JAMB UTME - Physics - 1998

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The speed of a wave in a stretched string is given by the formula v = √(F/μ), where v is the speed of the wave, F is the tension in the string, and μ is the linear mass density of the string (mass per unit length). The fundamental frequency of a stretched string is given by the formula f = (1/2L)√(F/μ), where L is the length of the string. In this question, we are given the length of the steel wire (L = 0.50m) and its fundamental frequency (f = 200Hz). We are asked to find the speed of the wave in the wire. Using the formula for the fundamental frequency, we can rearrange it to find the tension in the string: F = (4L^2μf^2) Substituting this expression for F into the formula for the wave speed, we get: v = √((4L^2μf^2)/μ) v = 2Lf Substituting the values given in the question, we get: v = 2(0.50m)(200Hz) = 200m/s Therefore, the speed of the wave in the wire is 200 m/s. The correct option is (c): 200ms^-1.

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linear expansivity = $\frac{V_2-V_1}{V_1\times \Delta \theta }$

3 x 2 x 10-5 =$\frac{V_2-15}{15\times (100-0)}$

V2 = 15.09cm3

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The force of attraction between two point masses is given by the equation: F = G * (m1 * m2) / r^2 where F is the force of attraction, G is the gravitational constant, m1 and m2 are the masses of the two point masses, and r is the distance between them. In this case, we know that the force of attraction between the two point masses is 10^-4 N when the distance between them is 0.18m. We can use this information to find the value of G * (m1 * m2): G * (m1 * m2) = F * r^2 G * (m1 * m2) = (10^-4 N) * (0.18 m)^2 G * (m1 * m2) = 3.24 x 10^-6 N m^2 Now, if the distance between the two point masses is reduced to 0.06m, we can use the same equation to find the new force of attraction: F = G * (m1 * m2) / r^2 F = (G * (m1 * m2) / (0.06 m)^2 F = (3.24 x 10^-6 N m^2) / (0.06 m)^2 F = 9 x 10^-4 N Therefore, the force of attraction between the two point masses is 9 x 10^-4 N when the distance between them is reduced to 0.06m. So the correct option is: 9.0 x 10^-4 N

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Heat energy = Electrical energy

mc$\theta$ = power x time

0.6 x c x (100 - 25) = 500 x t1

and, 0.2 x c x (100 - 10)= 100 x t2
$\frac{t_1}{t_2}$ = 5

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8$\Omega$.....100oC

6$\Omega$.....$\theta$oC

3$\Omega$.....0oC

$\frac{6-3}{8-3}$ = $\frac{\theta -0}{100-0}$

therefore, $\theta$ = 60oC

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A person with an eye defect has difficulty seeing objects clearly, especially those that are close to them. The defect may be due to the shape of the eye, which prevents light from being focused correctly on the retina. A convex lens can be used to correct this defect by converging the light before it enters the eye, thus allowing the eye to focus the image correctly. The focal length of a lens is a measure of its ability to converge light. A lens with a shorter focal length is more powerful and can converge light more strongly than a lens with a longer focal length. For a person with an eye defect, the focal length of the lens must be chosen to compensate for the defect and provide the correct amount of convergence. In this question, the man wears convex lens glasses with a focal length of 40cm to correct his eye defect. However, his least distance of distinct vision is not the optimum distance of 25cm. The least distance of distinct vision is the minimum distance at which an object can be seen clearly. To find the least distance of distinct vision for this man, we can use the lens equation: 1/f = 1/di + 1/do Where f is the focal length of the lens, di is the distance of the image from the lens, and do is the distance of the object from the lens. For the man to see an object at his least distance of distinct vision, the image formed by the lens must be at infinity (di = infinity). Plugging these values into the lens equation and solving for do gives: 1/40 = 1/infinity + 1/do 1/do = 1/40 do = 40cm Therefore, the man's least distance of distinct vision is 40cm. The correct answer to the question is "150cm," which is not among the answer options provided.

