JAMB UTME - Physics - 2018

Which of the following is true of an electrical charge?

Answer Details

The correct answer is option D: "All of the above." An electrical charge refers to the presence of an excess or deficit of electrons in an atom or molecule. In this context, positive charge means a deficit of electrons, whereas negative charge means an excess of electrons. Electric current refers to the flow of charged particles, typically electrons, through a conductor. Therefore, an electric current means the movement of electrons. In summary, all of the given options are true of an electrical charge, and they all relate to the behavior of electrons in an electrically charged system.

Which of the following does NOT describe the Image formed by a plane minor?

Answer Details

The option that does NOT describe the image formed by a plane mirror is "Magnified". When an object is placed in front of a plane mirror, the image formed is: 1. Erect: The orientation of the object in the mirror is the same as the orientation of the object in real life. For example, if you raise your right hand in front of a plane mirror, the image in the mirror will also show your right hand raised. 2. Laterally inverted: The image formed in the mirror is flipped horizontally, which means that the left side of the object appears on the right side of the image and vice versa. For example, if you wear a shirt with the letter "H" on it and look at it in a plane mirror, the image will show the letter "H" flipped horizontally. 3. Same distance from the mirror as object: The image formed in the mirror is located behind the mirror at the same distance as the object is located in front of the mirror. For example, if you stand 1 meter away from a plane mirror, the image of yourself will also be located 1 meter away from the mirror, behind the mirror. 4. NOT magnified: The image formed in the plane mirror is of the same size as the object, which means that there is no magnification or reduction in the size of the image. For example, if you stand in front of a plane mirror with a height of 1 meter, the image of yourself in the mirror will also have a height of 1 meter. Therefore, the correct answer is "Magnified", as the image formed by a plane mirror is not magnified.

A force of 5N acts at a point Y on a rod XYZ as shown in this diagram. If XYZ is 2m, what is the moment of the force about point X?

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To find the moment of the force about point X, we need to first understand what moment is. Moment is the turning effect of a force around a pivot point. It is calculated by multiplying the force by the perpendicular distance between the pivot point and the line of action of the force. In this case, the force of 5N is acting on the rod at point Y. To find the moment of this force about point X, we need to find the perpendicular distance between point X and the line of action of the force. From the diagram, we can see that the perpendicular distance between point X and the line of action of the force is 2m (the length of the rod). So, the moment of the force about point X is: Moment = force x perpendicular distance = 5N x 2m = 10Nm Therefore, the correct answer is: 10Nm.

Which of the following is the dimension of pressure

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The dimension of pressure is ML^-1T^-2 Pressure is defined as the force per unit area. This means that pressure is dependent on the force applied and the area over which it is applied. The unit of force is measured in Newtons (N), and the unit of area is measured in square meters (m²). Therefore, the unit of pressure is N/m², which is also known as Pascals (Pa). To determine the dimension of pressure, we need to break down the units into their fundamental dimensions of mass (M), length (L), and time (T). Force is measured in N, which is kg m/s². Area is measured in m², which is L². Therefore, the dimension of pressure can be calculated as (kg m/s²)/(L²), which simplifies to ML^-1T^-2.

What type of reaction is represented by the following scheme?

${}_1^{2}X$ + ${}_1^{2}Y$  -----> ${}_2^{3}Z$ + ${}_1^{0}n$ + energy

Answer Details

The type of reaction represented by the given scheme is a nuclear fission reaction. Nuclear fission is a process where a heavy nucleus is split into smaller nuclei with the release of energy. In the given scheme, a heavy element X is split into two lighter elements, Y and Z, along with the release of energy and some neutrons (n). In a nuclear fission reaction, a neutron is usually absorbed by the nucleus of the heavy element, which then becomes unstable and splits into two smaller nuclei and some neutrons. These neutrons can then go on to split other heavy nuclei, resulting in a chain reaction. In the given scheme, the release of energy and the presence of neutrons suggest that it is a fission reaction. Moreover, the scheme depicts the process of splitting a heavy element into two lighter elements, which is a characteristic of a fission reaction. Therefore, the type of reaction represented by the given scheme is a nuclear fission reaction.

For what values of F and ? will the forces shown in the diagram below be in equilibrium.

