JAMB UTME - Physics - 1991

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To find the tension T1, we need to analyze the forces acting on the system and use the fact that it is in equilibrium, which means the net force in all directions is zero. First, let's consider the vertical forces. The weight of the hanging mass is acting downwards with a force of 100N. The tension T2 is also acting downwards with a force of T2*cos(30°) because it is at an angle of 30° to the vertical. Therefore, the net vertical force is: Net vertical force = T2*cos(30°) - 100N Since the system is in equilibrium, the net vertical force must be zero. Thus, we can solve for T2: T2*cos(30°) = 100N T2 = 100N/cos(30°) = 115.5N Next, let's consider the horizontal forces. The tension T2 is acting to the left with a force of T2*sin(30°) because it is at an angle of 30° to the horizontal. The tension T1 is acting to the right. Therefore, the net horizontal force is: Net horizontal force = T1 - T2*sin(30°) Since the system is in equilibrium, the net horizontal force must be zero. Thus, we can solve for T1: T1 = T2*sin(30°) = 115.5N*sin(30°) = 57.8N Therefore, the tension T1 is 57.8N. Option (B)  100/√3N
is closest to this value, but it is not the correct answer.

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To convert from the arbitrary scale S to Celsius, we need to use the following formula: C = (S - 32) x 5/9 First, we need to find the conversion factor between S and Fahrenheit: (Smax - Smin)/(Fmax - Fmin) = (90 - (-30))/(212 - 32) = 120/180 = 2/3 So, for a given temperature T on the arbitrary scale, the corresponding temperature on the Fahrenheit scale is: T_F = (T - Smin) x (Fmax - Fmin)/(Smax - Smin) + Fmin = (T - (-30)) x 180/120 + 32 = (T + 30) x 3/2 + 32 = 1.5T + 77 To convert 60 on the arbitrary scale to Celsius, we first need to find the corresponding temperature on the Fahrenheit scale: 60_S = 1.5 x 60 + 77 = 167 Then, we use the Celsius conversion formula: C = (F - 32) x 5/9 = (167 - 32) x 5/9 = 135 x 5/9 = 75.0°C Therefore, the answer is 75.0oC.

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P.E = $\frac{1}{2}$Fe

= $\frac{1}{2}$$\frac{F}{K}$

= $\frac{1}{2}$ x $\frac{75\times 75}{1500}$

= 1.9J

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When two sound waves with slightly different frequencies are played together, they interfere constructively and destructively, resulting in a periodic variation of amplitude, which is called beats. The frequency of beats produced is equal to the difference between the frequencies of the two sound waves. In this case, the two tuning forks have frequencies of 256Hz and 260Hz, respectively. Therefore, the difference between their frequencies is: 260Hz - 256Hz = 4Hz So the beats produced have a frequency of 4Hz. Therefore, the answer is: 4Hz.

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When a plane mirror is rotated through an angle θ, the reflected ray will be rotated through an angle of 2θ. To understand why, imagine a ray of light hitting a plane mirror at an incident angle θ. The angle of incidence is the angle between the incident ray and the perpendicular to the mirror surface at the point of incidence. According to the law of reflection, the angle of reflection is equal to the angle of incidence, and the reflected ray makes the same angle with the perpendicular as the incident ray. Therefore, if we rotate the mirror through an angle θ, the perpendicular to the mirror at the point of incidence will also be rotated through an angle θ. This means that the angle of incidence will also change by θ. Now, since the angle of reflection is equal to the angle of incidence, the angle of reflection will also change by θ. Therefore, the angle between the incident ray and the reflected ray will change by 2θ (θ for the change in angle of incidence and θ for the change in angle of reflection). Hence, the reflected ray will be rotated through an angle of 2θ.

