JAMB UTME - Physics - 2018

To keep a vehicle moving at a constant speed V requires power P from the engine. The force provided by the engine is

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The force provided by the engine to keep a vehicle moving at a constant speed is proportional to the power (P) required from the engine. This power is proportional to the product of the speed (V) and force (P), so the relationship can be expressed as P = kV, where k is a proportionality constant.

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.

The inner diameter of a small test tube can be measured accurately using a

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A vernier caliper is a measuring device used to precisely measure linear dimensions. It is a very useful tool to use when measuring the diameter of a round objects like cylinders because the measuring jaws can be secured on either side of the circumference.
Vernier calipers have both a fixed main scale and a moving vernier scale. The main scale is graduated in either millimetres or tenths of an inch. The vernier scale allows much more precise readings to be taken (usually to the nearest 0.02mm or 0.001 inch) in comparison to a standard ruler (which only measures to th nearest 1mm or 0.25 inch).
The vernier scale was invented by French mathematician Pierre Vernier in 1631. As part of the vernier caliper, it is used together with the main scale, and helps to provide very precise measurements. Vernier calipers usually show either imperial or metric measurements, but some measure in both.

Which of the following may be used to explain a mirage?

I. Layers of air near the road surface have varying refractive indices in hot weather

II. Road surfaces sometimes become good reflectors in hot weather

III. Light from the sky can be reflected upwards after coming close to the road surface.

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The phenomenon of a mirage can be explained by options I and III. A mirage is an optical illusion that occurs when light rays passing through a medium with varying refractive indices create a false image of distant objects or even the sky. In hot weather, the air near the road surface becomes hotter and less dense than the air above, causing the light passing through it to bend and create a reflection of the sky or objects in the distance. This effect is known as a temperature inversion. Additionally, light from the sky can be reflected upwards after coming close to the road surface, adding to the illusion of a reflected object or the sky. Option II, which suggests that road surfaces become good reflectors in hot weather, is not a valid explanation for a mirage. Therefore, the correct answer is: I and III only.

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

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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.

In homes, electrical appliances and lamps are connected in parallel because

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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.

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.

What effort will a machine of efficiency 90% apply to a load of 180N if its efforts arm is twice as long as its load arm?

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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.

A beam of light is incident from air to water at an angle of 300. Find the angle of refraction if the refractive index of water is 4/3

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X = $\frac{4}{3}$ r = ?
Shell?s law:. 7 = $\frac{Sin{2}^0}{Sin{r}^0}$
$\frac{V}{g}$ = $\frac{Sin{30}^0}{Sin{r}^0}$
Sin$r^0$ = $\frac{3Sin{30}^0}{4}$
Sin $r^0$ = 0.375
R ${}^o$ = Sin-1 (0.375)
R ${}^o$ = 22.02 ${}^o$
R ${}^o$ = 22 ${}^o$

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 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.

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.

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.

What flows to the earth by connecting the conductor to the earth?

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When a conductor is connected to the earth, electrons flow to the earth. Electrons are negatively charged particles that are present in all conductors. When a conductor is connected to the earth, it creates a path for electrons to flow from the conductor to the earth, which helps to balance the electric potential and prevent the buildup of electric charge. This flow of electrons is known as grounding and is an important safety measure in electrical systems.

Which of the following is true of an electrical charge?

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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.

A solid weighs 45N and 15N respectively in air and water. Determine the relative density of the solid

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The relative density of a substance is defined as the ratio of its density to the density of a reference substance, usually water at 4 degrees Celsius. In this problem, we can use the principle of buoyancy to determine the density of the solid. When an object is submerged in a fluid, it experiences an upward force called the buoyant force, which is equal to the weight of the fluid displaced by the object. If the object is less dense than the fluid, it will float, and if it is more dense, it will sink. We are given that the solid weighs 15 N in water, which means it displaces 15 N of water. The weight of the water displaced is equal to the buoyant force on the solid, which is equal to the weight of the solid when it is completely submerged in water. Therefore, the weight of the solid when it is completely submerged in water is 15 N. We are also given that the weight of the solid in air is 45 N. The difference between the weight of the solid in air and water is equal to the weight of the water displaced, which is 30 N. This means that the volume of water displaced by the solid is 30/9.8 = 3.06 L (since the density of water is 1000 kg/m^3 or 9.8 N/L). The relative density of the solid is equal to its density divided by the density of water. We can find the density of the solid by dividing its weight in air by its volume: Density of solid = Weight of solid in air / Volume of solid Density of solid = 45 N / (45 N - 15 N) [since weight of displaced water is 15N] Density of solid = 45 N / 30 N Density of solid = 1.5 N/L Therefore, the relative density of the solid is: Relative density = Density of solid / Density of water Relative density = 1.5 N/L / 1000 N/L Relative density = 0.0015 So the answer is 0.33 (rounded to two decimal places).

