JAMB UTME - Physics - 2024

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The power of a lens is a measure of its ability to converge or diverge light. It is defined as the reciprocal (or inverse) of the focal length of the lens. The formula for calculating the power (P) of a lens in diopters (D) is given by:

P = 1/f

where:

• P is the power of the lens in diopters (D).
• f is the focal length of the lens in meters.

In this case, the focal length given is 20 cm. To apply the formula, we first need to convert this focal length into meters because the diopter is the reciprocal of the focal length in meters:

f = 20 cm = 0.20 m

Now, substitute the focal length in meters into the formula for power:

P = 1 / 0.20

P = 5.00 D

Thus, the power of the convex lens is 5.00 diopters. This indicates that the lens is capable of converging light at a distance of 5.00 meters.

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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.

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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.

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To find the energy change when an electron falls from one energy level to another, we need to calculate the energy of the emitted photon. This energy can be found using the formula:

E = hν   or   E = hc/λ

where:

• h is Planck's constant, 6.63 x 10^-34 Js
• c is the speed of light, 3.0 x 10⁸ ms^-1
• λ is the wavelength of the emitted photon, 5.68 x 10^-6 m

Substitute these values into the equation:

E = (6.63 x 10^-34 Js) * (3.0 x 10⁸ ms^-1) / (5.68 x 10^-6 m)

First, calculate the numerator:

(6.63 x 10^-34) * (3.0 x 10⁸) = 1.989 x 10^-25 J·m

Then, divide by the wavelength:

E = 1.989 x 10^-25 J·m / 5.68 x 10^-6 m = 3.5 x 10^-20 J

Therefore, the energy change when the electron falls is approximately 3.5 x 10^-20 J.

Checking the options provided, the closest value is 3.49 x 10^-20 J.

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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 calculate the speed of the wave, we need to understand some fundamental wave properties: **wavelength**, **frequency**, and **wave speed**.

1. **Wavelength (\( \lambda \))**: The wavelength is the distance between two successive crests of a wave. In this case, the wavelength is given as **0.25 meters**.

2. **Frequency (\( f \))**: Frequency is the number of complete oscillations or cycles that occur per second. It is given that a particle on the surface of the water makes **four complete vertical oscillations in one second**. So, the frequency is **4 Hz (hertz)**.

3. **Wave Speed (\( v \))**: The speed of a wave is calculated using the formula:

\( v = f \times \lambda \)

Where:

\( v \) is the wave speed,

\( f \) is the frequency, and

\( \lambda \) is the wavelength.

Substitute the given values into the formula:

\( v = 4 \text{ Hz} \times 0.25 \text{ m} \)

\( v = 1 \text{ m/s} \)

Therefore, the **speed of the wave** is 1 m/s.

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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.

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The mass of an object can be calculated using the formula:

Mass = Density × Volume

In this case, we need to find the mass of a solid cube of aluminum. Given:

• Density of aluminum = 2700 kg/m³
• Edge length of the cube = 1.5 cm

First, we need to calculate the volume of the cube. The volume V of a cube with edge length a is given by:

V = a³

Substitute the edge length:

V = (1.5 cm)³ = 1.5 × 1.5 × 1.5 cm³ = 3.375 cm³

Since the density is given in kg/m³, we should convert the volume from cm³ to m³. There are 1,000,000 cm³ in 1 m³, so:

Volume in m³ = 3.375 cm³ × (1 m³/1,000,000 cm³) = 3.375 × 10^-6 m³

Now, use the mass formula:

Mass = Density × Volume

Mass = 2700 kg/m³ × 3.375 × 10^-6 m³

This equals:

Mass = 9.1125 × 10^-3 kg

Convert kg to grams (since 1 kg = 1000 g):

Mass = 9.1125 grams

So, the mass of the cube is approximately 9.1 g. Thus, the correct answer is 9.1 g.

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The part labelled I in the diagram refers to **sunlight**.

