JAMB UTME - Physics - 2016

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When a person sits between two parallel mirrors, the mirrors reflect the person's image back and forth between them. Each reflection of the person's image is itself reflected in the other mirror, creating an infinite number of images. This happens because the light from the person's image bounces back and forth between the mirrors, with each bounce creating a new reflection. Although the person can only see a limited number of reflections, the light continues to bounce back and forth, creating an infinite number of images. Therefore, the correct answer is "Infinite."

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The upthrust on a body is equal to the weight of the water displaced by the body when it is partially or fully immersed in a fluid. Given that the body weighs 50N in air and displaces 3.7kg of water, we need to first convert the mass of the water displaced to weight. Using the formula weight = mass x gravitational acceleration (g), where g is approximately 9.81 m/s^2, we have: Weight of water displaced = 3.7 kg x 9.81 m/s^2 = 36.297 N Therefore, the upthrust on the body is 36.297 N, which is closest to option B, 37.0N. Note that the upthrust on a body depends on the density of the fluid it is immersed in. If the body is less dense than the fluid, it will experience a buoyant force pushing it upwards. If the body is more dense than the fluid, it will sink. If the body has the same density as the fluid, it will remain suspended in the fluid at a constant depth.

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The correct option is "The rate of condensation is equal to that of vaporization". When a liquid is enclosed and heated, the temperature and pressure increase causing the liquid to turn into a vapor or gas. As the vapor rises, it cools and reaches a point where the temperature and pressure are just right for the vapor to condense back into a liquid. At this point, the rate of condensation (the amount of vapor turning back into liquid) is equal to the rate of vaporization (the amount of liquid turning into vapor). This is called being "saturated". So, when vapor is said to be saturated on top of an enclosed liquid, it means that the rate of condensation and vaporization are equal, and the amount of vapor and liquid are in balance.

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The angular magnification of a telescope can be calculated using the formula: m = -fo/fe where m is the angular magnification, fo is the focal length of the objective lens, and fe is the focal length of the eyepiece. In this case, the focal length of the objective lens is 30cm, and the focal length of the eyepiece is 3cm. Plugging these values into the formula gives: m = -30/3 = -10 Therefore, the angular magnification of the telescope is -10. The negative sign indicates that the image formed by the telescope is inverted. To understand this result, consider that the objective lens forms a real inverted image of the object being viewed. This image is located at a distance equal to the focal length of the eyepiece. The eyepiece then acts as a magnifying glass to further magnify the image. The angular magnification tells us how much larger the image appears through the telescope compared to the naked eye. In this case, the image appears 10 times larger, but inverted, when viewed through the telescope.

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The instrument used to view stars is the telescope. A telescope is a tool that gathers light and focuses it to create a magnified image of distant objects, such as stars, planets, and galaxies. It works by using a series of lenses or mirrors to capture and amplify light, allowing us to see objects that would otherwise be too dim or far away to be seen with the naked eye. Telescopes are essential tools for astronomers, who use them to study the properties and behavior of celestial objects, including stars.

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Boiling occurs when the vapor pressure of a liquid becomes equal to the atmospheric pressure. When the vapor pressure of a liquid reaches atmospheric pressure, it means that the pressure of the vaporized liquid is enough to overcome the atmospheric pressure, and the liquid starts to boil. This means that the liquid is converting into gas, and bubbles of gas are forming in the liquid and rising to the surface. Think of it this way: when you heat up a pot of water, the heat causes the water to vaporize, or turn into steam. As the steam rises, it creates pressure, and if that pressure is strong enough to overcome the atmospheric pressure, the steam will escape from the pot and you'll see boiling.

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t1/2 = $\frac{0.693}{\gamma }$ = $\frac{0.693}{{10}^{-}6}$

= 6.93 x 107

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Semiconductors are a type of solid material that can conduct electricity, but not as well as metals. Their ability to conduct electricity increases as more electrons are freed up to move around the material. This can happen in a few different ways, but the most common is by adding energy to the material. When we add energy to a semiconductor, for example by shining light on it or heating it up, some of the electrons in the material gain enough energy to break free from their atoms and move around. These free electrons can then carry an electric current through the material. As we add more energy to the material, more electrons are freed up, and the conductivity increases. So, the answer to the question is: Temperature. As the temperature of a semiconductor increases, more electrons gain enough energy to break free and conduct electricity, which increases the conductivity of the material.

