JAMB UTME - Physics - 2024

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.

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.

The main feature of trees in the savanna habitat is the possession of thick, corky bark. The savanna is characterized by a distinct wet and dry season. During the dry season, fires are common as dry grasses and leaves become highly flammable. To adapt to this environmental condition, many trees in the savanna have developed a thick, corky bark which helps protect them against these frequent fires. This bark acts as an insulator, shielding the vital inner tissues of the tree from the heat of the flames. Additionally, this adaptation helps the trees retain moisture, which is crucial during the arid months when water is scarce.

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.

To determine the effort needed to lift a load using a machine, we first need to understand some key concepts: **Load**, **Effort**, **Velocity Ratio** (VR), and **Efficiency**.

1. **Load** is the force or weight that needs to be lifted by the machine. In this case, the load is 300N.

2. **Velocity Ratio (VR)** is the ratio of the distance moved by the effort to the distance moved by the load. Given here as 2.

3. **Efficiency** of a machine is expressed as a percentage and is the ratio of the useful work output to the input work done by the effort. Here, the efficiency is 60% or 0.60 as a decimal.

The formula to calculate the **Effort** is derived from the relationship between these factors:

\[ \text{Efficiency} = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \]

Where:

\[ \text{Mechanical Advantage (MA)} = \frac{\text{Load}}{\text{Effort}} \]

From the above, we have:

\[ \text{MA} = \text{VR} \times \text{Efficiency} \]

Replacing with the given values:

\[ MA = 2 \times 0.60 = 1.2 \]

Now, calculate the **Effort** using the relation:

\[ \text{Effort} = \frac{\text{Load}}{\text{MA}} \]

\[ \text{Effort} = \frac{300N}{1.2} = 250N \]

Therefore, the **Effort** needed to lift the load is 250N.

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

The bursting of water pipes during very cold weather is primarily attributed to the expansion of water on freezing.

Here's why this happens:

1. **Normal water behavior below freezing:** Typically, when most substances freeze, they contract because the molecules get closer together. However, water behaves differently due to its unique molecular structure. As water freezes, it forms a crystalline structure that makes ice less dense than liquid water, causing it to expand.

2. **Effect of expansion:** When water inside a pipe freezes, it expands. This expansion puts tremendous pressure on the pipe walls because the solid ice takes up more space than the liquid water. Most pipes are rigid and do not have enough room to accommodate the expanded volume of ice.

3. **Resulting pressure:** The increased pressure caused by the expanding ice can cause the pipe to crack or burst, especially if there is no other outlet for the water or ice to expand into.

In summary, pipes burst during cold weather primarily due to the expansion of water as it freezes, which creates pressure that the pipe cannot withstand. This phenomenon is due to the unique property of water where it expands upon freezing, unlike most other substances which contract in their solid form.

To calculate the distance between two objects based on the gravitational force acting between them, we need to use the formula for gravitational force:

F = (G * m1 * m2) / r²

Where:

• F is the gravitational force between the two masses (6.67 N).
• G is the gravitational constant (6.6 x 10^-11 Nm²/kg²).
• m1 is the first mass (10²⁴ kg).
• m2 is the second mass (10²⁷ kg).
• r is the distance between the centers of the two masses.

We need to compute r by rearranging the formula:

r² = (G * m1 * m2) / F

Therefore, the distance r is:

r = √((G * m1 * m2) / F)

Substitute the given values into the equation:

r = √((6.6 x 10^-11 Nm²/kg² * 10²⁴ kg * 10²⁷ kg) / 6.67 N)

Calculating inside the square root:

G * m1 * m2 = 6.6 x 10^-11 * 10²⁴ * 10²⁷ = 6.6 x 10⁴⁰ Nm²

Then divide by the force:

6.6 x 10⁴⁰ Nm² / 6.67 N = 0.99 x 10⁴⁰ m²

Finally, calculate the square root:

r = √(0.99 x 10⁴⁰)

r ≈ 1.0 x 10²⁰ m

Therefore, the distance between the two objects is approximately 1.0 x 10²⁰ m.

