JAMB UTME - Physics - 2024

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An ideal transformer is a hypothetical concept used in electrical engineering to simplify the analysis of real transformers. In an ideal transformer, several assumptions are made to avoid losses and inefficiencies. Here's what an ideal transformer has:

No flux leakage: In an ideal transformer, it is assumed that all the magnetic flux generated in the primary coil is perfectly linked with the secondary coil. This means there is no flux leakage. This assumption ensures maximum efficiency, as all the energy is transferred from the primary to the secondary coil without losses.

Let's briefly discuss the other concepts to understand why they don't pertain to an ideal transformer:

Maximum primary resistance: In an ideal transformer, the resistance of the windings is assumed to be zero. If the primary has maximum resistance, it would result in power loss due to the resistance, contradicting the idea of an ideal transformer.

Hysteresis: This refers to the energy loss that happens in the core material due to the cyclic magnetization and demagnetization processes. An ideal transformer assumes there is no hysteresis loss, meaning the core material does not absorb any energy during these cycles.

Eddy current: These are loops of electric current induced within conductors by a changing magnetic field, which can cause significant energy loss. In an ideal transformer, it is assumed that there are no eddy currents, hence no energy loss due to this effect.

In summary, an ideal transformer is characterized by having no flux leakage, and it assumes that there are no losses due to resistance, hysteresis, or eddy currents. This makes the ideal transformer a perfect, lossless device for the purposes of theoretical analysis.

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To solve this problem, we need to determine how far the aircraft travels in the 5 seconds after it passes the anti-aircraft gun. The problem gives us two key pieces of information:

• The speed of the aircraft is 335 m/s.
• The time duration after passing the gun is 5 seconds.

To find the distance traveled, we use the formula for distance:

Distance = Speed × Time

Plugging in the given values:

Distance = 335 m/s × 5 s

Calculating this, we get:

Distance = 1675 meters

This means the aircraft is 1675 meters away from the point where it passed the anti-aircraft gun after 5 seconds.

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When light passes from one medium to another, such as from air to water, it bends or refracts. This phenomenon is described by Snell's Law, which states: n₁ * sin(θ₁) = n₂ * sin(θ₂), where:

• n₁ is the refractive index of the first medium (air),
• θ₁ is the angle of incidence (the angle made by the light ray with the normal in the first medium),
• n₂ is the refractive index of the second medium (water),
• θ₂ is the angle of refraction (the angle made by the light ray with the normal in the second medium).

The refractive index of air is approximately 1, and the refractive index of water is approximately 1.33. Given the angle of incidence in air is 30º:

Using Snell's Law:

1 * sin(30º) = 1.33 * sin(θ₂)

You will find:

sin(θ₂) = sin(30º) / 1.33

sin(θ₂) ≈ 0.5 / 1.33

sin(θ₂) ≈ 0.375

Now, solve for θ₂ by taking the inverse sine (arcsin):

θ₂ ≈ arcsin(0.375)

θ₂ ≈ 22.09º

Thus, when a light ray passes from air into water at an angle of 30º from the normal in air, it will make an angle less than 30º from the normal in water, approximately 22.09º. This is because the light ray bends toward the normal as it enters a denser medium (water).

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In a galvanometer setup intended to measure voltages, you often encounter a configuration known as a voltmeter, where a resistor is added in series with the galvanometer to increase its range of measurement.

The basic principle is that the total resistance of the voltmeter (comprising the galvanometer's resistance and the additional series resistor) allows it to handle a higher voltage by limiting the current that flows through the galvanometer. The maximum voltage (V) that can be measured by the galvanometer is determined by Ohm's Law: V = I * R,

Where:

• V is the maximum voltage (40V in this case),
• I is the full scale current rating of the galvanometer,
• R is the total resistance needed so that the galvanometer is not damaged.

Assuming the galvanometer has a known internal resistance (G) and a known full-scale current (I_fullscale), the resistance R required in series can be calculated via the formula:

R = (V / I_fullscale) - G

For this solution, you need either the values of G and I_fullscale or their product (G * I_fullscale). Without those exact specifications provided, it would be imprudent to give an exact numeric answer.