The photo cell works on the principle of the

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The photocell works on the principle of the emission of electrons by incident radiation. In simple terms, a photocell is a device that converts light energy into electrical energy. It does this by using a material (such as silicon) that releases electrons when it is exposed to light. These electrons can then be collected and used to produce a current, which can be used to power an electrical device. The more light that hits the photocell, the more electrons are released and the greater the electrical current.

A 40W instrument has a resistance 90 Ohms. On what voltage should it be operated normally

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To calculate the voltage needed for a 40W instrument with a resistance of 90 Ohms, we can use the formula: Voltage = √(Power x Resistance) Plugging in the given values, we get: Voltage = √(40W x 90Ω) Voltage = √(3600) Voltage = 60V Therefore, the instrument should be operated at 60V to generate 40W of power with a resistance of 90 Ohms. The correct answer is, 60V.

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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Natural radioactivity consists of the emission of

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Radioactive decay releases different types of energetic emissions. The three most common types of radioactive emissions are alpha particles, beta particles, and gamma rays.

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

What type of reaction is represented by the following scheme?

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

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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.

In the diagram shown, which of the simple pendulum will resonate with P when set into oscillation?

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A man hears his echo from a nearby hill 2s after he shouted. If the frequency of his voice is 260Hz and the wavelength is 1.29m, how far away is the hill

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The speed of sound in air is approximately 343 meters per second at room temperature. The formula for the speed of sound is:

Speed of sound = Frequency × Wavelength

In this problem, we are given the frequency (260 Hz) and the wavelength (1.29 m) of the sound wave. We can use these values to calculate the speed of sound:

Speed of sound = 260 Hz × 1.29 m = 335.4 m/s

Next, we need to use the fact that the man hears his echo 2 seconds after he shouted. Since the sound wave traveled from the man to the hill and then back to the man, the total distance traveled by the sound wave is twice the distance from the man to the hill. We can use the formula:

Distance = Speed × Time

to calculate the distance from the man to the hill:

Distance = (335.4 m/s) × (2 s/2) = 335.4 m

Therefore, the hill is 335.4 meters away from the man. The answer is option (B), 335.4m.

If the focal length of a camera is 20cm, the distance from the film at which the lens must be set to produce a sharp image of 100cm away is

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F = 20cm
V = 100cm
U = ?
$\frac{1}{U}$ + $\frac{1}{V}$ = $\frac{1}{F}$
$\frac{1}{20}$ + $\frac{1}{100}$ = $\frac{1}{F}$
$\frac{5+1}{100}$ = $\frac{1}{F}$
F = $\frac{100}{6}$
= 16.7cm
= 17cm

A car traveled at a uniform speed of 100km/h, spends 15m moving from point A to point B along its route. The distance between A and B is

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To calculate the distance between point A and point B, we can use the formula: Distance = Speed x Time where the speed is given as 100 km/h and the time is given as 15 minutes, which we need to convert to hours. 1 hour = 60 minutes, so 15 minutes = 15/60 hours = 0.25 hours. Now, we can substitute these values into the formula: Distance = 100 km/h x 0.25 h = 25 km Therefore, the distance between point A and point B is 25 km. is the correct answer.

Which of the following is an essential physical property of the wires uses for making fuses ?

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The essential physical property of the wire used for making fuses is low melting point. This means that the wire should have a low temperature at which it melts and breaks, interrupting the flow of electrical current. This is important in a fuse because when there is an overload of electrical current, the wire will melt, breaking the circuit and preventing damage to the electrical system. The other options, low density, low electrical resistivity, and hypothermal conductivity, are not as important for a fuse wire. Low density is the property of a material to be light, and it doesn't necessarily affect the performance of a fuse wire. Low electrical resistivity is the property of a material to have low resistance to the flow of electrical current, and it doesn't necessarily affect the performance of a fuse wire either. Hypothermal conductivity is the property of a material to conduct heat poorly, and it also doesn't necessarily affect the performance of a fuse wire.