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Heat by water = mc$\theta$

Heat by steam = mc$\theta$ + mL

Difference = mL = 4 x 2,260,000

= 9,040,000J

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The mean period of oscillation of the pendulum can be calculated by dividing the total time for the oscillations by the number of oscillations measured. In this case, the boy measured 30 oscillations three times, with times of 1min. 10s, 1min. 12s, and 1min. 7s. First, we need to convert the times to seconds: 1min. 10s = 70s 1min. 12s = 72s 1min. 7s = 67s Next, we can calculate the total time for the 90 oscillations: 70s + 72s + 67s = 209s Finally, we can calculate the mean period by dividing the total time by the number of oscillations: 209s / 90 oscillations = 2.32s Therefore, the mean period of oscillation of the pendulum is 2.32s. Answer option (C) is correct.

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$\frac{4}{3}$ = $\frac{12}{\text{Apparent depth}}$

Apparent depth = 9cm

Height by which coin is raised = 12 - 9

= 3cm

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Efficiency = m.A x $\frac{1}{V.R}$ x 100%

85 = $\frac{load}{1200}$ x $\frac{10}{80}$ x $\frac{100}{1}$

load = 8160N

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Difference in pressure = 75 - 63

= 12cmHg

pressure = hge

difference in height = $\frac{12}{10\times \frac{0.00013}{13}}$

= 1200m

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When an atom loses or gains a charge, it becomes an ion. An ion is an atom or molecule that has a net electrical charge because it has either lost or gained one or more electrons. A positively charged ion is called a cation and a negatively charged ion is called an anion.

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The absolute temperature of a perfect gas is proportional to the average kinetic energy of the molecules. This means that as the temperature of the gas increases, the average kinetic energy of its molecules also increases, and vice versa. The temperature of a gas is a measure of the average kinetic energy of its particles, where the higher the temperature, the more kinetic energy the particles have. Therefore, the option that correctly completes the sentence is "kinetic energy of the molecules".

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When an object of weight W rests on an inclined plane, the weight force can be resolved into two components: one perpendicular to the plane (W cosθ) and the other parallel to the plane (W sinθ). The component of weight parallel to the plane is what we are interested in, as this is the force that will cause the object to slide down the plane if it is not held in place. Therefore, the resolved part of the weight in Newtons along the plane is W sinθ. This is because the weight force is proportional to the sine of the angle of inclination, meaning that the steeper the slope, the greater the force parallel to the plane. So, option A (W sinθ) is the correct answer.

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F = $\frac{uv}{u+v}$

F = -ve

-12 = $\frac{4\times v}{4+v}$

v = -3cm

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Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle consisting of two protons and two neutrons, reducing its atomic number by two and its mass number by four. Therefore, statement i is correct. The atomic number is the number of protons in the nucleus, and in alpha decay, two protons are lost. Hence, statement ii is also correct. However, the number of neutrons in the nucleus remains the same in alpha decay, so statement iii is incorrect. Therefore, the correct option is "i and ii only."

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If a ray of light passes through the optic center of a thin converging lens, it will pass through undeviated. This is because the optic center is the point on the lens where the principal axis crosses and it is equidistant from the lens surfaces. Therefore, any ray of light that passes through the optic center will not be refracted or deviated because it is passing through the center of the lens and hitting the surface perpendicularly. A converging lens is thicker in the middle than at the edges and refracts light rays in such a way that they converge at a focal point on the opposite side of the lens. Rays that are not parallel to the principal axis will converge at a point on the opposite side of the lens after refraction. However, if the ray passes through the optic center, it will not bend or deviate from its original path and will pass through undeviated. Therefore, if a ray of light is not parallel to the optic axis but passes through the optic center of a thin converging lens, it will pass through undeviated.

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The image in a pin-hole camera is inverted and formed by the light from each point travelling in a straight line. This is because a pin-hole camera works by letting light through a tiny hole (pin-hole), which then creates an inverted image on the opposite side of the box or surface that is receiving the light. The smaller the pin-hole, the sharper the image will be, but it will also be dimmer. The image formed in a pin-hole camera is not refracted by a lens or created through dispersion, but rather through the straight-line propagation of light.