However, if this is a typical example and you have a typical galvanometer with a full-scale current of 50 μA and an internal resistance of 500 Ω, you can compute:

R = (40 / 50 x 10^-6) - 500 = 2000 - 500 = 1500 Ω

Therefore, you would need an additional R = 1990 Ω - 1500 Ω = 490 Ω, meaning the closest possible practical value from your choices is 1990 Ω (including the internal resistance).

If the specific parameters of the galvanometer differ, adjust the calculation accordingly, but the general process is as laid out here.

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The dimension of power in physics is expressed in terms of the base units of mass (M), length (L), and time (T). Power is the rate at which work is done or energy is transferred over time, and it has the unit of watt (W) which is equivalent to one joule per second.

To derive the dimension of power:

1. Work has the dimension of energy, which is force applied over a distance. The dimension of work (or energy) is M L² T^-2 because force has the dimension M L T^-2 and distance adds another L.

2. Since power is work done per unit time, you would divide the dimension of work by time (T).

Thus, the dimensional formula for power is:

M L² T^-3

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According to Faraday's laws of electromagnetic induction, an electromotive force (e.m.f) is induced in a conductor whenever it **cuts magnetic flux**. This means that for an e.m.f to be induced, the conductor must move in such a way that it intersects the magnetic lines of force. It is the relative motion between the conductor and the magnetic field that leads to the change in magnetic flux, resulting in the induction of e.m.f.

Let's explore why this is the correct answer using reasoning:

• When the conductor lies parallel to the magnetic flux: In this case, there is no motion or cutting of magnetic lines of force, leading to no change in magnetic flux through the conductor, and thus no e.m.f is induced.


• When the conductor lies in a magnetic field: Simply being within a magnetic field without any motion or change to the field does not induce e.m.f. There must be a change in the flux linkage for induction to occur.


• When the conductor lies outside but close to a magnetic field: Proximity alone without interaction doesn't change the magnetic flux linked with the conductor, thereby not inducing any e.m.f.


• When the conductor cuts magnetic flux: This is the condition necessary for the induction of e.m.f. The number of magnetic field lines interacting with the conductor changes, leading to a change in flux linkage, and consequently, e.m.f is induced.

Therefore, the phenomenon where a conductor cuts magnetic flux is essential for electromagnetic induction as per Faraday's laws.

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To determine the angular velocity of a body whirled in a horizontal circle at a rate of 800 revolutions per minute (rpm), we need to convert this to the standard unit of angular velocity, which is radians per second (rad/s).

Here’s how you can calculate it:

• First, understand that one complete revolution is equal to 2π radians.
• The body completes 800 revolutions in one minute.

Now let's perform the conversion:

• Convert the revolutions per minute to revolutions per second:
• \( \frac{800 \text{ revolutions}}{1 \text{ minute}} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = \frac{800}{60} \text{ revolutions per second} \), which simplifies to approximately \( 13.33 \text{ revolutions per second} \).
• Convert revolutions to radians by multiplying by \(2π\) radians per revolution:
• \( 13.33 \text{ revolutions per second} \times 2π \text{ radians per revolution} = 26.66π \text{ radians per second} \).

Rounding up the decimal to a consistent significant figure, the angular velocity is approximately 26.7π radians per second.

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Aneroid barometers are compact and lightweight, making them suitable for use in aircraft where space and weight are critical considerations. They provide a reliable measurement of altitude based on changes in atmospheric pressure.

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When you push a wheelbarrow inclined at an angle to the horizontal, the applied force can be divided into two components: a **horizontal component** and a **vertical component**. To find the horizontal component of the force, you need to use the concept of resolving vectors.

The force of 150N is acting at an angle of 60º to the horizontal. The horizontal component of this force can be calculated using the cosine of the angle. The formula to determine the horizontal component \( F_{\text{horizontal}} \) is given by:

F_horizontal = F_applied \times \cos(\theta)

Where:

• F_applied is the magnitude of the applied force, which is 150N.
• \(\theta\) is the angle of inclination to the horizontal, which in this case is 60º.

Substitute the values into the formula:

F_horizontal = 150N \times \cos(60º)

We know that \(\cos(60º)\) equals 0.5.

