JAMB UTME - Physics - 2024

Answer Details

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.

Answer Details

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.

Answer Details

Young's modulus, denoted by E, is a measure of the stiffness of a solid material. It is defined as the ratio of stress to strain in a material that is behaving elastically. Stress is the force applied per unit area, and strain is the deformation experienced by the material in response to the applied stress.

Let's break down the dimensions for Young's modulus:

Stress: Stress is defined as force per unit area. Thus, the dimension of stress can be expressed as:

Stress = Force / Area

The dimension of force is given by mass × acceleration, i.e., Force = MLT^-2 (where M is mass, L is length, and T is time).

The dimension of area is length × length = L².

Therefore, the dimension of stress is:

Stress = (MLT^-2) / (L²) = ML^-1T^-2

Strain: Strain is the ratio of the change in length to the original length and is dimensionless because it is a ratio of two lengths.

Thus, the dimension of strain is simply 1 (dimensionless).

Since Young's modulus is the ratio of stress to strain, its dimension is the same as that of stress. Therefore, the dimension of Young’s modulus E is:

ML^-1T^-2

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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.

Answer Details

The diagram is that of the virus. Viruses are obligate parasites, meaning they can't produce their own energy or proteins. They enter the host cell and use the cell's machinery to make their own nucleic acids and proteins. Viruses also use the host cell's lipids and sugar chains to create their membranes and glycoproteins. This parasitic replication can severely damage the host cell, which can lead to disease or cell death. They usually enter your body through your mucous membranes. These include your eyes, nose, mouth, penis, vagina and anus.

Viruses are a unique type of organism that are not plants, animals, or bacteria. They are often classified in their own kingdom. However, for the sake of the question, since most of their attributes and metabolic activities are more of the bacteria, we'll go with option A - Monera

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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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The diagram in the image represents the urinary system, as indicated by the correct answer. The urinary system includes the kidneys, ureters, bladder, and urethra, which are responsible for filtering blood and excreting waste in the form of urine.

Main Parts of the Urinary System:

1. Kidneys – Filter waste and excess fluids from the blood to form urine.

2. Ureters – Tubes that carry urine from the kidneys to the bladder.

3. Urinary Bladder – Stores urine before it is expelled from the body.

4. Urethra – A tube that allows urine to exit the body.

This system plays a crucial role in maintaining the body's fluid balance and removing waste products.

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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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The average translational kinetic energy of gas molecules is directly related to the temperature of the gas. This relationship is based on the principles of kinetic molecular theory, which explains the behavior of gas molecules in terms of their motion.

Let's break this down simply:

1. Temperature and Kinetic Energy:

The average translational kinetic energy of gas molecules is given by the equation:

\( KE_{avg} = \frac{3}{2} k_B T \)

where \( KE_{avg} \) is the average translational kinetic energy, \( k_B \) is the Boltzmann constant, and \( T \) is the absolute temperature in Kelvin. This formula shows that the kinetic energy is directly proportional to the temperature.

2. What This Means:

As the temperature of a gas increases, the molecules move faster, which increases their translational kinetic energy. Conversely, as the temperature decreases, the molecules slow down, resulting in lower kinetic energy.

It is important to note that this relation is independent of the pressure and the number of moles of the gas. While pressure and the number of moles do affect the overall behavior of a gas, they do not directly influence the average translational kinetic energy of individual molecules.

Therefore, the correct explanation is that the average translational kinetic energy of gas molecules depends on temperature only.