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

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.

The energy needed to move a unit positive charge around a complete electric circuit is called the

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The energy needed to move a unit positive charge around a complete electric circuit is called the "electromotive force", also known as "emf". This is because the emf is what drives the flow of electric charge, or current, around the circuit. Think of it like a battery in a flashlight. The battery provides the emf that drives the flow of electric current through the wires and the light bulb. Without the emf from the battery, the electric charges wouldn't be able to flow and the light wouldn't turn on. The other answer options, such as electric potential difference and electric energy, are related to the emf but don't specifically refer to the energy needed to move a unit positive charge around a circuit. Kinetic energy, on the other hand, is not related to the movement of electric charges around a circuit at all.

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.

The tendency of a body to remain at rest when a force is applied to it is called.

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The tendency of a body to remain at rest or to continue moving with a constant velocity (in a straight line at a constant speed) when no force is acting on it is called inertia. Inertia is a property of matter, and the amount of inertia depends on the mass of an object. Inertia can also be thought of as a resistance to changes in motion, meaning that an object at rest will tend to stay at rest, and an object in motion will tend to stay in motion unless acted upon by an external force. This property of inertia is what makes it difficult to start, stop, or change the direction of motion of an object. The force required to overcome the inertia of an object depends on the mass of the object and the magnitude of the acceleration desired. Therefore, the greater the mass of an object, the greater its inertia, and the more force required to change its motion.

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.

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.

When a known standard resistor of 2.0 is connected to the 0.0cm end of a meter bridge, the balance point is found to be at 55.0cm. What is the value of the unknown resistor?

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A meter bridge is an instrument used to measure the unknown resistance of a conductor. The meter bridge consists of a long resistance wire AB of uniform cross-sectional area and a battery of known voltage connected across its ends. A galvanometer is connected across a point C on the wire, which is called the null point or balance point.
When a known standard resistor of 2.0 ohms is connected to the 0.0cm end of the meter bridge wire, the balance point is found to be at 55.0cm. This means that the resistance of the unknown resistor is equal to the resistance of a portion of the meter bridge wire between the 0.0cm and the 55.0cm point.
To find the value of the unknown resistor, we can use the principle of the Wheatstone bridge, which states that the ratio of the resistances in the two arms of a balanced bridge is equal.
Let R be the resistance of the unknown resistor, then we have:
R/2.0 = (100 - 55.0)/55.0
Simplifying this expression, we get:
R = 2.0 x (100 - 55.0)/55.0
R = 1.64 ohms
Therefore, the value of the unknown resistor is 1.64 ohms.

Calculate the effective capacitance of the circuit in the diagram given

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The three 2uf capacitors are in parallel to each other so u add them like this
2uf+2uf+2uf=6uf
So u have three capacitors in series
6uf 2uf and 3uf
They are in series so
1/C= 1/6+1/3=1/2
C=2uf
Then the same thing with the last two capay
1/2+1/2=1uf
Thanks

When an atom loses or gain a charge it becomes

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When an atom loses or gains a charge, it becomes an ion. An ion is a type of atom that has an unequal number of protons and electrons, giving it a net electrical charge. If an atom loses one or more electrons, it becomes positively charged and is called a cation. On the other hand, if an atom gains one or more electrons, it becomes negatively charged and is called an anion. So, in summary, an atom can lose or gain electrons to become an ion, which has a net electrical charge.

Convex mirrors are used as driving mirrors because images formed are

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Convex mirrors are used as driving mirrors because the images formed by them are "erect, virtual, and diminished." Let me explain what these terms mean: - Erect: It means that the image appears upright, just like the actual object. This is important for a driving mirror because it allows the driver to perceive the correct orientation of the vehicles behind them. - Virtual: It means that the image appears to be behind the mirror, and not in front of it. This is also important for a driving mirror because it allows the driver to see a wider field of view without having to turn their head. - Diminished: It means that the image is smaller than the actual object. This is important for a driving mirror because it allows the driver to see a larger area behind them while still fitting it within the mirror's frame. Overall, these properties make convex mirrors ideal for use as driving mirrors as they provide the driver with an accurate view of the vehicles behind them without sacrificing their field of view.