s.

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The wave that travels through stretched strings is a mechanical wave. Mechanical waves are waves that require a medium, such as a solid, liquid, or gas, to travel through. In the case of a wave traveling through a stretched string, the string serves as the medium. As the string is stretched and then released, it vibrates back and forth, creating a disturbance that propagates along the length of the string. This disturbance is what we perceive as a wave. The wave will have properties such as wavelength, frequency, and amplitude, which can be measured and used to describe the wave. Electromagnetic waves, on the other hand, do not require a medium to travel through and can travel through a vacuum. Examples of electromagnetic waves include radio waves, microwaves, and light. Seismic waves are waves that travel through the Earth's crust and are associated with earthquakes.

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When a brick is taken from the Earth's surface to the Moon, its mass remains constant. Mass is an intrinsic property of an object and does not depend on the object's location or surroundings. However, the weight of the brick will change. Weight is the force exerted on an object due to gravity, and it depends on both the object's mass and the strength of the gravitational field it is in. The gravitational field on the Moon is weaker than the gravitational field on Earth, so the weight of the brick will be less on the Moon than it was on Earth. To summarize, the mass of the brick is the same on Earth and the Moon, but its weight will be less on the Moon due to the weaker gravitational field.

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A transverse wave and a longitudinal wave traveling in the same direction in a medium differ essentially in their direction of vibration of the particles of the medium. In a transverse wave, the direction of vibration of the particles is perpendicular to the direction of wave propagation. This means that the particles move up and down as the wave moves forward. An example of a transverse wave is a wave on a string, such as a wave you might see in a flag flapping in the wind. In a longitudinal wave, the direction of vibration of the particles is parallel to the direction of wave propagation. This means that the particles move back and forth along the direction of wave propagation. An example of a longitudinal wave is a sound wave, where the particles of the medium are compressed and rarefied as the wave moves through the medium. The other two options, frequency and amplitude, describe different characteristics of a wave, but do not describe the essential difference between a transverse wave and a longitudinal wave.

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The sentence "The particle nature of light is demonstrated by the photoelectric effect" means that light can behave as particles, which is demonstrated by the photoelectric effect. The photoelectric effect is a phenomenon where electrons are emitted from a material when light is shone on it, and this can only be explained by treating light as particles, or photons. Therefore, the correct answer is "photoelectric effect". Options (b) "speed of light", (c) "colours of light", and (d) "diffraction of light" are not directly related to the particle nature of light.

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F = 50Cos30o = 43.3

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The height of the image of the man on the screen can be found using the principles of optics and the formula for the size of an image formed by a pinhole camera. In a pinhole camera, light from a distant object passes through a small hole and forms an inverted image on a screen located on the other side of the hole. Let's call the height of the man H and the height of the image of the man on the screen I. The distance between the man and the hole is d1 = 3m and the distance between the hole and the screen is d2 = 0.1m. Using the formula for the size of an image formed by a pinhole camera, we have: I/H = d2/d1 Substituting the values, we get: I/1.5 = 0.1/3 Solving for I, we get: I = 1.5 * 0.1/3 = 0.05 m So, the height of the image of the man on the screen is 0.05m.

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The boiling point of pure water is 100°C at normal atmospheric pressure, which is defined as 101.3 kPa or 1 atm. The pressure at 30m below sea level is greater than normal atmospheric pressure due to the weight of the water above it. This increased pressure will raise the boiling point of the water. This means that the water will need to be heated to a temperature higher than 100°C in order to boil. Therefore, the boiling point of pure water when it is heated in a place 30m below sea level will be higher than 100°C.

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The power of the pump can be calculated using the formula: Power = (Work done)/time where Work done = force x distance In this case, the force is the weight of the water (5000 kg) and the distance is the height to which it is lifted (60 m). We can calculate the work done as: Work done = force x distance = 5000 kg x 9.81 m/s^2 x 60 m (using the acceleration due to gravity, g = 9.81 m/s^2) = 2,943,000 J (joules) The time taken is 15 minutes, which is equivalent to 900 seconds. Therefore, the power of the pump can be calculated as: Power = Work done / time = 2,943,000 J / 900 s = 3270 J/s This answer is not listed among the options. However, we can convert J/s to the more commonly used unit of power, watts (W), by dividing by 1 watt = 1 J/s. Therefore, the power of the pump is: Power = 3270 J/s = 3270 W This answer is not exactly the same as any of the options listed, but it is closest to which is 3.3 x 10^3 J/s or 3,300 W.