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In a closed organ pipe, the air column is closed at one end, and open at the other. When a sound wave is produced, it travels down the length of the pipe and is reflected at the closed end. This reflection causes a standing wave pattern to form within the pipe, with points of maximum vibration called antinodes and points of no vibration called nodes. Since the air column at the closed end is prevented from moving, it creates a node at that point. Therefore, the antinode will always be produced at the open end of a closed organ pipe producing a musical note. This is where the air column is free to vibrate, resulting in maximum displacement and maximum amplitude of the sound wave. So, the correct answer is: "the open end."

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When an object is dropped from a height, it experiences two forces: the force of gravity, which pulls the object down, and the air resistance, which pushes the object up. As the object falls faster, the air resistance also increases until it reaches a point where the two forces are equal and opposite. At this point, the net force on the object becomes zero and it stops accelerating. This is called the terminal velocity. A parachute works by increasing the air resistance on the person wearing it. When the parachute is deployed, it catches the air and creates a large surface area. This causes the air resistance to increase, slowing down the person's descent. Eventually, the air resistance becomes large enough to balance the force of gravity on the person, and they reach their terminal velocity. Therefore, the correct answer to the question is that a parachute attains a terminal velocity when the viscous force of the air and the upthrust completely counteract its weight. Answer "the viscous force of the air and the upthrust completely counteract its weight," is the correct answer.

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When two objects are rubbed against each other, they can become electrically charged. This happens because the rubbing causes electrons to transfer from one object to the other. One object loses electrons and becomes positively charged, while the other gains electrons and becomes negatively charged. In this case, when the ebonite rod is rubbed with fur, it gains electrons and becomes negatively charged. When the glass rod is rubbed with silk, it loses electrons and becomes positively charged. Opposite charges attract each other, so the negatively charged ebonite rod and positively charged glass rod will be attracted to each other. Therefore, the correct answer is that the ebonite rod has a negative charge while the glass rod has a positive charge.

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Energy = mc2

= 1 x (3 x 108)2 x 106

= 9 x 1010J

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The time taken for an object to fall from a given height in free fall depends only on the height and the acceleration due to gravity. It is independent of the mass of the object. The formula for the time taken for an object to fall from rest from a height h in free fall is given by: t = √(2h/g) where h is the height and g is the acceleration due to gravity. In this question, we are given that a body of mass 1 kg falls from a height of 125 m in 5 s. Using the formula above, we can find the value of g: t = √(2h/g) 5 s = √(2 x 125 m / g) 25 s^2 = 250 m / g g = 250 m / (25 s^2) g = 10 m/s^2 We are then asked to find how long it will take for a body of mass 2 kg to fall from rest from the same height. Using the same formula as before, but with the new value of g, we get: t = √(2h/g) t = √(2 x 125 m / 10 m/s^2) t = √(25) t = 5 s Therefore, it will take the body of mass 2 kg the same amount of time as the body of mass 1 kg to fall from the same height, which is 5 s. The correct option is (a): 5s.

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Number of image = $\frac{360}{\theta }$ -1

7 = $\frac{360}{\theta }$ -1

thus,$\theta$ = 45o

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F =$\frac{1}{4\pi {\epsilon }_o}$ x $\frac{q_1{q}_2}{r^2}$

F =$\frac{5\times 10\times 8\times 10}{0.002\times 0.002}$ x 9 x 10

F = 900N

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When light passes through a medium with a different refractive index, it changes its direction. This effect is known as refraction. The amount of bending that occurs depends on the angle of incidence and the refractive indices of the two media involved. In this case, we are looking at the displacement produced in a glass block of thickness t and refractive index n when an object is viewed through it. The amount of displacement (d) can be calculated using the formula: d = t (1 - 1/n) Where t is the thickness of the glass block and n is the refractive index of the glass. Therefore, the correct option is (C), which gives the displacement as t (1 - 1/n).