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To determine the new pressure exerted by the gas when it is heated, we'll apply **Gay-Lussac's Law**. This law states that at constant volume, the pressure of a given amount of gas is directly proportional to its absolute temperature. Mathematically, it can be expressed as:

P1/T1 = P2/T2

Where:

• P1 = Initial pressure of the gas (40 mmHg)
• T1 = Initial temperature (298 K)
• P2 = Final pressure of the gas, which we want to find
• T2 = Final temperature (348 K)

By rearranging the formula to solve for the final pressure (P2), we get:

P2 = P1 * (T2/T1)

Now, insert the given values into the equation:

P2 = 40 mmHg * (348 K / 298 K)

Perform the calculations:

P2 = 40 mmHg * (348 / 298)

P2 = 40 mmHg * 1.1678

P2 = 46.71 mmHg

So, the new pressure exerted by the gas when it is heated from 298 K to 348 K at constant volume is 46.71 mmHg.

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To solve this problem, we need to understand the relationship between pressure, volume, and temperature of a gas. The relevant law here is the **Combined Gas Law**, which is expressed as:

(P1 * V1) / T1 = (P2 * V2) / T2

Where:

• P1 is the initial pressure
• V1 is the initial volume
• T1 is the initial temperature in Kelvin
• P2 is the final pressure
• V2 is the final volume
• T2 is the final temperature in Kelvin

In the given problem:

• The initial temperature, T1, is 27ºC, which is 300K (since we convert to Kelvin by adding 273).
• The final temperature, T2, is 127ºC, which is 400K.
• The pressure is doubled, so P2 = 2 * P1.

Applying the Combined Gas Law:

(P1 * V1) / 300 = (2 * P1 * V2) / 400

Simplifying this equation:

V1/300 = 2V2/400

Multiply both sides by 400 to clear the fraction:

400 * V1 / 300 = 2 * V2

Which further simplifies to:

(4/3) * V1 = 2 * V2

Dividing both sides by 2:

(2/3) * V1 = V2

This shows that the final volume, V2, is **2/3 of the initial volume, V1**. Therefore, the volume of the gas will **decrease by 1/3**.

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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.

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Mechanical advantage of a machine = LOADEFFORT $\frac{\text{<br>}}{}$

In this case of a wedge, we can consider the dimensions given:

Load distance (height of the machine): 15 cm
Effort distance (movement of the effort): 0.5 cm

M.A = 150.5 $\frac{\mathrm{<br>}}{}$ = 30.0

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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 solve this problem, we need to understand the relationship between tension and frequency in a sonometer wire. The frequency of a vibrating string, such as one in a sonometer, is directly proportional to the square root of the tension in the string. Mathematically, this relationship is expressed as:

f ∝ √T

Where f is the frequency and T is the tension. In the given problem, the original frequency is 50 Hz, and the tension is increased to four times its original value. Let's analyze how this change in tension affects the frequency:

- Original tension = T

- New tension = 4T

Substitute the new tension into the formula:

f_new = 50 Hz × √(4T/T)

Simplify the equation:

f_new = 50 Hz × √4

f_new = 50 Hz × 2

f_new = 100 Hz

Thus, when the tension is four times the original tension, the new frequency of the sonometer's fundamental note becomes 100 Hz.

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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.

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To determine the efficiency of a cell with an internal resistance of 2 Ω while supplying current to a 6 Ω resistor, we can use the concept of power dissipation. Efficiency in this context is the ratio of the power delivered to the external resistor to the total power supplied by the cell. It can be calculated using the formula:

Efficiency (%) = (Power across load resistor / Total power output by cell) × 100

Let's break it down step by step:

• Step 1: Total Resistance - The total resistance in the circuit is the sum of the internal resistance and the resistance of the external resistor:
• Total Resistance (R_total) = Internal Resistance (R_internal) + External Resistance (R_load)
• R_total = 2 Ω + 6 Ω = 8 Ω
• Step 2: Current Calculation - The current flowing through the circuit can be calculated using Ohm's Law, which states V = IR. Assume the electromotive force (EMF) of the cell is E volts:
• Current (I) = E / R_total
• I = E / 8 (Note: We keep E as a variable as it cancels out in the efficiency equation)
• Step 3: Power Delivered to Load - The power delivered to the external resistor can be calculated as:
• Power_load = I² × R_load
• Power_load = (E/8)² × 6
• Step 4: Total Power Supplied by the Cell - The total power supplied by the cell is given by:
• Power_total = EMF × Current = E × (E/8)
• Power_total = E² / 8
• Step 5: Calculate Efficiency: Finally, plug in the power values into the efficiency formula:
• Efficiency (%) = [(E/8)² × 6 / (E² / 8)] × 100
• Simplify to Efficiency (%) = [(6/8)] × 100 = 0.75 × 100 = 75%