To calculate the energy consumption of an appliance, you can use the formula:

Energy (in KWh) = Power (in kW) × Time (in hours)

First, convert the power rating of the refrigerator from watts (W) to kilowatts (kW). Since 1 kW is equal to 1000 W, you can convert 150W to kilowatts by dividing by 1000:

150 W = 0.150 kW

Next, calculate the energy consumed over the period the refrigerator is kept on, which is 336 hours. Use the formula:

Energy = 0.150 kW × 336 hours

Now, perform the multiplication:

Energy = 50.40 kWh

Therefore, when the refrigerator is kept on for 336 hours non-stop, it consumes 50.40 kWh of energy. This is the correct choice.

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.

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.

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.

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.

To find the density of the fluid, we need to apply the principle of floatation, which states that the weight of the fluid displaced by the submerged part of the object is equal to the weight of the object. Let's walk through the steps:

Step 1: Understand the volume submerged

The hydrometer has a total volume of 2y x 10^-5 m³. It floats with 20% of its volume above the fluid. Hence, 80% of its volume is submerged in the fluid.

Submerged Volume, V_sub = (0.80) x (2y x 10^-5 m³) = 1.6y x 10^-5 m³

Step 2: Apply the principle of floatation

The weight of the fluid displaced equals the weight of the hydrometer.

Weight of hydrometer = Mass x Gravity = y kg x g (where g is the acceleration due to gravity). For the purpose of calculations, g can be considered as 9.81 m/s².

Weight of displaced fluid = Density of fluid (ρ_fluid) x Submerged Volume x g

According to the principle of floatation:

y x g = ρ_fluid x 1.6y x 10^-5 m³ x g

g is common on both sides and can be canceled out:

y = ρ_fluid x 1.6y x 10^-5

Step 3: Solving for the density of the fluid

ρ_fluid = y / (1.6y x 10^-5)

The y on both numerator and denominator cancels out:

ρ_fluid = 1 / (1.6 x 10^-5)

ρ_fluid = 6.25 x 10⁴ kg/m³

Thus, the density of the fluid is 6.25 x 10⁴ kg/m³.

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}**.

In voltage measurement, a **potentiometer is preferred to a voltmeter** primarily because it **consumes negligible current**. Let me explain this in simpler terms:

A **voltmeter** is an instrument used to measure the potential difference (voltage) across two points in an electrical circuit. However, when a voltmeter is connected, it draws a small amount of current from the circuit to make the measurement, which can slightly alter the voltage being measured. This is particularly an issue in high-resistance circuits where even a small current draw can significantly affect the measurement.

On the other hand, a **potentiometer** is a device designed to measure voltage by comparing it with a known reference voltage without drawing current from the circuit under test. It comes into balance at a point where no current flows through it, ensuring that the measurement is not influenced by the potentiometer itself. This makes it a non-invasive method of measuring voltage, which is particularly useful for precise measurements in sensitive circuits.

Here’s a brief explanation about why the other options listed are less relevant:

• A **wider range** is not a definitive advantage of potentiometers over voltmeters, as it depends on the settings and design of the specific instrument.
• **Bulkiness** is not a factor that inherently makes a potentiometer preferable; in fact, it can sometimes be a disadvantage due to space constraints.
• **Faster response** is not typically associated with potentiometers compared to voltmeters, as both can be designed to have quick response times depending on the technology used.

Therefore, the key advantage of the potentiometer is its **ability to measure voltage without altering the circuit**, which stems from its negligible current consumption. This **ensures more accurate and reliable measurements** in many applications.

In insects, the structure responsible for the exchange of gases is the tracheae. Insects have a unique respiratory system where air is taken in through tiny openings called spiracles located on the surface of their body.

The air then travels directly into a network of tubes known as the tracheae. The tracheae branch out extensively throughout the insect's body, allowing oxygen to diffuse directly to the insect's tissues and cells. The carbon dioxide produced in the cells travels back through the tracheae and exits the body through the spiracles.

Other structures like the skin, Malpighian tubules, and flame cells have different functions:

• Skin: Insects do not use their skin for gas exchange like some other animals do; their skin is generally designed to protect them from environmental elements.
• Malpighian tubules: These are involved in the excretory system of insects, helping to remove waste products from their bodies.
• Flame cells: These are structures found in certain flatworms and are part of their excretory system; they are not present in insects.

Thus, the correct answer is the tracheae as they specifically enable the exchange of gases in insects.

The process by which plants lose water to the atmosphere is called transpiration.