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The correct answer is: "dissolved substances on the boiling point". When salt (or any other substance) is dissolved in water, it raises the boiling point of the water. This means that the water needs to be hotter before it can boil. Therefore, when you cook food in salt water, the water will reach boiling point at a higher temperature than pure water. This higher temperature means that the food will cook quicker because it is exposed to more heat energy in a shorter amount of time. So, when you add salt to water, it increases the boiling point of the water and allows it to reach a higher temperature, which in turn makes the food cook quicker. This is why it's important to follow the recipe and add the right amount of salt when cooking!

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To convert a galvanometer to a voltmeter, a high resistance is connected to it in series. A galvanometer is an instrument used to measure small electric currents. It works by measuring the deflection of a coil of wire in a magnetic field. A voltmeter, on the other hand, is used to measure voltage or potential difference in a circuit. To convert a galvanometer to a voltmeter, we need to add a resistor in series with the galvanometer. The resistor will increase the overall resistance of the circuit, which will reduce the current flowing through the galvanometer. This is important because a galvanometer is designed to measure small currents, and if too much current flows through it, it can be damaged. By adding a resistor in series with the galvanometer, we can create a voltage divider circuit. The voltage drop across the resistor will be proportional to the voltage drop across the entire circuit, which includes the galvanometer. By choosing the appropriate value for the resistor, we can scale the voltage drop across the galvanometer to the desired level, allowing us to use the galvanometer as a voltmeter. The resistor used should have a high resistance, typically on the order of thousands or millions of ohms. This is because we want to minimize the amount of current flowing through the galvanometer while still allowing enough current to flow to make a measurement. Connecting a low resistance in series or a high resistance in parallel will not work to convert a galvanometer to a voltmeter because these configurations will not create a voltage divider circuit that scales the voltage drop across the galvanometer to the desired level. Therefore, the correct answer is high resistance is connected to it in series.

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To calculate the cost of keeping the bulbs lit for 10 hours, we need to determine the total energy consumed by all the bulbs in the house, expressed in units of electricity. The 40W bulbs consume 40/1000 = 0.04 kW per hour, while the 100W bulbs consume 100/1000 = 0.1 kW per hour. To calculate the total energy consumed by all the bulbs, we can multiply the power consumption of each bulb by the number of bulbs and add the results: Total power consumption = (10 bulbs x 0.04 kW/bulb) + (5 bulbs x 0.1 kW/bulb) = 0.4 kW + 0.5 kW = 0.9 kW Next, we need to calculate the total energy consumed over 10 hours: Total energy consumed = 0.9 kW x 10 hours = 9 kWh Finally, to calculate the cost of this energy, we need to multiply the total energy consumed by the cost per unit of electricity: Cost of energy = 9 kWh x 5N/kWh = N45 Therefore, the cost to the owner of the house to keep the bulbs lit for 10 hours is N45.

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When a ray of light passes through the center of curvature of a concave mirror, it reflects back on itself and retraces its path. Therefore, the angle of incidence is equal to the angle of reflection, and both angles are measured with respect to the normal, which is a line perpendicular to the surface of the mirror at the point of incidence. Since the ray of light is passing through the center of curvature, it is hitting the mirror at a right angle to the normal, which means that the angle of incidence is 0 degrees. According to the law of reflection, the angle of reflection is also 0 degrees, so the ray of light is reflected back on itself in the same direction that it came from. Therefore, the correct answer is 0 degrees.

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$E_3=\frac{E}{n^2}$

$E_3=\frac{-24.8}{3^2}$

$E_3=2.75eV$

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r = $\frac{E}{I}-R$

r = $\frac{1.5}{0.3}-1$

r = 4$\Omega$

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The fraction of the volume of the cork that will be immersed in the liquid is 0.2. This can be determined by using the concept of buoyancy. Buoyancy is the upward force exerted on an object submerged in a fluid, and it is equal to the weight of the fluid displaced by the object. If the upward force of buoyancy is greater than the downward force of gravity acting on the object, then the object will float. The volume of the cork that is immersed in the liquid is equal to the volume of the fluid displaced by the cork. The density of the fluid is greater than the density of the cork, so the volume of the fluid displaced is less than the volume of the cork. Therefore, only a fraction of the cork's volume will be immersed in the liquid, and that fraction is 0.2.