Therefore:

F_horizontal = 150N \times 0.5 = 75N

Thus, the **horizontal component** of the applied force is 75N.

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To calculate the monthly electrical bill, we first need to determine the total energy consumption of the household in kilowatt-hours (kWh). Here are the steps:

1. Calculate the total power consumption of the appliances daily:

• The appliances' power ratings are 80W, 100W, and 120W.
• Total power consumption: 80W + 100W + 120W = 300W.

2. Convert the daily power consumption from Watts to kilowatts (kW):

• Since 1kW = 1000W, the daily power consumption in kW is 300W / 1000 = 0.3 kW.

3. Calculate the energy used daily in kWh:

• The appliances are used for 6 hours daily.
• Energy used daily: 0.3 kW * 6 hours = 1.8 kWh.

4. Calculate the monthly energy consumption:

• An average month is 31 days.
• Monthly energy consumption: 1.8 kWh/day * 31 days = 55.8 kWh.

5. Calculate the cost based on the rate:

• The cost of electricity is ₦24.08 per kWh.
• Monthly electricity cost: 55.8 kWh * ₦24.08 = ₦1343.664.

Therefore, the monthly electrical bill is approximately ₦1343.66k.

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A standard meter rule has markings that are usually every millimeter (1 mm). The least count, which is the smallest measurement that can be accurately read, is often 1 mm.
The least possible error is generally considered to be half of the smallest division, so it is ±0.05cm (or ±0.5mm).

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A photometer is an instrument designed to measure the intensity of light. It is used to determine how much light is received over a particular area. Photometers are vital in various fields such as photography, astronomy, and laboratory science for ensuring that light levels are appropriate for specific applications.

The device operates by assessing the brightness or illumination coming from a light source and comparing it with a standard light. The measurement can be displayed in different units such as lumens or lux, depending on the context of the measurement.

While photometers are focused on the intensity of light, they do not measure kinetic energy of liberated electrons, the frequency of light, or the wavelength of light. These quantities are measured using other specialized instruments, such as spectrometers or frequency analyzers.

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To find the area expansivity of a metal when given its cubic expansivity, you should understand the relationship between linear, area, and cubic expansivity.

Cubic expansivity (\( \beta \)) is defined as the fractional change in volume per change in temperature, and is given by the formula:

\[ \Delta V = \beta V \Delta T \]

Area expansivity (\( \alpha_{A} \)) corresponds to the fractional change in area per change in temperature and can be derived from the linear expansivity (\( \alpha \)). The relationship between these expansivities is as follows:

\[ \text{Area Expansivity (\( \alpha_{A} \))} = 2 \times \text{Linear Expansivity (\( \alpha \))} \]

The cubic expansivity (\( \beta \)) is related to the linear expansivity by:

\[ \text{Cubic Expansivity (\( \beta \))} = 3 \times \text{Linear Expansivity (\( \alpha \))} \]

Thus, based on these relationships, we can express the area expansivity in terms of the cubic expansivity:

\(\text{Area Expansivity (\( \alpha_{A} \))} = \frac{2}{3} \times \text{Cubic Expansivity (\( \beta \))}

Given that the cubic expansivity \( \beta \) is \( 3.9 \times 10^{-6} \, \text{K}^{-1} \):

The area expansivity can be calculated as follows:

\[ \text{Area Expansivity (\( \alpha_{A} \))} = \frac{2}{3} \times 3.9 \times 10^{-6} \, \text{K}^{-1} = 2.6 \times 10^{-6} \, \text{K}^{-1} \]

Therefore, the **correct answer** is **2.6 x 10^{-6} K^{-1}**.

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The simple form of the lead acid accumulator often has a negative pole of lead plate. In a lead-acid battery, the key components include two electrodes and an electrolyte. The **negative pole**, also known as the cathode during discharge, is typically made of **lead (Pb)**, which is in the form of a **lead plate**. When the battery is in use or discharging, this lead reacts with sulphuric acid (the electrolyte) to create lead sulfate.