Answer Details

Resolve vertically, 40cos? = 20, ? = 60${}^o$
Resolve horizontally, f = 40sin? = 40sin60${}^o$
= 40($\frac{\sqrt{3}}{2}$)
= 20?3 N

Musical instruments playing the same note can be distinguished from one another owing to the difference in their

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Different musical instruments playing the same note can be distinguished from one another due to the difference in their "timbre" or "tone color." Timbre refers to the unique character or quality of a sound that allows us to distinguish it from other sounds even when they have the same pitch and loudness. For example, a piano and a guitar playing the same note will sound different due to the differences in their timbre. This is why we can tell the difference between different instruments and why some instruments are better suited to certain styles of music than others.

Which of the following best describes the energy changes which take place when a steam engine drives a generator which lights a lamp?

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The energy changes that take place when a steam engine drives a generator which lights a lamp can be described as: Heat energy from burning fuel is used to create steam in the boiler of the steam engine. This steam is then used to drive the turbine, which generates kinetic energy as it spins. The kinetic energy is transferred to the generator, which converts it into electrical energy (electricity). The electricity then flows through the wires to the lamp, where it is converted back into light energy, which is what we see. Therefore, the correct option would be: Heat ----> Kinetic ----> Electricity ----> Light

What is the resultant resistance of the circuit in the image shown?

Answer Details

Formulae resistance in parallel
= 1/R = 1/R1 +1/R2
1/R = 1/2 +1/2 = 1
Resistance are now in series
R = 1 + 3 + 4
= 8 ohms

A ball of mass 800g moving horizontally with a speed of 5m/s hits a vertical wall and rebounds with the same speed. The impulse experienced by the ball is?

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The impulse experienced by the ball can be calculated using the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, the momentum of the ball before the collision is: p1 = m * v1 where m is the mass of the ball and v1 is its velocity before the collision. Substituting the values given in the problem, we get: p1 = 0.8 kg * 5 m/s = 4 kg m/s After the collision, the ball rebounds with the same speed but in the opposite direction, so its velocity after the collision is: v2 = -5 m/s The momentum of the ball after the collision is: p2 = m * v2 Substituting the values, we get: p2 = 0.8 kg * (-5 m/s) = -4 kg m/s The negative sign indicates that the direction of the momentum is opposite to that before the collision. The change in momentum of the ball is given by: Δp = p2 - p1 Substituting the values, we get: Δp = (-4 kg m/s) - (4 kg m/s) = -8 kg m/s The negative sign indicates that the impulse experienced by the ball is in the opposite direction to its initial momentum, which is the direction of the wall. Therefore, the impulse experienced by the ball is 8 kg m/s. Therefore, the correct option is: 8kgm/s.

An electric heating coil rated at 1KW is used to heat 2kg of water for 2 minutes. The initial water temperature is 30${}^o$C. Taking the specific heat of the water as 4,000Jkg ${}^{-1}$ and neglecting that of the container, the final water temperature is

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To determine the final temperature of the water, we can use the formula: Q = mcΔT where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. We know that the power of the electric heating coil is 1KW, which means it transfers 1000 Joules of energy per second. In 2 minutes, or 120 seconds, it transfers 120,000 Joules of energy to the water. The mass of the water is given as 2kg and the specific heat capacity of water is 4000 J/kg°C. We can assume that the initial temperature of the water is 30°C. Using the formula, we can solve for the change in temperature: 120,000 J = (2 kg)(4000 J/kg°C)(ΔT) ΔT = 15°C Therefore, the final temperature of the water is 30°C + 15°C = 45°C. So, the final water temperature is 45.0oC.

In a series R-L-C circuit at resonance, the voltages across the resistor and the inductor are 30V and 40V respectively. What is the voltage across the capacitor?

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Mercury which is spilled onto a glass surface forms ball-like shapes because____.

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In case of small drops of mercury, the gravitational potential energy is negligible in comparison to the potential energy due to surface tension.Consequently, to keep the drop in equilibrium, the mercury drop’s surface tends to contract so that its surface area will be the least for a sphere and the drops will be spherical.
But in the case of bigger drops of mercury, the potential energy due to gravity is predominant over the potential energy due to surface tension.Consequently, to keep equilibrium , the mercury drop tends to assume minimum potential energy as possible, the drop becomes oval in shape and lower center of gravity.

Which of the following concepts is not an evidence of the particles nature of matter?