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The correct option is: "they both transmit energy". Both light and sound waves are forms of energy that are transmitted through space. Light waves are electromagnetic waves that can travel through a vacuum, while sound waves are mechanical waves that require a medium, such as air, to propagate. Unlike light waves, sound waves are longitudinal waves, meaning that they vibrate in the direction of their motion, whereas light waves are transverse waves, meaning that they vibrate perpendicular to their direction of motion. The velocities of light and sound waves are not equal in air, with light waves traveling much faster than sound waves.

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To convert an alternating current (AC) dynamo into a direct current (DC) dynamo, you need to replace the slip rings with a split-ring commutator. Slip rings allow the current to change direction every half-turn, resulting in an AC current output. However, a split-ring commutator ensures that the current flows in the same direction at all times, creating a direct current output. The number of turns in the coil, strength of the field magnet, and the material of the armature do not affect the conversion from AC to DC.

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The phenomenon called photoelectric effect is when a metal absorbs quanta of light and then emits electrons. This means that when light shines on a metal, the energy from the light is absorbed by the metal atoms, which causes electrons to be emitted from the metal surface. This effect is important in many technologies such as solar cells and photo detectors. The other options are not examples of the photoelectric effect. The first option describes the reverse effect, where high energy electrons cause the emission of photons, which is known as the Bremsstrahlung effect. The second option describes the process of photon emission through the release of energy by a particle as it slows down, which is known as the Cerenkov radiation. The third option describes a similar effect to the photoelectric effect, but instead of emitting electrons, the metal would emit light, which is known as the photoluminescence effect. Finally, the fourth option describes the process of photon absorption, which is not related to the photoelectric effect.

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Time from tower to top, t = $\frac{u-v}{g}$

= $\frac{20-0}{10}$

= 2s

distance from tower to top

x = ut - $\frac{1}{2}$gt2

= (20 x 2) - ($\frac{1}{2}$ x 10 x 2 x 2)

= 20m

Time from the top to the ground, t = 6 - 2

= 4s

distance from top to ground,

x = ut - $\frac{1}{2}$gt2

= (0 x 4) + ($\frac{1}{2}$ x 10 x 4 x 4)

= 80cm

therefore, height of tower = 80 - 20

= 60m

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v = $\lambda$F

260 x 1.29 =335.4ms-1

Echo time = $\frac{2}{2}$ = 1sec.

distance = v x t

= 335.4 x 1 = 335.4m

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The phenomenon you're describing is called resonance. When the tuning fork is brought in contact with the wooden box, the box starts vibrating at the same frequency as the tuning fork, which amplifies the sound waves produced by the tuning fork. This happens because the wooden box is able to resonate, or vibrate, at the same frequency as the tuning fork. Resonance occurs when an object is able to vibrate at its natural frequency in response to another object vibrating at the same frequency. This causes the amplitude (or loudness) of the vibration to increase. In this case, the wooden box is able to resonate at the same frequency as the tuning fork, so the sound produced by the tuning fork is amplified, resulting in a louder sound.