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This question can be solved using the gas laws, specifically Charles's law which states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature. We are given that the initial volume of the gas is 100 cm^3 at a temperature of 27 degrees Celsius. We need to find the temperature T at which the final volume of 120 cm^3 is attained. Since the pressure is constant, we can use Charles's law to solve for T. First, we need to convert the initial temperature of 27 degrees Celsius to its absolute temperature (in kelvin). We do this by adding 273 to 27 to get 300K. Next, we use the formula for Charles's law: V1/T1 = V2/T2 where V1 is the initial volume (100 cm^3), T1 is the initial temperature in kelvin (300K), V2 is the final volume (120 cm^3), and T2 is the final temperature in kelvin (which we are solving for). Substituting the values, we get: 100/300 = 120/T2 Cross-multiplying and simplifying, we get: T2 = 120 x 300 / 100 = 360K Finally, we need to convert the temperature in kelvin back to degrees Celsius by subtracting 273. So the final answer is: T2 = 360 - 273 = 87°C Therefore, the answer is 87°C.

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C = $\frac{{\epsilon }_{o}A}{d}$

= $\frac{5\times {10}^{-8}\times {10}^{-12}\times 9}{2\times {10}^{-3}}$

= 22.5 x 10-17F

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An induction coil is a device that converts low voltage into high voltage, and it does this by inducing an electric current in a coil of wire. The iron core of an induction coil is made from bundles of wire so as to minimize eddy-currents. Eddy currents are small, swirling currents of electricity that can be generated in the core of the coil when an alternating current is passed through it. These eddy currents can cause heating, energy loss, and interfere with the operation of the coil. By making the core from bundles of wire, the eddy currents are minimized, and the induction coil operates more efficiently. Therefore, the correct option is "minimize eddy-currents."

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To solve this problem, we need to use the formula for power: Power = work done / time taken We also need to use the formula for work done: Work done = force x distance The force here is the weight of the man, which is given by: Force = mass x gravity where g is the acceleration due to gravity. We can rearrange the formula for work done to get the distance: Distance = work done / force Combining these formulas, we get: Power = force x distance / time taken We can rearrange this to get: Distance = Power x time taken / force Substituting the given values: Distance = 120 x 20 / (80 x 10^-2) = 300m Therefore, the height of the staircase is 300m. However, this answer seems unreasonable because it is very high. We need to check if we made an error. We can use another formula to check: Distance = 1/2 x acceleration x time taken^2 where acceleration = gravity. Substituting the values: Distance = 1/2 x 10 x 20^2 = 2000m This is an even higher value, which confirms that we made an error. On closer inspection, we can see that we forgot to convert the mass to weight. Weight = mass x gravity = 80 x 10 = 800N Using this value, we can recalculate the distance: Distance = Power x time taken / force = 120 x 20 / 800 = 3m Therefore, the height of the staircase is 3m. Hence, the correct option is: 3.0m.

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The most suitable type of mirror used for the construction of a searchlight is the parabolic mirror. A parabolic mirror is a type of mirror that has a parabolic shape, meaning it is curved in such a way that it reflects incoming light rays to a single focal point. This makes it ideal for use in searchlights because it allows for the concentration of the light into a powerful beam that can be directed in a specific direction. On the other hand, convex mirrors diverge light rays, making them unsuitable for searchlights because they would disperse the light in different directions. Spherical mirrors, on the other hand, are not specifically designed to focus light to a single point, so they are less effective than parabolic mirrors for this purpose. Finally, while concave mirrors can focus light to a single point, they are not as effective as parabolic mirrors in doing so because they tend to produce more spherical aberration, which can distort the shape of the reflected image.

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The electrochemical equivalent of a metal is the amount of the metal deposited per unit charge passed through an electrolyte. In this case, the electrochemical equivalent of the metal is given as 1.3 x 10^-7 kgC^-1. To find the mass of the metal deposited by 2.0 x 10^4 C of electricity, we can use the formula: mass = (charge x electrochemical equivalent) Substituting the values given, we get: mass = (2.0 x 10^4 C) x (1.3 x 10^-7 kgC^-1) = 2.6 x 10^-3 kg Therefore, the mass of the metal deposited by 2.0 x 10^4 C of electricity is 2.6 x 10^-3 kg. So, the correct option is: 2.6 x 10-3kg.