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The particle nature of matter refers to the idea that matter is made up of tiny particles that are constantly moving. Diffusion, Brownian motion, and crystallization are all examples of phenomena that can be explained by the particle nature of matter. However, diffraction is not an evidence of the particle nature of matter. Diffraction is a phenomenon that occurs when waves encounter an obstacle or a slit, causing them to spread out and interfere with each other. While particles can also exhibit diffraction, this is a property of waves and is not specific to particles. In summary, diffusion, Brownian motion, and crystallization are all evidences of the particle nature of matter, but diffraction is not.

A body of mass 100g moving with a velocity if 10ms-1 collides with a wall. If after collision it moves with a velocity of 2.0ms−1 in the opposite direction, calculate the change in momentum.

Answer Details

Momentum = Mass x Velocity
Change in Momentum = Mass x (change in velocity)
Change in Momentum = Mass x (v - u)
Mass = 100g = 0.1kg
U = 2ms${}^{-1}$
V = 10ms${}^{-1}$
Change in momentum = m (v − u)
= 0.1 (10 − 2)
= 0.1 (8)
= 0.8Ns

If the fraction of the atoms of a radioactive material left after 120years is $\frac{1}{64}$, what is the half-life of the material?  $\frac{1}{64}$

Answer Details

The half-life of a radioactive material is the time it takes for half of the atoms in a sample to decay. The fraction of atoms left after a certain number of half-lives can be calculated using the formula: fraction left = (1/2)^(number of half-lives) Let's use this formula to solve the problem. We know that the fraction of atoms left after 120 years is 1/64, which means that: (1/2)^(number of half-lives) = 1/64 To solve for the number of half-lives, we can take the logarithm of both sides: log[(1/2)^(number of half-lives)] = log(1/64) Using the rule that log(a^b) = b*log(a), we can simplify the left side of the equation: number of half-lives * log(1/2) = log(1/64) Dividing both sides by log(1/2), we get: number of half-lives = log(1/64) / log(1/2) Using a calculator or the change of base formula, we can evaluate this expression: number of half-lives = 6 Therefore, the half-life of the material is 120/6 = 20 years.

Temperature is the property of a body which is proportional to the ____.

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Temperature is proportional to the average kinetic energy of the molecules in a body. This means that as the average kinetic energy of the molecules increases, so does the temperature. Think about it like this: the hotter an object, the more energy its molecules have. This energy is what makes the molecules move faster, and therefore, the temperature of the object increases. The average kinetic energy of the molecules is a better measure of temperature than the maximum speed of the molecules because temperature is a measure of the overall energy distribution, not just the energy of a single molecule.

Which of the following obeys Ohm's law?

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Ohm's law states that the current passing through a conductor is directly proportional to the voltage applied across it, given the temperature and other physical conditions remain constant. Among the given options, only "all metals" obey Ohm's law. This is because metals have a linear relationship between their resistance and the applied voltage, meaning that the resistance of a metal remains constant regardless of the voltage applied. As a result, the current passing through a metal is directly proportional to the voltage applied, following Ohm's law. On the other hand, a diode, all electrolytes, and glass do not obey Ohm's law. A diode is a semiconductor that has a non-linear current-voltage relationship, and its resistance is not constant. Similarly, electrolytes and glass are non-metallic substances that do not have a linear relationship between their resistance and the applied voltage. Their resistance can change significantly with the voltage applied, and hence they do not follow Ohm's law.

An object moves in a circular path of radius 0.5m with a speed of 1ms${}^{-1}$. What is its angular velocity?

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Angular velocity is a measure of how fast an object is rotating around a center point. It's usually measured in radians per second (rad/s). To calculate angular velocity, we use the formula: angular velocity = linear velocity / radius. In this case, the linear velocity is 1 m/s, and the radius is 0.5 m. So, the angular velocity would be: 1 m/s / 0.5 m = 2 rad/s Therefore, the answer is 2 rad/s or 2rads^-1

The process whereby a liquid turns spontaneously into vapour is called

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The process whereby a liquid turns spontaneously into vapor is called evaporation. Evaporation is the process by which a liquid changes into a gas at a temperature below its boiling point. This happens when the molecules of the liquid gain enough energy to escape from the surface of the liquid into the air as a gas. The rate of evaporation depends on factors such as the temperature, the humidity of the air, and the surface area of the liquid. For example, a shallow pool of water will evaporate faster than a deep one because it has a larger surface area. Boiling, on the other hand, is the process by which a liquid changes into a gas at its boiling point. This happens when the pressure of the gas generated by the boiling liquid is equal to the atmospheric pressure. The temperature remains constant during boiling. Regelation and sublimation are different processes altogether. Regelation is the process by which a solid changes into a liquid when it is subjected to pressure. Sublimation is the process by which a solid changes directly into a gas, bypassing the liquid state.