To break it down further:

• **The positive pole** is usually composed of a lead dioxide (PbO₂) plate, which is sometimes referred to as lead peroxide.
• **The electrolyte** in the lead-acid battery is a diluted sulphuric acid solution, but this is not a solid pole or electrode.
• **The negative pole** is simply a solid **lead plate**, as noted earlier.

Thus, by analyzing the composition and reactions within a lead-acid battery, it is clear that the **negative pole** is made from a **lead plate**.

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A rectifier is a device that changes alternating current (A.C) to direct current (D.C). Alternating current is the type of electrical current that changes direction periodically, while direct current flows in a single, constant direction.

Rectifiers are essential in numerous electrical devices, particularly those that require a stable and consistent power supply. For example, most electronic devices like mobile phone chargers, laptop adapters, and televisions operate on D.C. power, and rectifiers convert the household A.C. power supply to D.C. so that these devices can function properly.

In summary, a rectifier converts A.C., which is alternating power supply, into D.C., which is a steady flow of electricity in one direction, making it usable for electronic devices and various applications that require direct current.

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The capacitance of a capacitor is primarily determined by three key factors: the area of the plates, the distance between the plates, and the dielectric material used between the plates.

Capacitance (C) is calculated using the formula:

\(C = \frac{\varepsilon A}{d}\)

Where:

• A is the area of one of the plates.
• d is the distance between the two plates.
• &varepsilon is the permittivity of the dielectric substance between the plates.

Let's analyze the relationship:

• The area of the plates (A): The larger the area, the greater the capacitance. This means capacitance is directly proportional to the area.
• The distance between the plates (d): The greater the distance, the lower the capacitance. Therefore, capacitance is inversely proportional to the distance between the plates.
• The dielectric substance: Different materials have different permittivity values. The capacitance is directly proportional to the permittivity of the dielectric substance.
• The direction of the plate has no effect on the capacitance.

In summary, the capacitance of a capacitor is inversely proportional to the distance between the plates. Hence, you increase capacitance by decreasing the distance between the plates.

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Fat is the food nutrient with the highest energy value, providing 9 calories per gram, while carbohydrates and proteins provide 4 calories per gram. 

Fat is the body's most concentrated source of energy, providing more than twice as much potential energy as carbohydrates or proteins.However, carbohydrates burn fastest in metabolism. Fats are a type of lipid. Lipids are a group of organic compounds that are insoluble in water but soluble in organic solvents. Fats are solid at room temperature, while oils are liquid at room temperature. 

Therefore, the correct answer is option C.

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Given: Ig ${}_g$ = 50mA = 0.05A, I to be measured = 2A, r = 2Ω $\mathrm{\Omega }$, Is ${}_s$ = I - Ig ${}_g$ = 2 - 0.05 = 1.95A

Shunt(R) = IgIs $\frac{I_g}{I_s}$ x r

R =  0.051.95 $\frac{0.05}{1.95}$ x 10 = 0.2564Ω

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The concept of an inclined plane is all about simplifying the forces involved in moving or holding a load. The **velocity ratio (VR)** for an inclined plane is defined as the ratio of the distance moved by the effort to the distance moved by the load. This can also be expressed in terms of the lengths involved in the triangle made by the inclined plane.

For an inclined plane placed at an angle **θ** to the horizontal, the velocity ratio is given by the formula:

VR = 1/sin(θ)

Given that the inclined plane is at an angle of **60º**:

First, find the sine of 60º:

sin(60º) = √3/2 (approximately 0.866)

Now, substitute this value into the formula for VR:

VR = 1/sin(60º) ≈ 1/0.866 ≈ 1.155

The **velocity ratio** for an inclined plane at **60º** to the horizontal is **approximately 1.155**.

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Stress is defined as the force applied per unit area. In the context of a wire being loaded by a weight, the weight acts as the force exerted, and the cross-sectional area of the wire is the area over which this force is distributed.

Force (F): This is given by the weight, which is y² N.

Cross-sectional Area (A): For a wire with a diameter, the area can be calculated using the formula for the area of a circle: A = πr², where r is the radius of the wire.