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The mechanism of heat transfer from one point to another through the vibration of the molecules of the medium is called conduction. This is because in conduction, heat energy is transferred through a material without the bulk motion of the material itself. The molecules in the material vibrate, and this vibration is passed on to neighboring molecules, causing a flow of heat energy from hotter to cooler regions of the material.

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The bond between silicon and germanium is covalent. Covalent bonds occur when atoms share electrons to fill their outermost electron shells. In this case, silicon and germanium share electrons to form a strong bond between them. Covalent bonds are typically very strong and stable, which makes silicon-germanium alloys useful in electronics and other applications that require high-performance materials.

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First let's find z

z = $\frac{M}{It}$

z = $\frac{1.8}{2.5\times (3\times 60\times 60)}$

Therefore, the new M equals

M = zIt

M = $\frac{1.8\times 4\times 4.8\times 60\times 60}{2.5\times 3\times 60\times 60}$

M = 4.6g

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The mass of an object is a measure of its amount of matter, and it is independent of its location. So, when a brick is taken from the Earth's surface to the moon, its mass remains constant. It does not become zero, reduce, or increase. The weight of the brick, which is the force exerted on the brick due to gravity, would change because the gravitational field strength is different on the moon than it is on Earth. However, the mass of the brick remains the same.

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The force acting on an electron in an electric field can be calculated using the formula F = qE, where F is the force, q is the charge of the electron, and E is the electric field intensity. So, in this case, the force acting on an electron of charge 1.5 x 10^-19 C placed in an electric field of intensity 10^5 V/m can be calculated as: F = qE = 1.5 x 10^-19 C * 10^5 V/m = 1.5 x 10^-14 N Therefore, the force acting on the electron is 1.5 x 10^-14 N, which is closest to the option 1.5x10-14N.

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Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. In other words, as the voltage increases, so does the current, and vice versa, as long as the temperature and other physical conditions remain constant. With that said, metals are the materials that most closely obey Ohm's law because their electrical resistance does not vary significantly with changes in temperature or current. Conductors made of metals such as copper, silver, and gold have a nearly constant resistance, and their resistance does not depend on the amount of current flowing through them. On the other hand, electrolytes, diodes, and glass are materials that do not obey Ohm's law. Electrolytes are materials that conduct electricity when dissolved in water, and their resistance depends on the concentration of ions in the solution. Diodes are electronic components that only allow current to flow in one direction, and their resistance depends on the voltage applied to them. Glass is an insulator and has an extremely high resistance, which does not vary significantly with changes in voltage or current.

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W = $\frac{1}{2}Fe$

W = $\frac{1}{2}\times 20\times 0.05$

W = 0.5J

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$L_2=L_1+\alpha ({\theta }_2-{\theta }_1)$

= 100 + 0.00002(-10-30) = 99.92

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When a beam of white light passes through a triangular prism, it refracts or bends due to the change in speed of the light as it enters the prism. This causes the different colors of the white light to separate because each color has a slightly different wavelength, and thus a slightly different refractive index. This separation of colors is called dispersion, and it creates a spectrum of colors, from red to violet. The angle of deviation is the angle between the incident ray of white light and the emergent ray of the dispersed colors. This angle is different for different colors because each color is refracted at a slightly different angle. In a triangular prism, the angle of deviation increases with increasing wavelength of light. This means that the color with the longest wavelength, which is red, is refracted the least, while the color with the shortest wavelength, which is blue or violet, is refracted the most. Therefore, the correct option is "red → green → blue", which indicates the order of increasing wavelengths and increasing angles of deviation.

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W = $\frac{W_1\times V_1}{V_2}$

W = $\frac{10\times 0.6}{1.2}$

W = 6.0 x 10 4J

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The frequency of the fifth overtone of a sonometer with a fundamental frequency of 450Hz is 2700Hz. An overtone is a higher frequency harmonic that is present in a complex waveform. In a sonometer, the fundamental frequency is the first overtone, and the higher overtones are multiples of the fundamental frequency. The fifth overtone would be 5 times the fundamental frequency, which is 5 * 450Hz = 2700Hz.

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At 100oC = 400

Therefore,

At 20oC = $\frac{400}{100}\times \frac{20}{1}$ = 80