Here's a simple explanation:

The given chemical equation is a representation of **photosynthesis**, a process by which green plants, algae, and some bacteria convert light energy, typically from the sun, into chemical energy stored in glucose (C₆H₁₂O₆) and release oxygen (O₂) as a by-product.

In the context of the equation:

- **6CO₂ (Carbon Dioxide) + 6H₂O (Water) → C₆H₁₂O₆ (Glucose) + 6O₂ (Oxygen)**

The arrow indicates the transformation that occurs during the process. The **chlorophyll** (labelled in the diagram) indicates the presence of chlorophyll pigments in the chloroplasts of plant cells which are essential for **absorbing sunlight**.

Since **sunlight** is the source of energy that powers this transformation, it is the correct component for the part labelled I in the diagram.

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When it comes to a model rocket, it is crucial to understand the different parts that make up the rocket and their functions:

• The Body Tube: This is the main frame of the rocket. It holds all the other components together and serves as the backbone of the rocket.
• The Nose Cone: This is the pointed part at the top of the rocket. It is designed to reduce aerodynamic drag and also aids in stabilizing the rocket during flight.
• The Fin: Fins are attached at the lower end of the rocket. They help stabilize the rocket's flight path by reducing wobble and assisting in maintaining a straight trajectory.

Now, “Not recovery devices” is listed among the options. A recovery device is actually a part of a model rocket system. Common recovery devices include parachutes or streamers that deploy after the rocket reaches its peak altitude, allowing it to return safely to the ground. Such devices are indeed part of a model rocket design.

Therefore, the option “Not recovery devices” itself is not recognized as a part of a model rocket. Instead, the sentence is stating that they are not part of the main components, which implies it's indicative rather than being the name of a component. Hence, it does not pertain to a single component like the body tube, nose cone, or fins.

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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 find the value of the capacitance, we need to use the formula for capacitance:

Capacitance (C) = Charge (Q) / Voltage (V)

In this problem, the charge (Q) is given as 30 Coulombs (C) and the voltage (V) is 5 Volts (V). We can plug these values into the formula:

C = 30 C / 5 V

Calculating the above expression gives:

C = 6 Farads (F)

Therefore, the value of the capacitor is 6 Farads.

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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.

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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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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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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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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 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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To calculate the quantity of heat absorbed or released by a substance, we can use the formula:

Q = C × ΔT

where:

• Q is the quantity of heat.
• C is the thermal capacity of the substance.
• ΔT is the change in temperature.

Given:

• C = 400 J/°C
• Initial temperature = 60°C
• Final temperature = 80°C

First, calculate the change in temperature:

ΔT = Final temperature - Initial temperature = 80°C - 60°C = 20°C

Now, substitute the values into the formula to find the quantity of heat:

Q = 400 J/°C × 20°C

Calculate the answer:

Q = 8000 J

Since the options provided are in kilojoules (KJ), we need to convert joules (J) to kilojoules (1 KJ = 1000 J):

Q = 8000 J ÷ 1000 = 8 KJ

Therefore, the quantity of heat for the copper rod, given the specified conditions, is 8 KJ.

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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%.

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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).

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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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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.

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To understand when a vapor is considered saturated, it is crucial to consider the rates of two significant processes: evaporation and condensation. **Evaporation** is the process where liquid molecules escape into the vapor phase, and its rate is denoted as **y**. On the other hand, **condensation** is the process where vapor molecules return to the liquid phase, with its rate denoted as **x**.

A vapor is said to be **saturated** when the rate of evaporation of the liquid is equal to the rate of condensation of the vapor. In simpler terms, the number of molecules leaving the liquid to become vapor is exactly equal to the number of molecules returning from the vapor to the liquid.

In mathematical terms, this condition can be described as **x = y**. Under this condition, the system reaches a dynamic equilibrium, and the vapor pressure of the system is at its maximum for the given temperature. At this point, the vapor cannot accommodate any more molecules, and thus, the vapor is in a saturated state.