Given the diameter of the wire as yπ meters, the radius (r) is half of the diameter:

r = (yπ)/2

So, the area (A) is:

A = π[(yπ)/2]²

Simplifying the area:

A = π(y²π²/4)
A = y²π³/4

Stress (σ) is given by the formula:

σ = F/A

Substituting the given weight (force) and the calculated area:

σ = (y²) / (y²π³/4)

By simplifying the expression:

σ = (4y²) / (y²π³)

Cancel out y² from numerator and denominator:

σ = 4/π² Nm⁻²

Thus, the correct stress experienced by the wire is 4π Nm⁻², as provided in one of the options. The explanation shows clearly how the force and area are used to derive the stress experienced by the wire.

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A practical application of total internal reflection is found in fiber optics.

To understand this, let's break it down:

When light travels from one medium to another (such as from glass to air), it changes direction. This is known as refraction. However, there is a phenomenon called total internal reflection which occurs when light is traveling within a denser medium towards a less dense medium (like from glass to air) and hits the boundary at an angle greater than a certain critical angle. Instead of passing through, the light is completely reflected back into the denser medium.

Fiber optics technology makes use of this principle. In fiber optics, light is transmitted along the core of a thin glass or plastic fiber. The core is surrounded by another layer called the cladding. This cladding has a lower refractive index than the core, which facilitates total internal reflection. As a result, the light continuously reflects internally along the length of the fiber, allowing it to travel long distances with minimal loss.

This property is harnessed in various applications such as in high-speed telecommunication systems, medical equipment like endoscopes, and other technologies that require the transmission of data over long distances with high efficiency.

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To determine the quantity of heat required to melt ice, we use the formula for latent heat:

Q = m × L,

where:

• Q is the heat energy absorbed or released (in joules).
• m is the mass of the substance (in kilograms).
• L is the specific latent heat (in joules per kilogram, J/Kg).

For this problem, we have:

• Mass of ice, m = 0.2 kg
• Specific latent heat of ice, L = 3.4 × 10⁵ J/Kg

Now, substitute these values into the formula:

Q = 0.2 kg × 3.4 × 10⁵ J/kg

Calculate the product:

Q = 0.68 × 10⁵ J

To express this in standard scientific notation, it can be rewritten as:

Q = 6.8 × 10⁴ J

Thus, the quantity of heat required to melt 0.2 kg of ice is 6.8 × 10⁴ J.

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To determine the weight of a bowling ball on the moon, we need to understand the relationship between weight, gravity, and mass.

Weight is the force exerted by gravity on an object. On Earth, this force depends on the object's mass and the acceleration due to gravity, which is approximately 9.8 m/s². Weight can be calculated using the formula:

Weight = Mass x Gravity

On the moon, the acceleration due to gravity is only ¹/₆ of Earth’s gravity. This means the gravitational pull on the moon is much weaker compared to the Earth. If we take the Earth's gravity to be 9.8 m/s², the moon's gravity would be:

Moon's Gravity = (9.8 m/s²) x (1/6) ≈ 1.63 m/s²

Given that the weight of an object is directly proportional to the gravitational force, the weight of an object on the moon would be substantially less than its weight on Earth. Thus, the weight of the bowling ball on the moon would be:

Weight on Moon = (Mass) x (1.63 m/s²) = ¹/₆ of its weight on Earth

Therefore, the weight of a bowling ball on the moon is ¹/₆ of its weight on Earth.

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When capacitors are connected in series, the formula to find their combined capacitance \(C_{\text{total}}\) is given by:

\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]

where \(C_1\) and \(C_2\) are the capacitances of the individual capacitors. In this case, \(C_1 = 0.0003 \, \mu\text{F}\) and \(C_2 = 0.0006 \, \mu\text{F}\).

First, calculate the reciprocal of each capacitance:

\[ \frac{1}{C_1} = \frac{1}{0.0003} \]

\[ \frac{1}{C_2} = \frac{1}{0.0006} \]

Calculating each value:

\[ \frac{1}{0.0003} = \frac{10^6}{3} \] and \[ \frac{1}{0.0006} = \frac{10^6}{6} \]

Now, add these values together:

\[ \frac{1}{C_{\text{total}}} = \frac{10^6}{3} + \frac{10^6}{6} = \frac{10^6 \times 2}{6} + \frac{10^6 \times 1}{6} = \frac{10^6 \times 3}{6} = \frac{10^6}{2} \]

Finally, take the reciprocal of the resulting value to find \(C_{\text{total}}\):

\[ C_{\text{total}} = \frac{2}{10^6} = 0.0002 \, \mu\text{F} \]

So, the combined capacitance of the two capacitors in series is 0.0002 μF.

