JAMB UTME - Physics - 1995

What is the approximate critical angle for total internal reflection for diamond if the refractive index of diamond is 2.42?

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The critical angle for total internal reflection is the angle of incidence at which the angle of refraction is 90 degrees. This happens when light travels from a medium with a higher refractive index to a medium with a lower refractive index. The formula for calculating the critical angle is: critical angle = sin⁻¹(n2/n1) where n1 is the refractive index of the medium where the incident ray is traveling, and n2 is the refractive index of the medium where the refracted ray would travel. In this case, the incident medium is diamond, with a refractive index of 2.42. The refracted medium would be the air outside the diamond, with a refractive index of approximately 1. Therefore, we can substitute these values into the formula: critical angle = sin⁻¹(1/2.42) Using a calculator, we can evaluate this expression to get: critical angle = 24.41 degrees (approx.) Therefore, the approximate critical angle for total internal reflection for diamond is approximately 24 degrees. So the correct answer is option D: 24o.

If the maximum voltage across a 100ohms resistor is 20V, then the maximum power it can dissipate is

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The maximum power that a resistor can dissipate is determined by the maximum voltage applied to it and its resistance value. The formula for calculating the power is P = V^2/R, where P is power in watts, V is voltage in volts and R is resistance in ohms. Therefore, substituting the values given in the question, we have: P = (20V)^2 / 100ohms = 400 / 100 = 4.00W Hence, the maximum power that the resistor can dissipate is 4.00W.

The half-life of a radio-active element is 9 days, what fraction of atoms has decayed in 36 days?

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The length of a displaced pendulum ball which passes its lowest point twice every seconds is [g = 10m-2]

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This question is asking for the length of a pendulum that passes its lowest point twice every second, given that the acceleration due to gravity (g) is 10m/s^2. The period of a pendulum is given by the formula T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. In this case, the period is 1/2 seconds (since the pendulum passes its lowest point twice every second). We can rearrange the formula to solve for the length of the pendulum, l = g(T/2π)^2. Plugging in the given values, we get l = 10(1/(2π))^2 ≈ 0.25 meters. Therefore, the answer is  0.25 m.

A body of mass 40kg is being dragged along the floor by a rope inclined at 60 degrees to the horizontal. The frictional force between the box and the floor is 100N and the tension on the rope is 300N. How much work is done by dragging the box for a distance of 4m

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The work done in this situation can be calculated using the formula: Work = Force x Distance x cos(theta) where force is the net force acting on the object, distance is the distance traveled by the object, and theta is the angle between the direction of the force and the direction of motion. First, we need to calculate the net force acting on the object. We can do this by resolving the forces acting on the object along the horizontal and vertical directions. The vertical component of the tension force is equal to Tsin(60), which is equal to 300 x 0.5 = 150 N. The weight of the object is equal to mg, which is equal to 40 x 9.8 = 392 N. Since the object is not moving vertically, the vertical component of the net force acting on the object is zero. The horizontal component of the tension force is equal to Tcos(60), which is equal to 300 x 0.5 = 150 N. The frictional force acting on the object is equal to 100 N. Therefore, the net force acting on the object along the horizontal direction is equal to: Fnet = Tcos(60) - frictional force = 150 - 100 = 50 N Now we can calculate the work done by using the formula: Work = Force x Distance x cos(theta) = Fnet x distance x cos(0) = 50 x 4 x 1 = 200 J Therefore, the work done by dragging the box for a distance of 4m is 200J. The correct option is (C) 200J.

At different locations on the earth's surface, the earth's magnetic field is

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Two parallel plates at a distance of 8.0 x 10-3m apart are maintained at a p.d of 600 volts with the negative plate earthed. What is the electric field strength?

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The electric field strength between two parallel plates can be calculated using the formula E = V/d, where V is the potential difference between the plates, and d is the distance between the plates. In this case, the potential difference between the plates is given as 600 volts, and the distance between the plates is given as 8.0 x 10^-3 meters. So, substituting these values in the formula, we get: E = V/d = 600 / (8.0 x 10^-3) = 75,000 V/m Therefore, the electric field strength between the parallel plates is 75,000 V/m, which corresponds to option D.

