JAMB UTME - Physics - 1993

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$\theta$ = tan-1$\frac{3}{7}$

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volume of object = $\frac{400\times {10}^{-2}}{600}$

= 0.00067m3

volume of paraffin displaced = $\frac{1}{2}$ x 0.00067

= 0.00034m3

mass of paraffin = 900 x 34 x 10-5

= 0.3kg

weight of paraffin = 0.3 x 10

= 3N = upthrust = tension in the string

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The correct option that describes the energy changes in the generation of light by a hydroelectric power station is: "Potential energy → mechanical energy → electrical energy → light." This is because a hydroelectric power station converts the potential energy of water stored at a certain height into mechanical energy by allowing the water to flow down through turbines. The turbines are connected to generators that convert the mechanical energy into electrical energy. Finally, the electrical energy is used to power light bulbs and other electrical devices, producing light.

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V.R = $\frac{1}{sin\theta }$

= 10

sin = $\frac{1}{10}$

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The expression that gives the linear magnification produced by a concave mirror of radius of curvature r, if U and V are the object and image distances respectively is "-V/U" or "V/U = -h'/h", where "h'" is the height of the image and "h" is the height of the object. This is a well-known formula in optics, which states that the magnification produced by a mirror is equal to the ratio of the height of the image to the height of the object. Moreover, the negative sign indicates that the image is inverted with respect to the object. None of the options provided match this formula exactly. Option "Vr" and "V/r-1" involve only the image distance and the radius of curvature, but not the object distance, which is necessary to calculate the magnification. Option "Ur" and "U/r-1" involve only the object distance and the radius of curvature, but not the image distance. Finally, option "2Vr" and "2U/r-1" involve a factor of 2 that is not present in the formula for magnification.

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The atomic number of an element is the number of protons in its nucleus, while the mass number is the sum of protons and neutrons. In this question, the element X has an atomic number of 88 and a mass number of 226, which means it has 88 protons and (226-88) = 138 neutrons. When element X emits two beta particles and an alpha particle, it undergoes radioactive decay. A beta particle is an electron emitted from the nucleus, while an alpha particle is a particle consisting of two protons and two neutrons. The emission of a beta particle increases the atomic number by 1, while the emission of an alpha particle decreases the atomic number by 2 and the mass number by 4. Therefore, after emitting two beta particles and an alpha particle, the new element Z will have an atomic number of (88+2-2) = 88 and a mass number of (226+4-2x2) = 222. The symbol for this element Z is 22288Z, which means it has 88 protons and (222-88) = 134 neutrons. Therefore, the correct answer is 22288Z.

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L = - $\lambda$ $\Rightarrow$4L = 3 $\lambda$

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$\frac{4}{3}$ = $\frac{sin30}{sinr}$

r = 22oC

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The linear expansivity (α) of a material is defined as the change in length per unit length per degree Celsius (or Kelvin) change in temperature. In this problem, we are given the initial length of the metal rod (800 mm), the change in temperature (∆T = 95°C - 10°C = 85°C), and the change in length (∆L = 1.36 mm). We can use the formula: ∆L = αL∆T where L is the initial length of the rod. Solving for α, we get: α = ∆L / (L∆T) Substituting the given values, we have: α = (1.36 mm) / (800 mm x 85°C) Simplifying the denominator: α = (1.36 mm) / 68000 mm°C α = 0.00002°C^-1 Therefore, the linear expansivity of the metal is 2.0 x 10^-5 K^-1. Answer: (D) 2.0 x 10^-5 K^-1.

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The internal resistance of the battery can be calculated using the formula: R = (V1 - V2) / (I2 - I1) Where: V1 = voltage of the battery when supplying current I1 V2 = voltage of the battery when supplying current I2 I1 = current supplied to the battery when measuring V1 I2 = current supplied to the battery when measuring V2 Substituting the given values in the above formula, we get: R = (4.0V - 2.0V) / (3.0A - 2.0A) = 2.0Ω Therefore, the internal resistance of the battery is 2.0Ω. Explanation: The internal resistance of a battery is the resistance offered by the electrolyte inside the battery to the flow of current. When a battery is connected to an external circuit, the current flows through the external circuit and through the internal resistance of the battery. The voltage drop across the internal resistance reduces the terminal voltage of the battery. By measuring the terminal voltage of the battery at two different currents, we can calculate the internal resistance of the battery using the formula mentioned above.

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The correct thermometric property of a thermocouple is that its "e.m.f. changes with temperature." A thermocouple is a device used to measure temperature, and it works by generating a small electrical voltage in response to changes in temperature. This voltage is called an electromotive force or "e.m.f." The amount of voltage generated by a thermocouple depends on the difference in temperature between its two junctions. As the temperature changes, the e.m.f. also changes, and this change can be measured and used to determine the temperature. The other options given in the question are not correct for a thermocouple. Resistance, volume, and pressure can all change with temperature, but they are not the primary properties that are used to measure temperature with a thermocouple.