Transpiration is a fundamental process in the life of a plant. During this process, water is absorbed by the roots from the soil and is then transported through the xylem vessels in the stem and leaves. Once in the leaves, water evaporates into the atmosphere from the surface of tiny pores known as stomata.

Here's a simple breakdown of how transpiration works:

• Water from the soil enters plant roots.
• The water travels through the plant's vascular system (xylem) to reach the leaves.
• In the leaves, the water changes from liquid to vapor and exits through the stomata.

Transpiration is crucial for a number of reasons:

• It helps in the cooling of the plant, similar to how sweating cools our bodies.
• It enables the upward movement of water and minerals from the roots to the leaves.
• Transpiration plays a vital role in maintaining the water cycle within ecosystems.

Understanding transpiration is essential in fields like agriculture, where managing water resources efficiently can significantly impact plant growth and crop yield.

The mouthpart adapted for piercing and sucking is found in the mosquito. Mosquitoes have a specialized mouth structure called a proboscis. This proboscis is long and slender, allowing mosquitoes to puncture the skin of their hosts and suck blood. The proboscis is a complex structure that contains several needle-like parts that make the piercing and sucking process efficient and effective.

To understand which of these gas laws is equivalent to work done, we must first understand the basic concept of work in the context of gases. For gases, work is done when there is a change in volume under pressure, typically expressed as W = P ΔV, where W is work, P is pressure, and ΔV is the change in volume.

Let's consider the given gas laws:

• Charle's law states that the volume of a gas is directly proportional to its temperature at constant pressure.
• Pressure law (often referred to as Gay-Lussac's law) says that the pressure of a gas is directly proportional to its temperature at constant volume.
• Boyle's law states that the pressure of a gas is inversely proportional to its volume at constant temperature. In equation form, this is P₁V₁ = P₂V₂.
• Gay-Lussac's law is another name for the Pressure law.

Among these, Boyle's law relates directly to work done because it involves a change in volume at constant temperature, implying that work occurs as a gas expands or compresses. The equation P₁V₁ = P₂V₂ is foundational for calculating work done in reversible processes, which aligns with the expression for work done on a gas, W = P ΔV. Thus, **Boyle's law** is most directly connected to the concept of work done on a gas.

Newton's Law of Cooling states that the rate of heat loss of an object is directly proportional to the difference in temperature between the object and its surroundings, provided that this temperature difference is small.

Therefore, this law is only valid within a small temperature range.

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.

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.

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.

To solve this problem, we need to calculate the specific latent heat of vaporization of the liquid. The specific latent heat of vaporization, denoted as \(L\), is defined as the amount of heat required to convert 1 kilogram of a liquid into a gas at constant temperature and pressure. The formula for specific latent heat of vaporization is given by:

L = \(\frac{Q}{m}\)

Where:

• Q is the heat supplied to the liquid (in joules)
• m is the mass of the liquid that is evaporated (in kilograms)

First, we need to calculate the total heat energy \(Q\) generated by the resistor. The heat produced by an electrical resistor can be calculated using the formula:

Q = I^2Rt

Where:

• I is the current (in amperes)
• R is the resistance (in ohms)
• t is the time for which current is flowing (in seconds)

Given:

• I = 10 A
• R = 2 Ω
• t = 20 s

Substituting these values into the formula for Q:

Q = (10^2) * 2 * 20 = 100 * 2 * 20 = 4000 J

Now that we have the total heat energy supplied, let's calculate the specific latent heat of vaporization:

Given that the mass \(m\) of the liquid evaporated is \(5 \times 10^{-3}\) kg, we can substitute the values into the formula for \(L\):

L = \(\frac{4000}{5 \times 10^{-3}} = \frac{4000}{0.005} = 800,000 J/kg\)

Therefore, the specific latent heat of vaporization of the liquid is 8.0 x 10⁵ J/kg.

The major building block of an organism is Carbon. Let me explain why in a simple yet comprehensive manner:

Carbon is a unique element found in all living organisms. Its importance comes from its ability to form stable bonds with many other elements, including hydrogen, oxygen, nitrogen, phosphorus, and sulfur. This versatility allows carbon to act as a backbone for the building of complex organic molecules, including proteins, nucleic acids (such as DNA and RNA), carbohydrates, and lipids. These molecules are essential for the structure, function, and regulation of the body's tissues and organs.