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let the length be Lcm

$\frac{5-3}{25-L}$ = $\frac{10-5}{30-25}$

L = 23cm

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m = Itz

1 = 100 x 5 x 10-7 x t

t = 20,000sec

= 5.6hrs

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The buoyant force on an object is equal to the weight of the fluid displaced by the object. When the stone is immersed in water, the buoyant force is equal to the weight of the water that is displaced. Similarly, when the stone is immersed in the liquid of relative density 2.0, the buoyant force is equal to the weight of the liquid that is displaced. From the given information, we can calculate the volume of the stone. Let the volume of the stone be V. When completely immersed in water, the buoyant force on the stone is equal to the weight of the water displaced, which is equal to the weight of the stone in air minus the weight of the stone in water. Therefore, we have: Buoyant force = Weight of stone in air - Weight of stone in water V x density of water x g = (10.0g - 15.0g) x g V = 5.0g / (density of water x g) Similarly, when completely immersed in the liquid of relative density 2.0, we have: V x density of liquid x g = (10.0g - weight of liquid displaced) x g V x 2.0 x g = (10.0g - 15.0g) x g V = 5.0g / (2.0 x density of water x g) Since the volume of the stone is the same in both cases, we can set the two expressions for V equal to each other and solve for the density of water: 5.0g / (density of water x g) = 5.0g / (2.0 x density of water x g) density of water = 2.0 Now we can use the buoyant force equation to find the weight of the stone in air: Buoyant force = Weight of stone in air - Weight of stone in water V x density of water x g = (Weight of stone in air - 15.0g) x g Weight of stone in air = V x density of water x g + 15.0g Weight of stone in air = 5.0g + 15.0g Weight of stone in air = 20.0g Therefore, the mass of the stone in air is 20.0g. Answer: 20.0g.

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The saturated vapor pressure of a liquid is the pressure exerted by its vapor when it is in equilibrium with its liquid phase. This means that the rate of evaporation of the liquid is equal to the rate of condensation of its vapor. The saturated vapor pressure of a liquid increases with an increase in the temperature of the liquid. When the temperature increases, the kinetic energy of the liquid molecules increases, and more molecules are able to escape from the liquid surface and enter the vapor phase. This increases the number of vapor molecules in the air above the liquid, which leads to an increase in the vapor pressure. Therefore, the correct option is "temperature of the liquid increases."

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The Earth has a magnetic field that acts like a giant bar magnet with its magnetic field lines directed from the geographic North Pole to the geographic South Pole. The magnetic field of the earth is responsible for the phenomenon of magnetism, and it has three important elements: the angle of dip, the angle of declination, and the angle of inclination. The angle of dip is the angle that a freely suspended magnet makes with the horizontal plane. The angle of dip is also known as the angle of inclination. The angle of declination is the angle between the magnetic meridian and the geographic meridian. It is the angle that a magnetic compass makes with the geographic meridian. The magnetic meridian is the imaginary line that passes through the geographic North Pole and the south magnetic pole. Therefore, the correct statement is "the angle of declination is the angle between the magnetic meridian and the geographic meridian."

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The length of the brass rod changes with a change in temperature due to thermal expansion. The formula for linear expansion is given as: ΔL = αLΔT Where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length of the rod, and ΔT is the change in temperature. Substituting the given values, we get: ΔL = (18 x 10^-6) x 2 x 100 = 0.0036m Therefore, the new length of the brass rod is: L + ΔL = 2m + 0.0036m = 2.0036m Hence, the answer is 2.0036m.

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The occupant of the room standing away from the charcoal fire is mainly warmed by radiation. Radiation is the transfer of heat energy in the form of electromagnetic waves that can travel through empty space. In this case, the heat energy from the charcoal fire is transferred to the surrounding objects and the walls of the room through radiation. The objects and walls then re-radiate the heat energy towards the occupant, warming them up. Convection is the transfer of heat energy through the movement of fluids or gases, but in this scenario, the air in the room is not moving enough to contribute significantly to the warming of the occupant. Conduction is the transfer of heat energy through direct contact between objects, but the occupant is not in direct contact with the fire or the walls of the room. Reflection is the bouncing back of electromagnetic waves from a surface, but it does not play a significant role in the warming of the occupant in this scenario.

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To calculate the time it takes for a 750W heater to raise the temperature of 1kg of water from 20°C to 50°C, we can use the formula: Q = mcΔT where Q is the heat energy required to heat up the water, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. Solving for Q, we get: Q = mcΔT Q = 1kg x 4200J/kg°C x (50°C - 20°C) Q = 126000J Now, we can use the formula for power to find out how long it takes for the heater to produce 126000J of heat energy: P = E/t t = E/P where P is the power of the heater, E is the energy produced by the heater, and t is the time taken. Solving for t, we get: t = E/P t = 126000J / 750W t = 168 seconds Therefore, the answer is 168s.