The resultant capacitance in the figure above is

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The figure above shows two similar bulbs X and Y connected to suitable power supply with F as an appropriate fuse rating, if the filament of X breaks then the

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The difference between sound waves and light waves is that sound waves

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The difference between sound waves and light waves is that sound waves require a medium to travel while light waves do not. Sound waves are mechanical waves that travel by compressing and expanding the medium they are passing through, such as air or water. In contrast, light waves are electromagnetic waves that can travel through a vacuum, like space, as they do not need a medium to propagate. While sound waves are longitudinal waves, meaning the particles of the medium move parallel to the direction of the wave, light waves are transverse waves, meaning the particles oscillate perpendicular to the direction of the wave. This is not the main difference between the two, as both types of waves can be diffracted and light waves can be reflected, while sound waves cannot.

The pitch of an acoustic device can be increased by

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The pitch of an acoustic device refers to how high or low the sound is perceived by the human ear. It is directly related to the frequency of the sound wave. Therefore, to increase the pitch of an acoustic device, we need to increase its frequency. Thus, the correct option is "increasing the frequency". Increasing the amplitude of a sound wave would make it louder, but it would not affect the pitch. Similarly, decreasing the loudness would not affect the pitch either. Finally, decreasing the intensity of a sound wave would make it less powerful, but it would not affect the pitch either.

Which of the following is required to convert a milliammeter to an ammeter?

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To convert a milliammeter (which measures milliamperes) to an ammeter (which measures amperes), a low resistance in parallel is required. This is because an ammeter should ideally have zero resistance, and adding a low resistance in parallel with a milliammeter will effectively reduce its resistance, allowing it to measure higher current values without affecting the circuit being measured.

The value of T in the figure above is

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Which of the following is the dimension of pressure?

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Pressure = heg

= m x $\frac{kg}{m^3}$ x $\frac{m}{5^2}$

= ML-1T-2

A quantity of ice at 10oC is heated until the temperature of the heating vessel is 90oC. Which of the following constants is NOT required to determine the quantity of heat supplied to the vessel?

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A body is projected from the earth's surface with the intention of letting it escape from the earth's gravitational field. What is the minimum escape velocity of the body? [Earth's radius = 6.4 x 103km, g = 10ms-2]

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The minimum escape velocity of a body is the velocity required to escape from the gravitational field of a planet, which means that the body will move away from the planet and never return. The formula for escape velocity is given by: v = √(2GM/r) where G is the universal gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet to the point where the body is located. In this case, the planet is Earth, with a radius of 6.4 x 10^3 km, and g = 10 m/s^2. The mass of Earth is approximately 5.97 x 10^24 kg. The distance from the center of the planet to the surface is equal to the radius of the planet. Substituting these values into the formula, we get: v = √(2 x 6.67 x 10^-11 x 5.97 x 10^24 / 6.4 x 10^3) v ≈ 11.2 km/s Therefore, the minimum escape velocity of the body is approximately 11 km/s, which is closest to option D, 11 kms^-1.

Which of the following is the exclusive property of a transverse wave?

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The property that is exclusive to transverse waves is polarization. In a transverse wave, the particles of the medium vibrate perpendicular to the direction of wave propagation. This means that the wave has a direction of oscillation that is perpendicular to its direction of travel. Polarization refers to the orientation of the direction of oscillation of the wave. In a transverse wave, the direction of oscillation is perpendicular to the direction of travel, and this direction can be restricted to a single plane. This means that transverse waves can be polarized, while longitudinal waves cannot be. Diffraction, refraction, and compression are properties that are not exclusive to transverse waves. Diffraction refers to the bending of a wave around an obstacle, refraction refers to the bending of a wave as it passes through a medium with different properties, and compression is a property of longitudinal waves where the particles of the medium vibrate parallel to the direction of wave propagation, causing areas of high and low pressure. So the correct answer is option D: polarization.