The efficiency of the cell when supplying current to a 6 Ω resistor with an internal resistance of 2 Ω is 75%.

Answer Details

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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To calculate the electric field intensity due to a charge, we need to use the formula:

Electric Field Intensity (E) = Force (F) / Charge (q)

In this problem, we are given that the force (F) is 8 Newtons (N) and the charge (q) is 4 microcoulombs (μC). First, we need to convert the charge from microcoulombs to coulombs:

1 microcoulomb (μC) = 1 x 10^-6 coulombs (C)

Therefore, 4 μC = 4 x 10^-6 C.

Now we can use the formula to find the electric field intensity:

E = F / q

E = 8 N / (4 x 10^-6 C)

E = 8 / 4 x 10⁶

E = 2 x 10⁶

Thus, the value of the electric field intensity is 2 x 10⁶ N/C.

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During the process of glycolysis, a single glucose molecule is broken down into two molecules of pyruvate. During this metabolic pathway, there is a net gain of adenosine triphosphate (ATP) molecules. To understand how many ATP molecules are produced, let's break it down step by step.

1. **Initial ATP Investment:** Glycolysis initially requires an investment of 2 ATP molecules to phosphorylate glucose and convert it into a more reactive form during the early stages of the glycolytic pathway.

2. **ATP Production:** As glycolysis progresses, a total of 4 ATP molecules are produced. This occurs in the later steps of the pathway where adenosine diphosphate (ADP) is phosphorylated to form ATP. This is known as substrate-level phosphorylation.

3. **Net ATP Gain:** To find out the net gain of ATP through glycolysis, simply subtract the initial ATP investment from the total ATP produced:

Net ATP = Total ATP produced - Initial ATP investment

Net ATP = 4 ATP - 2 ATP

Net ATP = 2 ATP

Thus, the net total number of ATP produced during glycolysis is 2 molecules.

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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.

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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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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.

Answer Details

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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Object distance (u) = -25 cm (negative because the object is in front of the mirror)
Image distance (v) = +5 cm (positive because the image is behind the convex mirror)

Using  1f $\frac{1}{f}$ = 1u $\frac{1}{u}$ + 1v $\frac{1}{v}$

1f $\frac{1}{f}$ = 1−25 $\frac{1}{-25}$ + 15 $\frac{1}{5}$

f = 254 $\frac{25}{4}$ = 6.250cm.

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The property by which a material returns to its original shape after the removal of force is called Elasticity.

Let's break it down:

Elasticity: This is a property of a material that allows it to return to its original shape or size after the force that caused deformation is removed. Think of a rubber band—you can stretch it, but once you let it go, it snaps back to its initial shape.

Ductility: This property refers to a material's ability to be stretched into a wire. For example, materials like copper are ductile because they can be drawn into thin wires without breaking.

Malleability: This is a material's ability to withstand deformation under compressive stress. It is the property that allows metals to be hammered or rolled into thin sheets. Gold is a good example of a malleable metal.

Plasticity: This property describes the material's ability to undergo permanent deformation without breaking. When a plastic region is reached, the material will not return to its original shape after the removal of force.

Therefore, when we speak of a material returning to its original shape after the removal of force, we are specifically referring to Elasticity.

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To solve the problem, let's first understand the concept of efficiency in this context. Efficiency refers to the ratio of the useful power output to the total power output of a system. In simpler terms, it tells us how much of the power provided by the cell is being effectively used by the resistor, X.