A positively charged rod X is brought near an uncharged metal sphere Y and is then touched by a finger with X still in place. When the finger is removed, the result is that Y has

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A lead bullet of mass 0.05 kg is fired with a velocity of 200 ms into a lead block of mass 0.95 kg. Given that the lead block can move freely. the final kinetic energy after impact is

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Shadows and eclipses result from the

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The rectilinear propagation of light means that light travels in straight lines as a wave. This can be observed in the well-defined shadows formed when an object blocks a light source and through the use of a pinhole camera.
According to Sudipa Sarkar, the formation of shadows with sharp edges demonstrates the rectilinear propagation of light, i.e. The fact that light travels in straight line. When an opaque obstacle is placed between a source of light and a screen, a shadow of the obstacle is formed on the screen. The kind of shadow depends on the size of the source of light. If it is a point source (light from a small hole), the shadow obtained is a region of total darkness, called umbra.
If an extended source of light, e.g. a bulb, is used, the umbra is surrounded by a region of partial darkness, called penumbra. The moon is seen because it reflects the sun's light. An eclipse of the moon (lunar eclipse) occurs when the earth comes between the sun and the moon and prevents some of the light from the sun from reaching the moon. In other words, the earth casts its shadow on the moon. The solar eclipse occurs when the moon comes between the sun and the earth.

In the diagram given if the atmospheric pressure is 760mm, the pressure in the chamber G Is

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A resistor connected to a 12V battery draws a current of 2A. The energy dispatched in the resistor in 5 minutes is ___.

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To calculate the energy dispatched in the resistor, we need to use the formula: Energy = Power x Time Where Power is the amount of electrical power consumed by the resistor, and is equal to the product of the voltage across the resistor and the current flowing through it: Power = Voltage x Current In this case, the voltage across the resistor is 12V, and the current flowing through it is 2A. Therefore, the power consumed by the resistor is: Power = 12V x 2A = 24W Now, we can substitute this value of power along with the given time of 5 minutes into the formula for energy: Energy = 24W x 5min x 60s/min = 7,200J Therefore, the energy dispatched in the resistor in 5 minutes is 7,200J. is the correct answer.

Which of the following has the lowest internal resistance when new?

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Among the given options, the Accumulator has the lowest internal resistance when new. Internal resistance is the resistance that a battery or cell provides to the flow of electric current within itself. Lower internal resistance means that the battery can supply more current to an external circuit without losing much of its own energy as heat. An Accumulator, also known as a rechargeable battery, is designed to be charged and discharged multiple times. It has a relatively low internal resistance when new, meaning it can provide a higher current than the other cells listed while wasting less energy internally as heat. A Leclanche cell and Daniell cell are primary cells, meaning they are designed to be used once and discarded. They have higher internal resistance compared to the accumulator, which limits their ability to supply high currents. A Torch battery, also known as a dry cell, is also a primary cell and has a higher internal resistance than the accumulator. It is commonly used in small electronic devices and has a longer shelf life than Leclanche and Daniell cells. In summary, an Accumulator has the lowest internal resistance when new, which makes it an ideal choice for applications requiring high current delivery such as electric vehicles, power tools, and renewable energy systems.

Palm oil from a bottle flows out more easily after it has been heated because the

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Molecules cannot be given energy during the heating and the molecules of oil cannot force each other out

The time rate of loss of heat by a body is proportional to the

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The correct answer is "difference in temperature between the body and its surroundings." When a body is at a higher temperature than its surroundings, it will lose heat to the surroundings until it reaches thermal equilibrium, i.e., until the temperatures of the body and its surroundings are equal. The rate at which the body loses heat is proportional to the temperature difference between the body and its surroundings. This is known as Newton's law of cooling. The law of cooling applies to a wide range of situations, from the cooling of hot beverages to the cooling of electronic devices. It is important to understand this law because it allows us to predict how long it will take for a body to cool down to a certain temperature, and to design systems that can regulate the temperature of a body, such as heaters or refrigerators.