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A pinhole camera is a simple camera device that uses a tiny hole to project an inverted image of the scene in front of it onto a surface at the back of the camera. When you diminish the hole of a pinhole camera, meaning you make the hole smaller, a few effects occur on the resulting image. Here’s what happens:

• Firstly, when the pinhole is smaller, less light enters the camera. This results in the image becoming darker.
• Additionally, with a smaller hole, the path of light rays becomes narrower which helps to reduce blurring and overlaps from being out of focus. Consequently, the image becomes sharper.

Therefore, reducing the size of the pinhole in a pinhole camera results in the image becoming both darker and sharper.

Answer: II only (The image becomes sharper.)

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The device used for measuring the angle of dip is the dip circle.

Let me explain this in simple terms:

The angle of dip, also known as the magnetic inclination, is the angle made by the Earth's magnetic field lines with the horizontal plane. It varies depending on where you are on the Earth's surface. In some places, magnetic field lines are nearly vertical, while in others they are more horizontal.

A dip circle is a specialized scientific instrument used to measure this angle. It usually consists of a magnetic needle that is free to rotate in the vertical plane.

When using a dip circle, you align it so that its plane is parallel to the direction of the Earth's magnetic field. Then, you read the angle at which the magnetic needle stabilizes. This is the angle of dip. The instrument's mechanism allows for accurate measurement of this angle by compensating for any external influences or inclinations.

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In physics, the concept of work is defined as the process of energy transfer that occurs when a force makes an object move. The conditions for work to be done are:

• A force must be applied: There must be a force exerted on an object.
• The object must move: The object on which the force is applied must move from its original position.
• The movement must be in the direction of the force: The movement of the object should be in the direction of the applied force.

Now, let's evaluate each scenario:

A man supports a heavy load on his head with hands: In this case, although the man is applying a force upward to support the load, the load does not move in the direction of the force he is exerting (upward). Hence, no work is done.

A woman holds a pot of water: Similar to the first scenario, the woman applies an upward force to hold the pot. However, the pot remains stationary, and there is no movement in the direction of the force. Thus, no work is done.

A boy climbs onto a table: Here, as the boy climbs, he applies a force to move himself upward onto the table. The movement is in the direction of the upward force he is applying. Therefore, work is done.

A man pushes against a stationary petrol tanker: In this scenario, although the man is applying a force to the tanker, it does not move. Because there is no movement in the direction of the force, no work is done.

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To calculate the real depth of a swimming pool given the apparent depth, we can use the concept of refraction of light. When light passes from one medium to a denser medium, it bends towards the normal. This bending effect causes objects submerged in water to appear closer to the surface than they actually are. The formula to relate these depths is given by:

Real Depth = Apparent Depth × Refractive Index

Given the problem:

• Apparent Depth = 10 cm
• Refractive Index of water = 1.33

Using the formula:

Real Depth = 10 cm × 1.33

Calculating the above:

• Real Depth = 13.3 cm

Therefore, the depth of the swimming pool is 13.3cm.

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To determine the amount of current required, we need to use Faraday's laws of electrolysis. The first law states that the mass of the substance deposited at an electrode is directly proportional to the quantity of electricity (or charge) that passes through the electrolyte.

Here, we have:

• The mass of the metal deposited, \( m \), is 0.02 kg.
• The electrochemical equivalent, \( z \), is 1.3 x 10^-7 kg/C.
• The time during which the current is applied, \( t \), is 120 seconds.

According to Faraday's first law of electrolysis, the mass (\( m \)) can be calculated by the formula:

m = z \times I \times t

Where:

• m is the mass of the substance deposited (in kilograms).
• z is the electrochemical equivalent (in kg/Coulomb).
• I is the current (in amperes).
• t is the time (in seconds).