Here's why Carbon is indispensable:

• Versatility: Carbon can form four covalent bonds with various atoms, enabling the creation of diverse and complex molecules.
• Formation of Chains and Rings: Carbon atoms can bond with each other to create long chains and rings, serving as the framework for most biomolecules.
• Compound Diversity: Because of its ability to bind with different elements, carbon forms a range of compounds, promoting the complexity and diversity of life.

In summary, Carbon is the primary building block of life due to its unique chemical properties that allow the formation of complex molecules necessary for life's structure and processes.

In a series resonant circuit, the current flowing in the circuit is at its maximum. Let me explain why:

In a series resonant circuit, we have a resistor (R), inductor (L), and capacitor (C) connected in series with an AC source. At a particular frequency called the resonant frequency, these circuits exhibit some unique characteristics. This resonant frequency is determined by the values of the inductor and capacitor and is given by the formula:

f₀ = 1 / (2π√(LC))

At the resonant frequency:

• The inductive reactance (X_L) and capacitive reactance (X_C) become equal in magnitude but opposite in phase. Thus, they cancel each other out.
• This causes the impedance (Z) of the circuit to be at its lowest value, equal to the resistance (R) of the circuit alone.
• Since impedance is at its minimum, according to Ohm’s law (V = IZ), the current through the circuit is at its maximum value for a given applied voltage.

Thus, in a series resonant circuit, when it is operating at its resonant frequency, the current flowing is at its maximum.

To find out how much heat is given out when the piece of iron cools down, we can use the formula for heat transfer:

Q = mcΔT

Where:

• Q = heat energy released or absorbed (in Joules, J)
• m = mass of the substance (in kilograms, kg)
• c = specific heat capacity (in Joules per kilogram per degree Celsius, J/Kg·K)
• ΔT = change in temperature (in degrees Celsius, °C)

First, let's list the values given and convert the mass from grams to kilograms:

• mass (m) = 60g = 0.06kg
• specific heat capacity (c) = 460 J/Kg·K
• initial temperature = 75ºC
• final temperature = 35ºC

Now, calculate the change in temperature:

ΔT = final temperature - initial temperature = 35ºC - 75ºC = -40ºC

Note: Since we are calculating the heat given out as the iron cools, the temperature change will be negative, which will make Q positive, indicating heat is released.

Substitute these values into the heat transfer formula:

Q = mcΔT = (0.06 kg) x (460 J/Kg·K) x (-40ºC)

Q = 0.06 x 460 x -40

Q = -1104 Joules

Since the question asks for how much heat is given out, we consider the positive value of Q, which is 1104J. Therefore, 1104J of heat is given out when the piece of iron cools from 75ºC to 35ºC.

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.

Water is not suitable for use as a thermometric liquid because:

a) It wets glass: This can cause issues with reading the level of the liquid.
b) It needs to be coloured: Water is typically clear, making it difficult to see the level without coloring.
c) It has a low density: This can affect the sensitivity and accuracy of the thermometer.

The unit of impedance is Ohm, which is symbolized by the Greek letter Ω (Omega). In electrical circuits, impedance (Z) is a measure of opposition that a circuit offers to the passage of electric current when a voltage is applied. It is similar to resistance but extends to alternating currents (AC) and contains the effects of resistance as well as reactance (which accounts for capacitors and inductors).

Just like resistance, the unit of impedance is the ohm because they measure similar concepts; however, impedance also accounts for phase shifts between voltage and current, which are not considered in simple resistance. Ohm's Law is used in AC circuits as Z = V/I, where Z is impedance, V is voltage, and I is current. This relationship shows why the unit of impedance is the same as that of resistance.

The device that operates based on the magnetic effect of electric current is the Dynamo.

To explain further, let's look at the concept of the magnetic effect of electric current:

• Magnetic Effect of Electric Current: When an electric current flows through a wire, it creates a magnetic field around the wire. This is known as the magnetic effect of electric current, and it is the fundamental principle behind devices and systems like electromagnets, electric motors, and dynamos.

A Dynamo is a device that converts mechanical energy into electrical energy. It operates based on the phenomenon called electromagnetic induction, which occurs due to the magnetic effect of electric current. When a coil of wire within the dynamo rotates in the presence of a magnetic field, it induces an electric current in the coil. Thus, the operation of a dynamo relies on the interaction between electric current and magnetic fields.