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Heat lost = Heat gained

mc$\theta$ = mL

m x 4200 x 17 = 42 x 3.4 x 105

therefore, m = 200g

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The physical quantity that has the same dimensions as impulse is momentum. Impulse is defined as the change in momentum of an object over a certain period of time. Momentum, on the other hand, is the product of an object's mass and its velocity. The dimensions of momentum are given by the product of the dimensions of mass and velocity, which are respectively [M] and [L]/[T]. Therefore, the dimensions of momentum are [M][L]/[T]. Similarly, the dimensions of impulse are also given by the product of the dimensions of force and time, which are respectively [M][L]/[T]^2 and [T]. Thus, the dimensions of impulse are [M][L]/[T]. Since momentum and impulse have the same dimensions of [M][L]/[T], we can say that they have the same physical quantity. In other words, the units used to measure momentum and impulse are interchangeable, which means that they are related to each other in a very fundamental way.

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To solve this problem, we can use the formula for power: Power (in watts) = Voltage x Current Since the transformer has an efficiency of 80%, it means that 80% of the input power is transferred to the output. The remaining 20% is lost as heat. Therefore, we can say that: Output Power = Input Power x Efficiency We know the output voltage is 8V, and the output current is 15A. So, the output power can be calculated as: Output Power = 8V x 15A = 120W Substituting the values in the formula for efficiency, we get: 120W = Input Power x 0.80 Input Power = 120W/0.80 = 150W Now, we can calculate the input current using the formula: Input Power = Input Voltage x Input Current Substituting the values, we get: 150W = 240V x Input Current Input Current = 150W/240V = 0.625A Therefore, the current in the primary coil is 0.625A.

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Rd = $\frac{\text{upthrust in oil}}{\text{upthrust in}{H}_{2}O}$

thus; 0.875 = $\frac{0.21}{\text{upthrust in}{H}_{2}O}$

upthrust in H2O = 0.24N

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In the photoelectric effect, when light shines on a metal surface, electrons can be emitted from the surface of the metal. The energy of the photons in the light is transferred to the electrons, which can overcome the binding energy of the metal and escape from its surface. The minimum amount of energy required to remove an electron from the metal surface is called the work function. If the energy of the photons is less than the work function, the electrons cannot overcome the binding energy and will not be emitted from the surface. On the other hand, if the energy of the photons is greater than or equal to the work function, the electrons can be emitted. Therefore, to answer the question, if the photon energy is greater than the work function, the electrons will leave the metal surface when illuminated by light of appropriate frequency in the photoelectric effect. Answer "greater than the work function," is the correct answer.

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Velocity $\alpha \sqrt{temperature}$

$\frac{V_1}{V_2}=\sqrt{\frac{T_1}{T_2}}$

therefore, $\frac{360}{V_2}=\sqrt{\frac{27+273}{127+273}}$

$V_2=240\sqrt{3}$m/s

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A vapour is said to be saturated when a dynamic equilibrium exists between the molecules of the liquid and the vapour molecules at a given temperature. This means that the rate of evaporation of the liquid is equal to the rate of condensation of the vapour, resulting in a constant amount of vapour in the air. At this point, the vapour has reached its maximum capacity to hold water molecules, and any additional water molecules added to the system will result in condensation.

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The correct option is: i, ii, iv only Infrared radiation is a type of electromagnetic radiation that has a longer wavelength than visible light, and therefore it is invisible to the human eye. It is commonly known as heat radiation because it is associated with the heat energy that objects emit. Infrared radiation is a type of electromagnetic radiation, and like all electromagnetic radiation, it travels as a transverse wave, which means that the oscillations of the electric and magnetic fields are perpendicular to the direction of the wave's propagation. The statement "its frequency is higher than that of blue light" is incorrect. In fact, the frequency of infrared radiation is lower than that of blue light.