A vehicle of mass m is driven by an engine of power P from rest. Find the minimum time it will take to acquire a speed

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An electric kettle with negligible heat capacity is rated at 2000W. If 2.0kg of water is put in it, how long will it take the temperature of water to rise from 20OC to 100OC? [specific heat capacity of water = 4200Jkg-1k-1]

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To solve this problem, we can use the formula: heat energy = mass * specific heat capacity * temperature change First, we need to calculate the amount of heat energy required to heat up 2.0kg of water from 20°C to 100°C: heat energy = 2.0kg * 4200J/kg°C * (100°C - 20°C) heat energy = 672,000J Next, we can use the power rating of the kettle to calculate the time required: power = energy / time time = energy / power time = 672,000J / 2000W time = 336 seconds or 5.6 minutes (to 2 significant figures) Therefore, the answer is 336 seconds or 5.6 minutes. The correct option is (ii).

The equation PxVyTz = constant in charles' law when

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Temperature is the measure of the

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Temperature is the measure of the mean kinetic energy of the molecules of an object. It is a physical quantity that determines the direction of heat flow between two objects in contact. The higher the temperature of an object, the higher the mean kinetic energy of its molecules and the greater its capacity to transfer heat to other objects. Conversely, a lower temperature corresponds to a lower mean kinetic energy and a lower capacity to transfer heat. Temperature is usually measured in degrees Celsius (°C) or Fahrenheit (°F), or in kelvin (K) in the international system of units.

A light of energy 5eV falls on a metal and the electrons with a maximum kinetic energy of 2eV are ejected. The work function of the metal is

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When light of energy 5eV falls on a metal, it can cause electrons to be ejected from the surface of the metal. The maximum kinetic energy of these electrons is 2eV. The work function of a metal is the minimum amount of energy needed to remove an electron from the surface of the metal. We can use the formula: Maximum kinetic energy of electrons = Energy of the incident light - Work function Rearranging the formula to solve for the work function: Work function = Energy of the incident light - Maximum kinetic energy of electrons Plugging in the given values: Work function = 5eV - 2eV = 3eV Therefore, the work function of the metal is 3.0eV. Option (c) is the correct answer.

When a ball rolls on a smooth level ground, the motion of its center is

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When a ball rolls on a smooth level ground, the motion of its center is translational. Translational motion is when an object moves without rotation, i.e., when all parts of the object move through the same distance and direction at the same time. In the case of a rolling ball, the ball rotates about its own axis while also moving in a straight line. However, the motion of the center of the ball is only in a straight line, without any rotation. This is because the center of the ball is the point at which the ball's motion is purely translational. The other points on the ball's surface, except for the point in contact with the ground, are also moving in a circular path, which is a combination of translational and rotational motion. Therefore, the correct answer is option A: translational.

If a resistance is halved in value and the potential difference across it is tripled, then the ratio of the new current to the old one is

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$\frac{V_1}{V_2}$ = $\frac{I_1{R}_1}{I_2{R}_2}$

$\frac{I_1}{I_2}$V2 = 3V1 and R1 = 2R2

$\frac{V_1}{3V_1}$ = $\frac{I_1\times 2R_2}{I_2\times R_2}$

$\frac{I_1}{I_2}$ = $\frac{6}{1}$

In the above fig, PQ and R are vectors, which of the following options, gives a correct relationship between the vectors

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A hydraulic press has a large circular piston of radius 0.8m and a circular plunger of radius 0.2m. A force of 500N is exerted by the plunger. Find the force exerted on the piston

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Pressure on piston = pressure on the plunger

$\frac{520}{\pi \times 0.8\times 0.8}$ = $\frac{F}{\pi \times 0.2\times 0.2}$

F = 31N

A uniform rod PQ of length 1m and mass 2kg is pivoted at the end p. If load of 14N is placed at the center of the rod, find the force that should be applied vertically upwards at Q to maintain the rod at equilibrium horizontally [g = 10ms-2]

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The primary winding of a transformer has 400 turns and its secondary has 100 turns. If a source of e.m.f. of 12V is applied to the primary, the secondary e.m.f. will be

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The ratio of the number of turns in the primary winding to the number of turns in the secondary winding of a transformer is called the turns ratio. In this case, the turns ratio is 400:100, or 4:1. When a voltage is applied to the primary winding of a transformer, it creates a changing magnetic field which induces a voltage in the secondary winding. The magnitude of the induced voltage depends on the turns ratio. To calculate the secondary voltage in this transformer, we can use the turns ratio and the voltage applied to the primary. Since the turns ratio is 4:1, the secondary voltage will be one-fourth the primary voltage. Therefore, the secondary voltage in this transformer will be 12V divided by 4, which is equal to 3V. So the correct answer is option A: 3V.