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To produce a sharp image of an object, the light rays coming from the object must converge at a single point on the camera film. The distance between the lens and the film determines where the image will be in focus. In this case, the focal length of the camera lens is given as 20cm, and the distance from the object to the lens (object distance) is 100cm. To find the distance from the film to the lens (image distance) that will produce a sharp image, we can use the formula: 1/f = 1/o + 1/i where f is the focal length of the lens, o is the object distance, and i is the image distance. Substituting the given values, we get: 1/20 = 1/100 + 1/i Simplifying this equation gives: 1/i = 1/20 - 1/100 = 0.04 i = 1/0.04 = 25cm Therefore, the distance from the film at which the lens must be set to produce a sharp image of an object 100cm away is 25cm, which corresponds to option (C) in the given choices.

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The watt is a unit of power, which represents the rate at which energy is transferred or work is done. It is equal to one joule per second. Out of the given options, only "force x velocity" has the same unit as the watt, which is joules per second. This is because force times velocity gives us the unit of momentum, which is kilogram meters per second (kg m/s), and dividing this by time (in seconds) gives us the unit of power, which is joules per second (J/s) or watts (W). In contrast, "force x time" gives us the unit of impulse (newton seconds), "force x distance" gives us the unit of work or energy (joules), and "force x acceleration" gives us the unit of force times acceleration, which is not a unit of power.

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Actual thickness = 34 - 22 = 12

error thickness = 30 - 20 = 10

error = 12 - 10 = 2mm that is, (11 ± 1)mm

%error = $\frac{1}{11}$ x $\frac{100}{1}$

= 9%

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A mirage is a naturally occurring optical phenomenon in which light rays are refracted, or bent, to produce a displaced image of distant objects or the sky. The answer to this question is "i and iii only." A mirage is caused by the refraction of light in layers of air with varying temperatures. In hot weather, the air near the ground is hotter than the air above it, causing light to refract and bend upwards. This creates the appearance of an image or object that is not actually there. This explains option i. Option ii, which states that road surfaces become good reflectors in hot weather, is not a factor in the formation of a mirage. Option iii is also correct because light from the sky can be reflected upwards after coming close to the road surface, which can contribute to the formation of a mirage.

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The kinetic theory of photoelectrons liberated from a metallic surface depends on the frequency of the incident radiation. When a photon with enough energy (frequency) hits a metal surface, it can knock loose an electron, creating a photoelectron. The kinetic energy of the photoelectron will depend on the energy of the incident photon, which is directly related to its frequency. Therefore, higher frequency radiation will result in photoelectrons with greater kinetic energy. The intensity of the incident radiation and the time duration of the incident radiation can affect the total number of photoelectrons released from the metal surface, but not their individual kinetic energy. The temperature of the incident radiation, on the other hand, is not a significant factor in the kinetic theory of photoelectrons.

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C = $\frac{{\epsilon }_{o}A}{d}$

10-2 x 10-6 = $\frac{9\times {10}^{-12}}{d}$ x 10-4

= 9 x 10-7m

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Heat lost = heat gained

200 x c x (90 - $\theta$)

$\theta$= 70oC

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The thrust exerted by the gas on the rocket can be calculated using the formula: Thrust = Mass flow rate x Exhaust velocity Here, the mass flow rate is given as 10 kg/s and the exhaust velocity is given as 5 x 10^3 m/s. Plugging in the values, we get: Thrust = 10 kg/s x 5 x 10^3 m/s = 50,000 N Therefore, the thrust exerted by the gas on the rocket is 5.0 x 10^4 N, which is.

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Distance XX = $\frac{1}{2}$$\lambda$

= $\frac{1}{2}$ x $\frac{60}{1}$

= 30cm

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P = 2 x 1000 x 10

= 2 x 104NM-2

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The inductive reactance (XL) of a 30.0 mH inductor with a negligible resistance when connected to a 1.3 x 10^3 Hz oscillator can be calculated using the formula: XL = 2πfL where f is the frequency of the oscillator in Hz, and L is the inductance in Henries. Substituting the given values, we get: XL = 2π(1.3 x 10^3 Hz)(30.0 x 10^-3 H) XL = 245.0 Ω Therefore, the inductive reactance is 245.0 Ω.

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The correct option is: "magnetic field of the current interacts with external magnetic field". When a current-carrying conductor is placed in a magnetic field, the magnetic field of the current interacts with the external magnetic field. This interaction creates a force that causes the conductor to move. This phenomenon is known as the Lorentz force. The direction of the force is perpendicular to both the direction of the current and the external magnetic field. The magnitude of the force depends on the strength of the magnetic field, the amount of current flowing through the conductor, and the length of the conductor that is in the magnetic field.