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Impulse = m(v-u)

= 0.15(80-50)

= 4.5N/s

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F3 = 7Fo

= 7 x 280

= 1960Hz

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The wheel and axle mechanism is a simple machine used for lifting heavy loads. The mechanical advantage of a wheel and axle mechanism is given by the ratio of the radius of the wheel to the radius of the axle. In this case, the diameters of the wheel and axle are given, and so we need to calculate their radii. The radius of the wheel, r_w, is half the diameter of the wheel, so r_w = 20 cm. Similarly, the radius of the axle, r_a, is half the diameter of the axle, so r_a = 4 cm. The mechanical advantage of the wheel and axle mechanism is given by: MA = r_w / r_a Substituting the values we get: MA = 20 cm / 4 cm = 5 The efficiency of the machine is given as 80%, which means that 80% of the work put into the machine is used to lift the load. The remaining 20% is lost due to friction and other factors. Efficiency = (Output work / Input work) x 100% Since the output work is equal to the weight lifted (100 N) times the distance moved by the load, and the input work is equal to the effort required to lift the load times the distance moved by the effort, we can write: Efficiency = (100 N x d) / (E x d) x 100% where d is the distance moved by both the load and the effort. Simplifying this expression gives: Efficiency = 100 / MA Substituting the value of MA gives: 80% = 100 / 5 So, the effort required to lift a load of 100N is: E = (100 N x d) / (Output work) E = (100 N x d) / (Efficiency x Input work) Substituting the values of efficiency, output work and input work, we get: E = (100 N x d) / (0.8 x E x 5 x d) Simplifying this expression, we get: E = 25 N Therefore, the effort required to lift a load of 100N is 25N. Hence, the correct option is 25N.

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Pressure = heg = 1000 x 10 x 10 = 105Nm-2

Total pressure = (1.3 x 106) + (1 x 105)

= 1.4 x 106Nm-2

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Electricity supplied to a school through a cable has a certain resistance. This means that as current flows through the cable, some of the electrical energy is lost as heat due to the resistance of the cable. The amount of energy lost as heat is given by the formula: Energy = Current^2 x Resistance x Time In this question, we are given the resistance of the cable and the maximum current drawn from the mains, which is 100A. We are also told that we need to calculate the maximum energy dissipated as heat for 1 hour (which is 60 minutes). Using the formula above, we can calculate the maximum energy dissipated as heat as follows: Energy = Current^2 x Resistance x Time Energy = 100^2 x 0.5 x 3600 (since 1 hour = 3600 seconds) Energy = 18,000,000 J Energy = 1.8 x 10^7 J Therefore, the maximum energy dissipated as heat for 1 hour is 1.8 x 10^7 J. The correct option is: - 1.8 x 107J

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The work done by the resisting force of the wooden block is equal to the kinetic energy of the bullet just before it hits the wooden block. Therefore, we can equate the work done by the resisting force to the kinetic energy of the bullet: Work done = Force x distance = average resisting force x thickness of the block Kinetic energy of the bullet = (1/2) x mass x velocity^2 Since the bullet manages to penetrate the wooden block, we can assume that all its kinetic energy is used up in overcoming the resisting force of the wooden block. Therefore, we can equate the two expressions: (1/2) x mass x velocity^2 = average resisting force x thickness of the block Substituting the given values, we get: (1/2) x 0.025 x velocity^2 = 7.5 x 10^3 x 0.15 Simplifying this equation, we get: velocity^2 = (2 x 7.5 x 10^3 x 0.15) / 0.025 velocity^2 = 90,000 Taking the square root of both sides, we get: velocity = 300 m/s Therefore, the speed of the bullet just before it hits the wooden block is 300m/s. So the answer is from the given options.

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The work done in moving a charge in an electric field is given by the formula: W = qΔV Where W is the work done, q is the charge, and ΔV is the potential difference between the two points. In this problem, the charge is 2 C and the potential difference between the two points X and Y is 100 volts. Therefore, using the formula above, we get: W = 2 C x 100 V = 200 J Therefore, the work done in moving a 2 C charge between two points X and Y in an electric field with a potential difference of 100 volts is 200 J. Answer 200J, is the correct answer.

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To calculate the strain on the muscle, we can use the formula: Strain = (Change in length) / (Original length) Here, the change in length is the amount by which the tendon is stretched, and the original length is the length of the tendon before it is stretched. Substituting the values, we get: Strain = (2.0 x 10^-5 m) / (0.01 m) Strain = 2.0 x 10^-5 / 0.01 Strain = 2.0 x 10^-5 x 100 Strain = 2.0 x 10^-3 So, the strain on the muscle is 2.0 x 10^-3. Therefore, the correct option is: "2 x 10^-3."