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The energy stored in the capacitor = 12 $\frac{1}{2}$q2C $\frac{q^2}{C}$

Where C = 2F, q = 3C

=  12 $\frac{1}{2}$322 $\frac{3^2}{2}$ = 94 $\frac{9}{4}$ = 2.25J

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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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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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Bile is a greenish alkaline liquid that plays a crucial role in the digestive process, particularly in the digestion and absorption of fats. It is produced in the liver, but it is not stored there. Instead, the bile is transported to a small organ where it is concentrated and stored until the body needs it for digestion. This organ is the gall bladder.

The gall bladder stores the bile and releases it into the small intestine when food, especially fatty food, enters the digestive tract. This helps in breaking down the fats into smaller droplets, making it easier for enzymes to digest them.

To sum up, the gall bladder is the organ responsible for storing bile.

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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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For Hare's apparatus

Relative density = hwhl $\frac{h_w}{h_l}$

Given: height of liquid = 0.5cm, height of water = 0.3cm

Relative density = 0.30.5 $\frac{0.3}{0.5}$ = 0.6

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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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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.

Detalles de la respuesta

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.

Detalles de la respuesta

Upthrust(Force) = volume of object x density of liquid x g = V x ρ $\rho$ x g

U = 4.2 x 10−4 ${}^{-4}$ x  1028 x 10 ≊ $\approxeq$ 4.3N

Detalles de la respuesta

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.

Detalles de la respuesta

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.

Detalles de la respuesta

The thermal conductivity of a material is a measure of its ability to conduct heat. It is defined by the formula:

Q = k × A × ΔT/Δx × t

Where:

• Q is the heat energy conducted (in Joules)
• k is the thermal conductivity (in W/mK)
• A is the area through which heat is conducted (in square meters, m²)
• ΔT is the temperature difference (in Kelvin or Celsius, since a difference in degrees Celsius is equivalent to a difference in Kelvin)
• Δx is the thickness of the material (or the distance over which the temperature difference occurs, in meters)
• t is the time taken (in seconds)

We are given:

• Q = 288,000 J (since energy is in KJ and 1KJ = 1,000J)
• ΔT/Δx = 90 ºC/m (temperature gradient)
• t = 7,200 s

The cube has each side measuring 3 meters, so the area A of one face (since heat is conducted across two opposite faces, effectively using one face area for calculation) is:

A = 3m × 3m = 9 m²

Now, we need to solve for k (thermal conductivity):

Q = k × A × ΔT/Δx × t

288,000 J = k × 9 m² × 90 ºC/m × 7,200 s

k = 288,000 / (9 × 90 × 7,200)

Calculate the denominator:

9 × 90 × 7,200 = 5,832,000

Therefore:

k = 288,000 / 5,832,000 ≈ 0.0493 W/mK

This converts approximately to 4.93 × 10^-2 W/mK.

Therefore, the correct answer is 4.9 × 10^-2 W/mK.

Detalles de la respuesta

A monochromatic light is one that has a single wavelength or color. This means that it consists of light waves that all have the same frequency, resulting in a uniform appearance without any variation.

Detalles de la respuesta

A non-rechargeable cell, commonly known as a primary cell, is a type of chemical battery that is designed to be used once until the chemical reactions that produce electricity are exhausted. After this point, the cell cannot be reversed or recharged.

In the given examples, the dry leclanche cell is a well-known example of a non-rechargeable cell. It is commonly used in everyday devices like remote controls, wall clocks, and torches. This cell type utilizes zinc and manganese dioxide as electrodes and relies on a moist paste of ammonium chloride for the electrolyte.

The other examples, such as nickel iron, mercury cadmium, and lead-acid, involve rechargeable cells (secondary cells) that are specifically designed to endure multiple charges and discharges throughout their useful life. Thus, unlike the dry leclanche cell, these can be recharged after use.

Therefore, the dry leclanche cell is an ideal example of a non-rechargeable cell because it can only be used once. After depletion, it cannot be recharged or reused.

Detalles de la respuesta

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.