Rearranging the formula to solve for current \( I \):

I = \(\frac{m}{z \times t}\)

Substituting the given values into the formula:

I = \(\frac{0.02 \, \text{kg}}{1.3 \times 10^{-7} \, \text{kg/C} \times 120 \, \text{s}}\)

Calculating the denominator:

I = \(\frac{0.02}{1.56 \times 10^{-5}}\)

Solving for \( I \):

I = 1282.05 \, \text{A}

Thus, the appropriate amount of current required to deposit 0.02 kg of metal in 120 seconds is approximately 1.3 x 10³ A.

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When boiling water is poured into a thick glass tumbler, the inner surface of the glass is suddenly exposed to a much higher temperature compared to the outer surface. Glass is a poor conductor of heat, which means it does not transfer heat quickly. As a result, the inside of the tumbler becomes hot and attempts to **expand quickly**, while the outside remains cooler and does not expand at the same rate.

**This uneven expansion** creates tension between the inner and outer layers of the glass. The inner surface tries to expand but is constrained by the cooler, rigid outer surface, which isn't expanding as much or as quickly. This stress and tension can lead to cracking.

Therefore, the correct reason a thick glass tumbler cracks when boiling water is poured into it is because **the inside expands more rapidly than the outside.**

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When two sound waves of slightly different frequencies are sounded together, they interfere with each other in such a way that the intensity of the sound alternates between loud and soft. This phenomenon is known as "beats". The number of beats heard per second is called the "beat frequency".

The beat frequency can be calculated by subtracting the frequency of one wave from the frequency of the other. Mathematically, it is represented as:

Beat Frequency (f_beat) = | f₁ - f₂ |

Where:

• f₁ is the frequency of the first tuning fork.
• f₂ is the frequency of the second tuning fork.

In this case:

• f₁ = 6Hz
• f₂ = 4Hz

Using the formula:

f_beat = | 6Hz - 4Hz | = | 2Hz | = 2Hz

Therefore, the beat frequency is 2Hz. This means that you would hear 2 beats per second when the tuning forks of frequencies 6Hz and 4Hz are sounded together.

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According to the kinetic theory of gases, the pressure exerted by a gas on the walls of its container relates to the behavior and movement of its molecules. To understand how this pressure forms, let's explore the following essential concepts.

Molecules in a gas move rapidly and randomly in all directions. When these molecules collide with the walls of their container, they exert force due to the change in momentum during these collisions. The frequency and force of these collisions contribute directly to the pressure experienced by the container walls.

The **pressure** exerted by the gas can be described in terms of the rate of change of momentum imparted by the walls per second per unit area. This means that pressure is determined by considering how fast and how much the momentum of the gas molecules changes when they bounce off the container's walls, spread over a specific area and over time. In simpler terms, the faster and more frequently molecules hit the walls, and the higher their change in momentum, the greater the pressure is.

This explanation can be directly associated with the statement: "rate of change of momentum imparted by the walls per second per unit area", which accurately describes the concept of pressure in the context of the kinetic theory of gases.

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To determine the energy of light given its frequency, we can utilize the formula:

E = h × f

Where:

E is the energy of the photon in joules (J)

h is Planck's constant, approximately 6.63 × 10^-34 J·s

f is the frequency of light in hertz (Hz)

Given the frequency f = 2.0 × 10¹⁵ Hz, we can substitute the known values into our equation:

E = 6.63 × 10^-34 J·s × 2.0 × 10¹⁵ Hz

To simplify the calculation, multiply the numerical parts and then add the indices of 10:

E = (6.63 × 2.0) × (10^-34 × 10¹⁵)

E = 13.26 × 10^-19 J

This can be approximated to 1.33 × 10^-18 J. Thus, the energy of light with the given frequency is 1.33 × 10^-18 J.

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The process you are referring to is called doping. In simple terms, doping is the method of intentionally introducing impurities into an extremely pure semiconductor to change its electrical properties, which increases its conductivity.

Semiconductors, like silicon or germanium, are materials that have electrical conductivity between conductors (like metals) and insulators (like glass). By adding impurities, we can control and enhance their ability to conduct electricity. These impurities are atoms of other elements that either have more or fewer electrons in their outer energy levels compared to those in the semiconductor.