An electric current of 2 amperes flows in a heating coil of resistance 50 ohms for 3 minutes 20 seconds. Determine the heat produced

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Heat energy = Elect. energy

heat energy= I2RT

= 2 X 2 X 50 X 200

= 40000J

to convert to kJ, divide J by 1000

hence, $\frac{40000}{1000}$ = 40kJ

A 12V battery has an internal resistance of 0.5W.If a cable of 1.0W resistance is connected across the two terminals of the battery, the current drawn from the battery is

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The problem provides the voltage and internal resistance of a 12V battery and the resistance of an external cable that is connected to the battery terminals. To find the current drawn from the battery, we can use Ohm's law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. First, we need to calculate the total resistance in the circuit. The total resistance is the sum of the internal resistance of the battery and the resistance of the external cable. Therefore, Total Resistance = Internal Resistance of Battery + Resistance of External Cable = 0.5W + 1.0W = 1.5W Next, we can use Ohm's law to find the current drawn from the battery: Current = Voltage / Total Resistance = 12V / 1.5W = 8.0A Therefore, the current drawn from the battery is 8.0A. So, the correct option is 8.0A.

What is the acceleration due to gravity 'g' on the moon, if g is 10-2 on the earth?

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s = 10-2 on earth

g = 6 ms-2 on earth

Earth on moon = $\frac{10}{6}$

= 1.6ms-2

Which of the following pairs of colours gives the widest separation in the spectrum of white light?

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White light is made up of different colors that we can see when we pass it through a prism or see a rainbow. The colors are arranged in a specific order called the color spectrum. The question asks which pair of colors gives the widest separation in the spectrum of white light. The colors in the spectrum are red, orange, yellow, green, blue, indigo, and violet. The wider the separation between two colors, the more distant they are from each other in the spectrum. Out of the given options, the pair that gives the widest separation in the spectrum of white light is "Red and Violet". This is because red is at one end of the spectrum, and violet is at the other end, making them the farthest from each other. Therefore, when we pass white light through a prism, we can see the widest separation of colors between red and violet.

An alternating source is connected in series to a capacitor of capacity reactance ${10}^3\sqrt{3}$ and a resistor of resistance 103 Ohms. The Impedance of the circuit is...

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A real object is placed at a distance ucm in front of a curved mirror of focal length fcm. If the image is upright and magnified, then the mirror is

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The energy contained in a wire when it extended by 0.02m by a force 500 N is

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This question involves calculating the energy contained in a wire that has been extended by a certain distance due to a force applied to it. The formula used to calculate the energy contained in a spring is given by: Energy = (1/2) * force * extension Where force is the applied force and extension is the distance the wire has been extended. Using the values given in the question, we have: Energy = (1/2) * 500 N * 0.02 m Energy = 5 J Therefore, the answer is 5J. Explanation: When a force is applied to a wire, it gets stretched or extended. The amount of extension in the wire is proportional to the force applied to it. The energy stored in the wire due to the applied force is given by the formula (1/2) * force * extension, where force is the applied force and extension is the distance the wire has been extended. In this case, the wire has been extended by 0.02 m due to an applied force of 500 N, so the energy contained in the wire is 5 J.