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E = $\frac{E_o}{n^2}$ = $\frac{13.6}{3^2}$ = $\frac{13.6eV}{9}$

= 1.51eV

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Gamma rays have the shortest wavelength among the listed electromagnetic waves. Electromagnetic waves are a type of energy that can travel through space. They have different wavelengths, which determine their properties and characteristics. Wavelength is the distance between two consecutive peaks or troughs of a wave. The electromagnetic spectrum is the range of all types of electromagnetic radiation. Gamma rays have the shortest wavelength in the spectrum, which means that they have the highest frequency and energy. They are produced by nuclear reactions and radioactive decay. In contrast, visible light has a longer wavelength than gamma rays, and it can be seen by the human eye. Ultraviolet rays have a shorter wavelength than visible light, and they can cause sunburns and skin damage. Infrared rays have a longer wavelength than visible light, and they are used in remote controls and heat lamps.

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To find the focal length of a convex lens, we can use the formula: 1/f = 1/do + 1/di where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens. In this case, the image is virtual and the magnification is given as 3. This means that the image is 3 times larger than the object. We can use the magnification formula to find the distance of the image from the lens: m = -di/do where m is the magnification, di is the distance of the image from the lens, and do is the distance of the object from the lens. Substituting m = 3 and do = 10cm, we get: 3 = -di/10cm Solving for di, we get: di = -30cm Note that the negative sign indicates that the image is virtual. Now we can use the lens formula to find the focal length of the lens: 1/f = 1/do + 1/di Substituting do = 10cm and di = -30cm, we get: 1/f = 1/10cm + 1/-30cm Simplifying the equation, we get: 1/f = -1/15cm Multiplying both sides by -15cm, we get: f = -15cm Note that the negative sign indicates that the lens is a convex lens. Therefore, the focal length of the lens is -15cm or 15cm (taking the absolute value). Option D, 15cm, is the correct answer.

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The wave that is both transverse and mechanical is "water waves." Transverse waves are waves that vibrate perpendicular to the direction of the wave's motion. In the case of water waves, the water molecules move up and down, perpendicular to the direction of the wave's motion. Mechanical waves are waves that require a medium (such as air, water, or solids) to travel through. In the case of water waves, the medium is water. The water waves are created by a disturbance on the surface of the water, such as wind or a moving object. Therefore, water waves are both transverse and mechanical because they vibrate perpendicular to the direction of their motion and require a medium (water) to travel through. The other options listed are not both transverse and mechanical. Radio waves and X-rays are both examples of electromagnetic waves, which are not mechanical waves as they do not require a medium to travel through. Sound waves are mechanical waves, but they are not transverse waves as they vibrate parallel to the direction of their motion.

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F = Ma + mg = 60 x 10 x 60 x 10 = 1200N

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The neutral point in the diagram is at "X". The neutral point is the point in an electrical system where the voltage is equal to zero and there is no flow of current. It is a reference point for measuring the voltage and current in the electrical circuit. In this diagram, "X" is the point where the three phase wires are connected, making it the neutral point.

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n = $\frac{\text{Read depth}}{\text{Apparent depth}}$ = 1.33 = $\frac{Rd}{1}$

Rd = 1.33 x 1 = 1.330m

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The statement that is not true about atoms is "Atoms of all elements are identical." Atoms are the basic building blocks of matter, and they are made up of a central nucleus composed of positively charged protons and neutral neutrons, with negatively charged electrons orbiting around the nucleus. Each element has a unique number of protons in its nucleus, which is known as the atomic number. The number of protons also determines the chemical properties of the element. Therefore, the atoms of different elements are not identical, as they have different numbers of protons, neutrons, and electrons. This also means that the atoms of different elements have different atomic weights, as the atomic weight is determined by the number of protons and neutrons in the nucleus. In summary, while atoms share certain characteristics, such as having a nucleus and electrons, the atoms of different elements are not identical and have different atomic weights.

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If the distance between the object and the pinhole of a pinhole camera is reduced by half the size of the image of the object is doubled. In a pinhole camera, light from an object passes through a small hole (pinhole) and forms an inverted image on a screen or film at the back of the camera. The size of the image formed on the screen depends on the distance between the object and the pinhole. When the distance between the object and the pinhole is halved, the angle of the light rays from the object that reach the pinhole is doubled. As a result, the size of the image formed on the screen is also doubled. Therefore, the correct option is "Is doubled".

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When the humidity of the air is very low, the air is very dry and can absorb a lot of moisture. If there is a water pool in such an environment, the water will evaporate quickly because the air is eager to absorb the moisture from the pool. Therefore, the water in the pool will decrease rapidly and the pool may even dry out completely, depending on the size of the pool and the humidity of the air. So the correct answer is "Rapid evaporation".