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Infra-red waves can propagate through a vacuum. Unlike sound waves, which require a medium to propagate, and ultrasonic and acoustic waves, which are also sound waves, infra-red waves are electromagnetic waves that can travel through a vacuum. This is because electromagnetic waves consist of oscillating electric and magnetic fields that do not require a medium to propagate.

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The property of the eye known as its power of accommodation is controlled by the ciliary muscles. These muscles are responsible for changing the shape of the lens in the eye, allowing it to focus on objects at different distances. When we look at something up close, the ciliary muscles contract, causing the lens to thicken and increase its refractive power. When we look at something far away, the ciliary muscles relax, causing the lens to flatten and decrease its refractive power. This process of changing the shape of the lens to adjust focus is known as accommodation, and it is essential for clear vision at different distances.

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To calculate the voltage required to operate the 40-W instrument with a resistance of 90 Ω, we can use Ohm's law, which states that the voltage (V) equals the product of the current (I) and the resistance (R): V = I × R. First, we need to calculate the current that flows through the instrument. We can use the formula for power (P) in terms of current and resistance: P = I^2 × R. Rearranging this equation, we get: I = sqrt(P / R). Substituting the values given in the problem, we get: I = sqrt(40 W / 90 Ω) ≈ 0.632 A Now we can use Ohm's law to find the voltage: V = I × R = 0.632 A × 90 Ω ≈ 56.9 V Therefore, the voltage required to operate the instrument normally is approximately 56.9 volts. (60V) is the closest to this value. Note that this is a simple example of how to apply Ohm's law to a practical problem. In real-life situations, the calculation may be more complicated, and other factors such as the temperature coefficient of resistance may need to be considered.

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To solve this problem, we can use the principle of moments, which states that the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point. In this case, we can take moments about the pivot point P. Let's first calculate the weight of the load: Weight = mass x acceleration due to gravity Weight = 180 kg x 10 m/s^2 Weight = 1800 N Now, let's calculate the anticlockwise moment of the load about point P: Anticlockwise moment = weight x perpendicular distance from pivot to line of action of weight Anticlockwise moment = 1800 N x 20 m Anticlockwise moment = 36000 Nm To balance this moment, we need a clockwise moment produced by the force F applied at the end of the lever. The perpendicular distance from the pivot to the line of action of this force is 200 m - 20 m = 180 m. So, we can calculate the minimum force required as follows: Minimum force = clockwise moment / perpendicular distance from pivot to line of action of force Minimum force = 36000 Nm / 180 m Minimum force = 200 N Therefore, the minimum force required to lift the load is 200 N, which corresponds to option (D).

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Soft iron is preferred to steel in electromagnets because it is more readily magnetized than steel, which means it can be easily magnetized by a small amount of electric current. This property of soft iron allows electromagnets to be more responsive and efficient. On the other hand, soft iron is also more readily demagnetized than steel, which means it loses its magnetism quickly once the electric current is turned off. This property is important because it allows the electromagnet to be turned on and off quickly, which is necessary for many applications. Therefore, the correct answer is option "i and ii only". Soft iron is not preferred to steel because it retains magnetism more than steel.

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Time = 1 x 4 x 10-3sec

distance = velocity x time

= 3 x 108 x 4 x 10-3

= 6 x 105m

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The quantity of electricity transported is given by the formula Q = I x t, where Q is the quantity of electricity, I is the current, and t is the time. In this case, the current is 100mA (which is 0.1A) and the time is 2 minutes (which is 120 seconds). So we can plug these values into the formula: Q = I x t = 0.1A x 120s = 12C Therefore, the quantity of electricity transported is 12C. Option C is the correct answer.

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The force experienced by an object of mass 60.0kg in the moon's gravitational field is 1.002 x 10^2 N. To find the intensity of the gravitational field, we can use the formula: force = mass x intensity of gravitational field Rearranging this formula gives: intensity of gravitational field = force / mass Plugging in the given values, we get: intensity of gravitational field = 1.002 x 10^2 N / 60.0 kg Simplifying this expression gives: intensity of gravitational field = 1.67 N/kg Therefore, the correct answer is: 1.67N/kg. In simpler terms, the intensity of the gravitational field is the amount of gravitational force per unit mass that an object experiences in that field. The greater the intensity, the stronger the gravitational force, and the more an object will be pulled towards the source of gravity.

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According to the ideal gas law, pressure (P), volume (V), and temperature (T) of a gas are related as follows: P x V = n x R x T, where n is the number of moles of the gas and R is a constant. If the volume of a gas is halved (V/2) and its temperature is doubled (2T), then the new values of P and V can be found by plugging these new values into the ideal gas law: P x (V/2) = n x R x (2T) Simplifying this equation, we get: P/2 = n x R x 2T/V Multiplying both sides by 2, we get: P = n x R x 2T/V Since V is halved, the fraction 2T/V becomes twice as large. Therefore, the pressure (P) of the gas increases by a factor of 2 x 2 = 4. So, the correct option is "increases by a factor of 4".