Which of the following statements are TRUE of isotopes?

I. Isotopes of an element have the same chemical properties because they have the same number of electrons

II. Isotopes of elements are normally separated using physical properties

III. Isotopes of an element have the same number of protons in their nuclei

Answer Details

The correct answer is "I and III only". Isotopes of an element have the same number of protons in their nuclei, meaning they have the same atomic number and are therefore the same element. Because of this, they have the same chemical properties. However, isotopes of an element have different numbers of neutrons in their nuclei, which means they have different atomic masses. This is why isotopes can be separated using physical properties such as their mass or other characteristics related to their mass.

The pitch of an acoustic device can be increased by

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The pitch of an acoustic device refers to the perceived highness or lowness of a sound, and is determined by the frequency of the sound wave. To increase the pitch of an acoustic device, you need to increase the frequency of the sound wave. This can be done by increasing the number of vibrations per second that the device produces. So, the correct answer is to "increase the frequency".

Electrical appliances in homes are normally earthed so that

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Electrical appliances in homes are normally earthed so that a person touching the appliances is safe from electric shock. Earthing provides a safety mechanism by connecting the metal case of an electrical appliance to the earth through a conductor. In the event of a fault in the appliance, such as a short circuit, the current will flow through the earth wire instead of the person's body, preventing electric shock. By connecting the metal case of an appliance to the earth, the potential difference (PD) between the appliance and the earth is reduced to zero, ensuring that the appliance is maintained at a lower PD than the earth. Therefore, "the appliances are maintained at a lower pd than the earth" is the correct answer.

In the diagram given the hanging mass m2 is adjusted until m1 is on the verge of sliding. The coefficient of static

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I think the correct option is C ($\frac{m_2}{m_1}$). The coefficient of friction is a ratio of two forces and hence g will cancel out.

The diagram shown represents a block-and-tackle pulley system on which an effort of W Newtons supports a load of 120.0N. If the efficiency of the machine is 40, then the value of W is?

Answer Details

Let the total number of pulleys used in both the blocks be $n$.
In a block-and-tackle pulley system, the velocity ratio is equal to n.
Efficiency = $\frac{\text{MA}}{\text{VR}}\times 100\%$
$\text{MA}=\frac{\text{L}}{\text{E}},\text{VR}=n$
Efficiency = $\frac{\text{L}}{\text{E}}\times \frac{1}{\text{n}}\times 100\%$
$\text{E}=\frac{\text{L}}{\text{Eff.}\times n}\times 100\%$
$\text{E}=\frac{120\text{N}}{40\%\times 6}\times 100\%$
$\text{E}=50\text{N}$

The amount of heat needed to raise the temperature of 10kg of Copper by 1K is its

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The correct answer is "specific heat capacity." Specific heat capacity is a measure of how much heat energy is required to raise the temperature of a certain amount of a substance by 1 degree Celsius (or 1 Kelvin, which is the same size as 1 degree Celsius). In this case, we are dealing with 10kg of copper, so we need to know the specific heat capacity of copper. The specific heat capacity of copper is 0.385 J/g°C (joules per gram per degree Celsius). To calculate the amount of heat needed to raise the temperature of 10kg of copper by 1K, we need to know the total mass of copper (10kg) and the specific heat capacity of copper (0.385 J/g°C). The formula for calculating the amount of heat energy required is: Heat energy = mass x specific heat capacity x change in temperature Since we want to raise the temperature by 1K, the change in temperature is 1K. So, the amount of heat energy required to raise the temperature of 10kg of copper by 1K is: Heat energy = 10kg x 0.385 J/g°C x 1K = 3.85 kJ Therefore, it takes 3.85 kilojoules (kJ) of heat energy to raise the temperature of 10kg of copper by 1K.

An object weighs 30N in air and 21N in water. The weight of the object when completely immersed in a liquid of relative density 1.4 is

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Weight of water displaced = upthrust = 30 - 21 = 9N
Mass of water displaced = $\frac{9}{10}$ = 0.9kg
Volume of object = 9 × 10${}^{-4}$m${}^3$
= (9 × 10${}^{-4}$) (1.4 ×103)

 = 1.26kg = 12N
30 - 12.6 = 17.4N

The product of force and time is?