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When two tuning forks of slightly different frequencies are sounded close to each other, they produce what is called a beat. The beat frequency is the difference between the frequencies of the two tuning forks. In this case, the beat frequency can be calculated as follows: Beat frequency = |258 Hz - 270 Hz| = 12 Hz Therefore, the correct answer is 12Hz. When the two tuning forks are sounded together, they will produce a sound wave with a frequency that is the average of the two frequencies. However, since the frequencies are slightly different, the two sound waves will periodically reinforce and cancel each other out, producing the beat frequency that we hear. The beat frequency is the rate at which the sound waves reinforce and cancel each other out, and is equal to the difference between the frequencies of the two tuning forks.

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A manometer is an instrument used for measuring pressure in liquids and gases. It works by using a liquid, usually water or mercury, to balance the pressure being measured against the atmospheric pressure. The difference in height between the two sides of the liquid column is used to determine the pressure. This type of instrument is commonly used in scientific experiments and industrial applications to measure the pressure of gases and liquids in closed systems.

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The time required to bring a train to a complete halt can be calculated using the formula: Time = velocity / acceleration where velocity is the initial velocity of the train and acceleration is the deceleration (negative acceleration) experienced by the train. In this case, the initial velocity is 20 m/s and the deceleration is -2 m/s^2. So, we can calculate the time as follows: Time = 20 m/s / -2 m/s^2 = 10 s So, the correct answer is 10 seconds.

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A satellite revolving around the Earth is kept on its orbit by centripetal forces only. Centripetal force is the force that keeps an object moving in a circle, and it always acts towards the center of the circle. In the case of a satellite orbiting the Earth, the centripetal force is provided by the gravitational attraction between the Earth and the satellite. The gravitational force between the two objects is what keeps the satellite moving in a circular path around the Earth. The speed of the satellite is also important in maintaining its orbit, as it needs to be moving at a specific speed to balance the gravitational force and maintain a stable orbit. Frictional and centrifugal forces do not play a significant role in keeping a satellite in orbit around the Earth.

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The formula for inductance of a coil is given by L = V / (2 * π * f * I), where V is the voltage, f is the frequency, I is the current and π is pi. Since the resistance of the coil is 30 Ω and the current drawn by the coil is 2A, the voltage across the coil is 30 * 2 = 60V. The frequency of the AC source is not given, so we can assume it to be 50Hz (a commonly used frequency). Plugging in the values in the formula, we get: L = 60 / (2 * π * 50 * 2) L = 60 / (2 * π * 100) L = 0.6 / π L = 0.19H So, the inductance of the coil is approximately 0.19H, which is closest to 0.04H.

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When the temperature of a gas is reduced, the gas molecules lose kinetic energy and move slower. As a result, they collide less frequently and with less force with the walls of the container holding the gas, which means they exert less pressure on the walls. Therefore, if the temperature of a gas is reduced to -273°C (also known as absolute zero), the gas molecules will have no kinetic energy and will not be able to exert any pressure on the container. So the correct answer is: "It will drop to zero."

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To balance the ruler horizontally, the 15N force must hang at a distance of 20cm from the mid-point. The idea behind balancing the ruler is to ensure that the torques (or rotational forces) caused by the forces on either side of the pivot point are equal. Torque is calculated by multiplying the force by the distance from the pivot point. In this case, the 10N force creates a torque of 10N * 0.3m = 3Nm at a distance of 30cm from the pivot point. To balance this torque, we need to apply a force of 15N at a distance of x from the pivot point. The torque created by this force must equal 3Nm, so we can set up an equation to solve for x: 15N * x = 3Nm Dividing both sides by 15N, we get: x = 3Nm / 15N = 0.2m = 20cm So, the 15N force must hang at a distance of 20cm from the mid-point to balance the ruler horizontally.

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The correct answer is "heat capacity". Heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 Kelvin (or 1 degree Celsius). In other words, it measures the ability of a substance to store heat energy. Specific heat capacity is similar to heat capacity, but it is defined as the amount of heat energy required to raise the temperature of one unit of mass of a substance by 1 Kelvin. So, heat capacity is the total amount of heat energy required to raise the temperature of any given mass of a substance by 1 Kelvin, while specific heat capacity is the amount of heat energy required to raise the temperature of one unit of mass (such as one gram) of a substance by 1 Kelvin. Specific latent heat of vaporization and specific latent heat of fusion are measures of the amount of heat energy required to change the state of a substance from solid to liquid (latent heat of fusion) or from liquid to gas (latent heat of vaporization), without a change in temperature. Capacity latent heat of fusion is not a commonly used term in physics or chemistry.