The acceleration of the system show above is

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A rectangular metal block of volume 10-6m3 at 273k is heated to 573k. If its coefficient of linear expansion is 1.2 x 10-5k-1, the percentage change of it volume is

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Y = $\frac{\Delta V}{V\times \Delta \theta }$

3 x 10-5 x 1.2 = $\frac{\Delta V}{{10}^{-6}\times (573-273)}$

$\Delta$V = 1080 x 10-11m3

%$\Delta$V = $\frac{1080\times 10}{{10}^{-6}}$ x 100

= 1.08%

$\approx$ = 1.1%

The wavelength of signals from a radio transmitter is 1500mm and the frequency is 200kHz. What is the wavelength for a transmitter operating at 100kHz?

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The wavelength of a wave can be calculated using the formula: wavelength = speed of light / frequency where the speed of light is a constant value of 3 x 10^8 meters per second. In the given problem, the wavelength of signals from a radio transmitter is 1500mm and the frequency is 200kHz. We can use this information to calculate the speed of the radio waves: wavelength = speed of light / frequency 1500mm = (3 x 10^8 m/s) / 200000 Hz 1500mm = 1500 x 10^-6 m Now we need to find the wavelength for a transmitter operating at 100kHz. We can use the same formula: wavelength = speed of light / frequency wavelength = (3 x 10^8 m/s) / 100000 Hz wavelength = 3000 m However, the answer is not in meters, but in millimeters, so we need to convert it: wavelength = 3000 m x 1000 mm/m wavelength = 3,000,000 mm Therefore, the wavelength for a transmitter operating at 100kHz is 3,000,000 mm or 3,000 m. The correct option is (B) 300m.

Which of the following statements are TRUE about frictional force? i. it is always a disadvantage ii. it is sometimes a disadvantage iii. it always exist where there is a relative motion of two bodies that are in contact iv. it is sometimes very useful

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The statement that is true about frictional force is that it is sometimes very useful, which is represented by option ii, iv only. Frictional force is the force that opposes motion between two surfaces that are in contact with each other. While it can be a disadvantage in certain situations, such as when it causes wear and tear on machinery or creates heat, it can also be very useful. For example, friction allows us to walk without slipping, provides the necessary grip for car tires to adhere to the road, and allows us to write with a pen or pencil. Without frictional force, it would be challenging to perform many daily tasks that we take for granted. Therefore, statement ii and iv are true, as frictional force is sometimes useful, and it exists where there is relative motion of two bodies in contact. Statement i is false, as frictional force is not always a disadvantage, and statement iii is partly true, as frictional force does exist where there is relative motion of two bodies in contact, but it can also exist even if there is no relative motion.

A temperature scale has a lower fixed point of 40mm and a upper fixed point of 200mm. What is the reading on this scale when a thermometer reads 60oC?

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200mm ..... 100oC

Xmm ..... 60oC

400mm ..... 0oC

$\frac{x-40}{200-40}$ = $\frac{60-0}{100-0}$

X = 136mm

The purpose of a dielectric material in a parallel plate capacitor is to

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Which of the following statements give the TRUE difference between evaporation and boiling? i. Evaporation occurs at all temperatures while boiling occurs at a fixed temperature for a given pressure. ii. Evaporation is a surface phenomenon while boiling is an interior phenomenon. iii. Evaporation is affected by surface area while boiling is not.

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Total eclipse of the sun occurs when the

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A total eclipse of the sun occurs when the moon is between the sun and the earth. During this event, the moon blocks the sun's light completely or partially, causing a shadow on the earth's surface. Therefore, option C, "moon is between the sun and the earth," is the correct answer. Option A, "earth is between the moon and the sun," describes a lunar eclipse, and option B, "sun is between the moon and the earth," is not possible as the moon cannot pass behind the sun. Option D, "ozone layer is threatened," is unrelated to the occurrence of a total eclipse of the sun.

A well-lagged bar of length 100cm has its ends maintained at 100oC and 40oC respectively. What is the temperature at a point 60cm from the hotter end?

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100oC ....100cm

60oC ....60cm

40oC .... 0cm

$\frac{\theta -40}{100-40}$ = $\frac{60-0}{100-0}$

$\theta$ = 76oC

The volume of an air bubble increases from the bottom to the top of a lake at constant temperature because

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A piece of wood floats inside water at room temperature with a fraction of it above the liquid surface. As the temperature of the water is raised, the part of the wood above the liquid will

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