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The product of force and time is known as impulse. Impulse can be defined as the change in momentum that an object experiences as a result of a force being applied to it over a period of time. In simpler terms, impulse is the "push" that an object receives from a force acting on it for a certain amount of time. The more force applied, or the longer the time the force is applied, the greater the impulse and the greater the change in momentum of the object. It's important to note that impulse is a vector quantity, meaning it has both magnitude and direction. Impulse is a measure of the ability of a force to cause an object to change its velocity, and can be used to explain many phenomena in physics, such as why a heavy object is harder to stop than a lighter one, or why a soccer ball changes direction when it is kicked.

An object is placed 20cm from a concave mirror of focal length 10cm. The linear magnification of the image produced is?

Answer Details

The linear magnification of an image is given by the formula: magnification = height of image / height of object = -v/u where v is the image distance, u is the object distance, and the negative sign indicates that the image is inverted. In this problem, the object is placed 20cm from a concave mirror of focal length 10cm. Since the object is placed beyond the focal point, the image will be real and inverted. Using the mirror formula 1/f = 1/v + 1/u, we can find the image distance v: 1/10 = 1/v + 1/20 Solving for v, we get: v = -20 cm Now, we can use the magnification formula to find the linear magnification: magnification = -v/u = -(-20)/20 = 1 Therefore, the linear magnification of the image produced is 1, which means the image is the same size as the object and is also inverted. The answer is: 1.

The electrochemical equivalent of silver is 0.0012g/C. If 36.0g of silver is to be deposited by electrolysis on a surface by passing a steady current for 5mins, the current must be?

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The electrochemical equivalent of silver is a measure of the amount of silver that is deposited on a surface per unit of charge. In this case, the electrochemical equivalent of silver is 0.0012 grams per Coulomb of charge. To deposit 36.0 grams of silver by electrolysis, we need to know the amount of charge that must be passed through the solution. The amount of charge is given by: Q = m/z where m is the mass of silver to be deposited, 0.0012 is the electrochemical equivalent of silver, and z is the charge on one mole of electrons (z = 1 for a single electron). So, the amount of charge required is: Q = 36.0 g / 0.0012 g/C = 30000 C The current, I, is given by: I = Q / t where t is the time for which the current is flowing. In this case, t = 5 minutes. So, the current required is: I = 30000 C / (5 x 60 s) = 100 A Therefore, the current must be 100 Amperes.

Water of mass 150g at 60${}^o$c is added to 300g of water at 20${}^o$c and the mixture is well stirred. Calculate the temperature of the mixture.(neglect heat losses to the surroundings)

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To solve this problem, we can use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, the energy transferred is in the form of heat. We can use the formula: Q = m*c*(ΔT) where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. First, we can calculate the heat transferred from the hot water to the cold water: Q1 = 150g * 4.18 J/(g°C) * (60°C - T) Q1 = 627 * (60 - T) where T is the temperature of the mixture. Next, we can calculate the heat transferred from the cold water to reach the final temperature of the mixture: Q2 = 300g * 4.18 J/(g°C) * (T - 20°C) Q2 = 1254 * (T - 20) Since the heat transferred between the two water samples must be equal, we can set Q1 equal to Q2 and solve for T: 627 * (60 - T) = 1254 * (T - 20) 37620 - 627T = 1254T - 25080 1881T = 62760 T = 33.4°C Therefore, the temperature of the mixture is approximately 33°C. Answer: 33°C

A lens of focal length 15cm forms on erect image which is three times the size of the object. The distance between the object and the image is ___.

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We can use the lens formula, 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the distance between the lens and the image, and u is the distance between the lens and the object. From the problem, we know that the focal length of the lens is 15 cm, and the image is erect and three times the size of the object. This means that the image distance v is positive and the object distance u is negative (since the object is in front of the lens). Let's assume that the object distance u is -x cm, where x is a positive number. Then, the image distance v is +3x cm, since the image is three times the size of the object. Substituting these values into the lens formula, we get: 1/15 = 1/(+3x) - 1/(-x) Simplifying the right-hand side, we get: 1/15 = (1 + 3)/3x Multiplying both sides by 3x, we get: 3x/15 = 4 Simplifying, we get: x = 20 Therefore, the distance between the object and the lens is -20 cm (since it is in front of the lens), and the distance between the image and the lens is +60 cm (since it is behind the lens). The distance between the object and the image is the sum of these distances, which is: (-20) + (+60) = 40 cm Therefore, the answer is 40cm.