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When an object is placed in front of a plane mirror, the image formed is virtual and appears to be as far behind the mirror as the object is in front of the mirror. The image is upright and is the same size as the object. In this problem, the object is initially placed 15 cm in front of the plane mirror. The image will be formed 15 cm behind the mirror, and the distance between the object and the image will be twice the distance between the object and the mirror, which is 30 cm. Therefore, the image is formed at a distance of 30 cm from the object. If the mirror is moved 5 cm further away from the object, the new distance between the object and the mirror is 20 cm. Using the same reasoning as before, the distance between the object and the image is twice this distance, or 40 cm. Therefore, the image is now formed at a distance of 40 cm from the object. Hence, the correct option is: - 40 cm

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A dynamo is a device that converts mechanical energy into electrical energy. Mechanical energy refers to the energy possessed by an object due to its motion or position, while electrical energy is the energy associated with the flow of electric charge. In a dynamo, a rotating coil of wire is placed in a magnetic field. As the coil rotates, it cuts through the magnetic field lines, which induces an electrical current in the wire. This current can be used to power electrical devices. Therefore, option A is the correct answer.

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T = $\frac{PV}{nR}$ = $\frac{7.6x{10}^{6}x{10}^{-}3}{6x8.3}$

= 153oC

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The form of energy that can directly be converted to light energy is option IV, I and III only - Chemical and Electricity. Chemical energy can be converted into light energy in a process called chemiluminescence. This occurs when a chemical reaction releases energy in the form of light. Examples of chemiluminescence include the light emitted by glow sticks and fireflies. Electricity can also be directly converted into light energy through a process called electroluminescence. This occurs when an electric current is passed through certain materials, causing them to emit light. Examples of electroluminescence include the light emitted by LED (light-emitting diode) bulbs and the screens of electronic devices such as smartphones and televisions. Sound energy cannot be directly converted into light energy. However, sound waves can be used to indirectly create light through a process called sonoluminescence. This occurs when sound waves cause bubbles in a liquid to collapse, releasing energy in the form of light.

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The rate of cooling of a heated quantity of liquid in an enclosure depends on the temperature in the enclosure. This is because heat energy always flows from a hotter object to a colder one until they reach the same temperature. So, if the enclosure is colder than the heated liquid, the heat energy will flow from the liquid to the enclosure and the liquid will cool down. The pressure of the liquid, pressure of the enclosure, and volume of the liquid may affect the behavior of the liquid, but they do not directly impact the rate of cooling of the liquid in the enclosure.

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The direction of the force between the North (N) and South (S) poles in a magnetic field is from the North pole to the South pole. In the diagram above, the North pole is located at the top of the magnet (labeled "N") and the South pole is at the bottom (labeled "S"). Therefore, the direction of the force between N and S is downwards, which corresponds to option NS.

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The correct option is: "Temperature of a liquid increases." Saturated vapour pressure refers to the pressure of the vapour in equilibrium with its liquid form at a particular temperature. When the temperature of a liquid is increased, the kinetic energy of its molecules also increases, causing more molecules to escape from the liquid surface and enter the vapour phase. As a result, the concentration of vapour in the air above the liquid increases, leading to an increase in the pressure of the vapour. On the other hand, when the volume of the liquid is increased or decreased, the concentration of vapour in the air above the liquid remains the same, as long as the temperature remains constant. Therefore, the saturated vapour pressure does not change with a change in the volume of the liquid. Similarly, when the temperature of the liquid decreases, the kinetic energy of its molecules decreases, causing fewer molecules to escape from the liquid surface and enter the vapour phase. Therefore, the concentration of vapour in the air above the liquid decreases, leading to a decrease in the pressure of the vapour.

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t = $\frac{usin\theta }{g}$ = $\frac{300\text{sin}30}{10}$

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$\frac{g}{R^2}$ = $\frac{g}{4^2}$ = $\frac{g}{16}$

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The correct statement about a machine is: "Efficiency decreases with an increase in friction." A machine is a device that makes work easier by multiplying force, changing the direction of a force, or changing the distance or speed of a force. The efficiency of a machine is a measure of how much of the input work is converted into useful output work. Friction is a force that opposes motion between two surfaces in contact. It is a common factor that reduces the efficiency of machines by converting some of the input work into heat energy, which is wasted. When there is more friction between the moving parts of a machine, more input work is required to overcome the resistance, and less output work is produced. Therefore, the efficiency of the machine decreases as the friction increases. Velocity ratio and mechanical advantage are other important factors to consider when evaluating the performance of a machine. The velocity ratio is the ratio of the distance moved by the effort force to the distance moved by the resistance force, while the mechanical advantage is the ratio of the output force to the input force. These factors are not directly related to friction and can be affected by other factors such as the design and construction of the machine.

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