Given that the cell has an internal resistance (r) of 2Ω and we need the efficiency to be 75%, we will follow these steps:

• The total resistance in the circuit is the sum of the internal resistance and the resistance of the resistor X, so it is (r + X).
• Efficiency is given by the formula:

Efficiency (%) = (R / (R + r)) * 100

Where:

• R is the resistance of resistor X.
• r is the internal resistance of the cell.

According to the problem, efficiency is 75%, so:

(X / (X + 2)) * 100 = 75

First, let’s eliminate the percentage by dividing both sides by 100:

(X / (X + 2)) = 0.75

Now, let's solve for X:

1. Multiply both sides by (X + 2):

X = 0.75 * (X + 2)



2. Distribute the 0.75:

X = 0.75X + 1.5



3. Subtract 0.75X from both sides:

0.25X = 1.5



4. Finally, divide by 0.25:

X = 1.5 / 0.25



5. Solve for X:

X = 6 Ω

Hence, for the cell to have an efficiency of 75%, the value of the resistor X must be 6Ω.

Answer Details

The web-feet of frogs and toads is primarily for swimming. These webbed feet act like paddles, allowing the frog or toad to move efficiently through the water. When the animal spreads its toes, the webbing provides a larger surface area, which gives better propulsion in the water. This adaptation is essential, as many species of frogs and toads spend a significant amount of their time in aquatic environments where efficient swimming helps them in searching for food, escaping predators, and traveling from one place to another. In essence, the webbed feet are a vital feature for their aquatic lifestyle.

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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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In order to solve this problem, we can apply **Boyle's Law**, which states that the **pressure** and **volume** of a gas are inversely proportional at a constant temperature. Mathematically, this is expressed as:

P₁V₁ = P₂V₂

Where:

• P₁ is the initial pressure: 105 Nm^-2
• V₁ is the initial volume: 20 m³
• P₂ is the final pressure: 4 x 105 Nm^-2
• V₂ is the final volume, which we need to find

Rearranging the formula to solve for V₂:

V₂ = (P₁V₁) / P₂

Substituting the given values:

V₂ = (105 Nm^-2 x 20 m³) / (4 x 105 Nm^-2)

By calculating:

V₂ = (2100 m³) / 4 x 105

V₂ = 5 m³

Therefore, at a pressure of 4 x 105 Nm^-2, the volume of the gas is 5 m³.

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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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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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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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To calculate the percentage relative humidity of the air, we use the relationship between the saturation vapour pressure (SVP) and the actual vapour pressure. The formula for relative humidity is:

Relative Humidity (%) = (Actual Vapour Pressure / Saturation Vapour Pressure) * 100

In this problem, the "dew point" refers to the temperature at which air becomes saturated with moisture and water begins to condense. At the dew point, the actual vapour pressure is equal to the saturation vapour pressure at that dew point temperature.

From the problem, we have:

• Saturation Vapour Pressure (SVP) at 33ºC = 13.5 mmHg
• Saturation Vapour Pressure (SVP) at 7ºC (which is the dew point) = 7.3 mmHg

The actual vapour pressure of the air is equal to the SVP at the dew point, which is 7.3 mmHg.

Now we calculate the percentage relative humidity using the formula:

Relative Humidity (%) = (7.3 mmHg / 13.5 mmHg) * 100

Carrying out the calculation:

Relative Humidity (%) = (7.3 / 13.5) * 100 = 0.5407 * 100 = 54.07%

Rounding to the nearest whole number, we get **54%**. Therefore, the percentage relative humidity of the air is 54%.

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To solve this problem, we first need to understand the principle behind a potentiometer. A potentiometer is a device used to measure the electromotive force (e.m.f) of a cell by comparing it with a known voltage. The balance length on a potentiometer corresponds to a proportional measurement of the e.m.f.