To contrast with other options:

• Electric Heater: It works on the principle of the heating effect of electric current, not the magnetic effect.
• Photocell: This device operates based on the photoelectric effect, which involves the conversion of light energy into electrical energy.
• Cold Cathode: This operates by the emission of electrons when a material is exposed to low-pressure gas discharge, and it doesn't rely on the magnetic effect of electric current.

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.

The degree of precision of a vernier caliper is actually the **smallest value** that the vernier scale can measure, which can be considered as the resolution or least count of the instrument. The degree of precision for most standard vernier calipers is 0.01 cm (or 0.1 mm). This means that the caliper can measure dimensions down to a hundredth of a centimeter.

To understand why this is the case, consider the construction of a vernier caliper:

• The main scale is similar to a ruler, usually graduated in centimeters and millimeters.
• The vernier scale, which moves with the sliding jaws, is marked such that some small fraction of its divisions aligns with one division on the main scale.

This alignment allows more precise measurements than the main scale alone. If the vernier scale has 10 divisions which coincide over a length equal to 9 divisions on the main scale, then each division of the vernier scale represents an extra 0.01 cm. Therefore, it allows measuring smaller intervals between the main scale markings very precisely.

Thus, you won't find vernier calipers with a degree of precision of 0.005 cm, 0.1 cm, or 1.0 cm as options in standard practice for precise measurement tools.

The velocity ratio of a machine is a concept used to explain how much the machine is expected to amplify the input motion. If the velocity ratio of a machine is 4, it means that the distance moved by the effort is 4 times greater than the distance moved by the load.

To understand this concept better, consider what a machine does: it allows you to apply a small effort over a longer distance to move a heavy load over a shorter distance. In this scenario, if the velocity ratio is 4, then for every 4 meters (or units of distance) you exert effort, the load will move 1 meter (or unit of distance).

The mean acceleration of an object is determined by the change in velocity over the change in time. This is given by the formula:

Mean Acceleration (a) = (Final Velocity - Initial Velocity) / (Final Time - Initial Time)

From the velocity-time graph, we have the following points:

Initial Point: (2s, 5m/s)

Final Point: (4s, 15m/s)

Here, the Initial Velocity is 5m/s, the Final Velocity is 15m/s, the Initial Time is 2s, and the Final Time is 4s.

Plug these values into the formula:

Mean Acceleration (a) = (15m/s - 5m/s) / (4s - 2s)

Simplifying this, we get:

Mean Acceleration (a) = 10m/s / 2s = 5m/s²

The mean acceleration is therefore 5.0 m/s².

To understand the concept of resonance in an electrical circuit, it is crucial to know that resonance occurs when the inductive reactance and capacitive reactance are equal in magnitude. This typically happens in a series RLC (Resistor, Inductor, Capacitor) circuit. At resonance, the impedance of the circuit is purely resistive, meaning the circuit behaves as if it only contains a resistor. As a result, the voltages across the inductor and capacitor can be compared at resonance.

In this particular situation, the voltage across the inductor (VL) and the voltage across the capacitor (VC) are of interest due to their roles in resonance:

• At resonance, the inductor and capacitor voltages are equal and opposite. This means that their magnitudes are the same, and they cancel each other out. Therefore, at resonance, VL = VC.

Thus, the correct expression of interest in relation to resonance is VL = VC, which indicates that the voltage across the inductor is equal in magnitude but opposite in phase to the voltage across the capacitor.

Bifocal lenses are primarily used to correct the eye defect known as presbyopia. As people age, the lens of the eye naturally loses its flexibility, making it difficult to focus on objects that are close up. This condition is known as presbyopia. A bifocal lens is designed with two different optical powers to accommodate this need. The upper part of the lens is usually crafted for distance vision, while the lower segment is designed for near vision tasks, such as reading.

Astigmatism is a different eye condition caused by irregular curvature of the cornea or lens, resulting in blurred or distorted vision at all distances. This condition is typically corrected with cylindrical lenses rather than bifocals.

Hypermetropia, commonly known as farsightedness, is a condition where distant objects can be seen more clearly than near ones. Simple convex lenses are usually used for this correction.

Myopia, or nearsightedness, is a condition where nearby objects are seen clearly, while distant objects appear blurry. Concave lenses are generally used to correct this condition.

In summary, bifocal lenses are specifically designed to address the challenges of focusing at different distances simultaneously, making them ideal for managing presbyopia.

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.