When you add impurities with more electrons, it creates an n-type semiconductor because of the extra *negative* charge carriers (electrons). Conversely, adding impurities with fewer electrons makes a p-type semiconductor, as it creates 'holes' which act as positive charge carriers.

This process of doping is essential for creating various semiconductor devices, like diodes, transistors, and integrated circuits, which are foundational components in all electronic devices. Hence, doping plays a crucial role in the functionality and efficiency of electronic systems.

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Bilateral symmetry, cylindrical bodies, and double openings are characteristic features of nematodes. Nematodes, also known as roundworms, have a body structure that is symmetric along a single plane, which results in two mirror-image halves, thus exhibiting bilateral symmetry.

Furthermore, they usually have a cylindrical body shape, which means their bodies are long and narrow like a cylinder and taper at both ends. This shape helps them move through their environment easily. Additionally, nematodes have a complete digestive system with two openings: a mouth and an anus. This means that food enters through the mouth, gets digested, and waste exits through the anus.

In contrast, organisms like hydra, protozoa, and protists possess different anatomical features. Hydras, for example, typically show radial symmetry, and protozoa and protists generally do not have a well-defined body shape or bilateral symmetry as seen in nematodes. Therefore, the description fits nematodes best.

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apacitance in parallel = one at the top + one under = 2C

The two in the middle are in series = C2 $\frac{C}{2}$

The equivalent capacitance of the capacitors in the circuit above = C2 $\frac{C}{2}$ + 2C = 52 $\frac{5}{2}$C

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To determine the Mechanical Advantage (MA) of a machine, we use the formula:

MA = Load / Effort

Here, the Load is the weight of the mass being lifted, and the Effort is the force applied on the machine.

First, we need to calculate the Load. The Load is obtained by multiplying the mass of the object by the acceleration due to gravity (g = 10 m/s²).

So, the Load (weight of the mass) is:

Load = Mass × Gravity = 60 kg × 10 m/s² = 600 N

The Effort given is 40 N.

Now, we can calculate the Mechanical Advantage:

MA = Load / Effort = 600 N / 40 N = 15

Therefore, the Mechanical Advantage of the machine is 15.

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When a body moves in a straight line from one point, such as point P, to another point, such as point Q, the motion is called Translational Motion. This kind of motion refers to an object moving along a path in which every part of the object takes the same path as a reference point. This means that if you follow any point on the body, it covers the same amount of distance in the same time frame as any other point.

Let's break down the other options:

• Rotational Motion: This occurs when an object spins around an internal axis. For example, the rotation of the Earth on its axis is a rotational motion.


• Simple Harmonic Motion: This is a type of periodic motion where the restoring force is directly proportional to the displacement. An example of this is a pendulum swinging back and forth.


• Circular Motion: This occurs when an object moves along a circular path. For instance, the motion of the planets around the sun is circular motion.

In conclusion, since the body is moving from point P to point Q along a straight line, it exhibits Translational Motion.

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The elliptical shape of the Earth: The Earth is not a perfect sphere; it is slightly flattened at the poles and bulging at the equator. This shape causes variations in gravitational acceleration.

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An insulator is a material that has a very large energy gap between its valence band and conduction band. To understand this, let's first consider the concept of energy bands: In materials, electrons exist in different energy levels. These levels form bands called the valence band and the conduction band. A material is classified based on the size of the energy gap between these bands.

• Insulator: The energy gap is very large, which means electrons in the valence band require a lot of energy to jump to the conduction band where they can freely move. Because of this large gap, insulators do not conduct electricity well.
• Conductor: The valence band and conduction band overlap or have a very small gap, so electrons can move freely without requiring significant additional energy. Conductors actively conduct electricity.
• Semiconductor: The energy gap is moderate, which means some energy is required for electrons to move from the valence band to the conduction band. Semiconductors can conduct electricity under certain conditions, like when energy (in the form of heat or light) is provided.
• Intrinsic semiconductor: This is a pure type of semiconductor with no added impurities. It behaves like a semiconductor, having a moderate energy gap.

Thus, insulators have a very large energy gap band, making them poor conductors of electricity.