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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. Therefore, a material that obeys Ohm's Law will have a constant resistance at a given temperature. Metals are good conductors and generally obey Ohm's Law, which means their resistance remains constant over a wide range of voltages and currents. On the other hand, electrolytes, such as solutions of salts and acids, do not obey Ohm's Law because they have a non-linear relationship between current and voltage due to their ionic nature. Glass is an insulator and does not conduct electricity, while a diode is a semiconductor that exhibits nonlinear current-voltage characteristics and does not obey Ohm's Law. Therefore, the material that obeys Ohm's Law is "All metals".

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The current drawn by an equipment can be calculated using Ohm's Law, which states that: V = IR where V is the voltage, I is the current, and R is the resistance. In this case, we know that the power of the equipment is 1500W, and we can also use the formula: P = IV where P is the power, I is the current, and V is the voltage. By combining these two equations, we can eliminate V and get: I = sqrt(P/R) where sqrt represents the square root. Plugging in the values, we get: I = sqrt(1500W / 375 ohms) I = sqrt(4A) I = 2A Therefore, the current drawn by the equipment is 2A. Hence, the answer is 2.00A.

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The change in momentum is calculated by subtracting the initial momentum from the final momentum. The momentum of an object is given by the product of its mass and velocity. Initial momentum = mass × initial velocity Final momentum = mass × final velocity The change in momentum is therefore: change in momentum = final momentum - initial momentum change in momentum = mass × final velocity - mass × initial velocity change in momentum = mass × (final velocity - initial velocity) Substituting the given values: mass = 100g = 0.1kg initial velocity = 10.0ms^-1 final velocity = -2.0ms^-1 (since the body moves in the opposite direction) change in momentum = 0.1kg × (-2.0ms^-1 - 10.0ms^-1) change in momentum = 0.1kg × (-12.0ms^-1) change in momentum = -1.2Ns Therefore, the change in momentum is -1.2Ns. Since momentum is a vector quantity, the negative sign indicates that the direction of momentum has changed, which is in the opposite direction of the initial momentum.

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In a nuclear fusion process, four protons combine to form a nucleus X. According to the law of conservation of mass, the mass of the products of a chemical reaction must be equal to the mass of the reactants. Since the total mass of the four protons before fusion is 4M_p, the total mass of the resulting nucleus X after fusion must also be 4M_p. Therefore, the correct equation is 4M_p = M_x. Option (b) is correct.

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To find the force required to pull the 20kg mass up a slope inclined at 30 degrees to the horizontal, we need to consider the weight of the object and the force needed to overcome friction. The weight of the object is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity (10 m/s^2). So, W = 20 kg x 10 m/s^2 = 200 N. To find the force needed to overcome friction, we need to use the formula F = μN, where μ is the coefficient of friction and N is the normal force. The normal force is the component of the weight that is perpendicular to the slope, which is given by N = W cosθ, where θ is the angle of inclination (30 degrees in this case). So, N = 200 N x cos30 = 173.2 N. Assuming an efficiency of 75%, we know that only 75% of the force applied will go towards moving the object up the slope, while the rest will be lost to friction and other factors. So, the force required to pull the load up the plane is F = (1/0.75) x (200 N x sin30 + μN) = 266.67 N. Therefore, the answer is 266.67 N, which is closest to option C (133.3N).

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The Letanche cell uses a system of granulated carbon mixed with manganese (IV) oxide to prevent polarization in the cell. Polarization happens when the electrodes in a cell become coated with gas bubbles or other substances, hindering the flow of electricity. The mixture of carbon and manganese (IV) oxide acts as a catalyst to speed up the reaction and prevent polarization, ensuring a steady flow of electricity. This allows the cell to maintain a constant voltage and function efficiently. Therefore, option C, "prevent polarisation in the cell," is the correct answer.