Let's denote:

- \( V_1 \): the e.m.f of the first cell = 3.06V

- \( l_1 \): the balance length for the first cell = 75 cm

- \( V_2 \): the e.m.f of the second cell = 2.295V

- \( l_2 \): the balance length for the second cell (which we need to find)

The basic relationship for a potentiometer is given by:

\( V_1 / V_2 = l_1 / l_2 \)

Substituting the given values:

\( 3.06 / 2.295 = 75 / l_2 \)

We need to solve for \( l_2 \):

\( l_2 = (2.295 \times 75) / 3.06 \)

Now, calculating the above expression:

\( l_2 = 171.975 / 3.06 \approx 56.26 \) cm

Therefore, the new balance length for the cell with an e.m.f of 2.295V is approximately 56.26 cm.

Answer Details

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.

Answer Details

When selecting the best type of mirror for shaving, the key consideration is how the mirror reflects light and creates an image. For the purpose of shaving, it is important to have a mirror that magnifies the face and provides a clear view.

The best option for a shaving mirror is a concave mirror. Here is why:

• Magnification: A concave mirror curves inward, similar to the inside of a bowl. When you position your face close to a concave mirror, it produces an enlarged image, making it easier to see details while shaving.
• Focusing Light: Concave mirrors can focus light onto a specific point. This provides a bright and clear image, as the reflected light converges at a point in front of the mirror, enhancing visibility.
• Upright Image: When the object (your face) is placed between the mirror and its focal point, the image remains upright and enlarged. This is perfect for detailed activities like shaving.

Other types of mirrors, like convex and plane mirrors, and parabolic mirrors, do not provide the same level of magnification or focused reflecting properties, making them less suitable for shaving purposes.

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To calculate the power of an object, we need to use the formula for power in terms of work done over time. The formula is:

Power (P) = Work Done (W) / Time (t)

First, let's find the work done on the object. Work done can be calculated using the formula:

Work Done (W) = Force (F) × Distance (d)

Given:

• Force (F) = 50 N
• Distance (d) = 500 cm = 5 m (Note: We need to convert the distance from centimeters to meters because the unit of force is in newtons, and 1 m = 100 cm)

Substituting the values into the formula for work done, we get:

Work Done (W) = 50 N × 5 m = 250 Joules

Next, we consider the time it took for the object to move this distance:

• Time (t) = 1 s

Now, substituting the work done and time into the power formula:

Power (P) = 250 Joules / 1 s = 250 Watts

Thus, the power of the object is 250 Watts.

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The defect of the eye lens that occurs when the ciliary muscles are weak is known as Presbyopia.

Here's a simple explanation:

The ciliary muscles in the eye are responsible for helping the lens to change shape so that you can focus on objects at different distances. As people age, the ciliary muscles may become weaker. This weakness hampers their ability to properly adjust the lens. As a result, the lens cannot accommodate or focus as effectively, especially when looking at nearby objects. This leads to a difficulty in seeing objects up close clearly, which is known as presbyopia.

Presbyopia is a natural condition associated with aging, and it typically becomes noticeable in people in their 40s or 50s. This is different from other eye conditions like:

• Myopia, which is when distant objects appear blurry.
• Astigmatism, which is caused by an irregularly shaped cornea leading to blurry or distorted vision at all distances.
• Spherical aberration, which is a concept related to optical systems where light rays striking the edges of a lens do not focus at the same point as light rays passing through the center, but it is not specifically related to the ciliary muscles or biological aging.

So in summary, presbyopia is the condition that results from weakened ciliary muscles, affecting near vision as a person ages.

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The resultant emergent velocity of a charged ion moving through combined electric and magnetic fields can be derived from the condition where the electric force equals the magnetic force. This gives us the formula for the velocity v:

                                                                                q E = qvB

                                                                                v = EB $\frac{E}{B}$ (q will cancel out)

NOTE:  When both fields are present, for the ion to move without deflection, the electric force must equal the magnetic force.