JAMB UTME - Physics - 2024

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.

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.

To understand the color of a red rose under a blue light, we need to consider how we perceive color. Objects appear colored because they reflect certain wavelengths of light. A red rose appears red in white light because it reflects red wavelengths and absorbs others.

When you shine blue light on a red rose, the situation changes. A blue light primarily contains blue wavelengths. Since the red rose does not have red wavelengths to reflect anymore, and it cannot reflect blue light (as it absorbs it), the rose will appear to be the absence of any reflected wavelength visible to our eyes.

This means the rose will appear black under blue light, as black is perceived when no visible light is reflected into our eyes. Thus, the color of the red rose under a blue light is black.

The changes of living organisms over generations are referred to as organic evolution.

Organic evolution, also known as biological evolution, is the process through which species of organisms undergo changes over time due to genetic variations and environmental factors. This leads to the development of new traits and, over long periods, may result in the emergence of new species.

Here's a simple breakdown of the concept:

• **Genetic Variation:** Within a species, individuals have slight genetic differences, primarily due to mutations and the combination of parental genes.
• **Natural Selection:** In any given environment, some traits may offer a survival or reproductive advantage. Organisms with these traits are more likely to pass their genes to the next generation.
• **Adaptation:** Over generations, traits that confer advantages become more common in the population, leading to organisms that are better suited to their environment.
• **Speciation:** With significant changes over long periods, populations may diverge so much that they become new species.

This process is a key concept in biology and is fundamental to understanding the diversity of life on Earth. Organic evolution is distinct from other kinds of evolution mentioned, as it specifically deals with biological organisms.

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.

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.

To find the apparent weight of a man of mass 60 kg standing in a descending lift, we first need to understand the concept of apparent weight. Apparent weight is the force that the man feels as his weight due to the reaction of the lift floor on him. When the lift accelerates, the apparent weight changes from his actual weight.

In this case, the lift is descending with a constant velocity of 3 m/s². Since the acceleration is downward, it means the lift is accelerating negatively compared to an upward acceleration.

The formula to find the apparent weight (W_apparent) when in a lift is:

W_apparent = m(g - a)

Where:

• m is the mass of the man, which is 60 kg
• g is the acceleration due to gravity, approximately 9.8 m/s²
• a is the acceleration of the lift (3 m/s² downward)

Substituting these values into the formula, we get:

W_apparent = 60 (9.8 - 3)

Calculating further:

W_apparent = 60 × 6.8

W_apparent = 408 N

The closest option to 408 N in the answers provided is 420 N. Therefore, the correct answer is 420 N.

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.

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, let's first understand how sound works in a closed pipe. A closed pipe has one end closed and another end open. Sound waves inside such a pipe create standing waves, where nodes (points of no movement) and antinodes (points of maximum movement) are formed.

For a closed pipe, the fundamental frequency (also called the first harmonic) has one node at the closed end and one antinode at the open end. The wavelength is four times the length of the pipe.

The overtone sequence for a closed pipe includes only odd harmonics: 1st (fundamental), 3rd, 5th, 7th, etc. The nth overtone is the 2nth + 1 harmonic. The equation for the frequency of a harmonic in a closed pipe is:

f_n = n * f_1, where f_n is the frequency of the nth harmonic and f_1 is the fundamental frequency

In this case, the fourth overtone corresponds to the 9th harmonic because 2 * 4 + 1 = 9. Therefore, we have:

900 Hz = 9 * f_1

To find the fundamental frequency (f_1), we solve for f_1:

f_1 = 900 Hz / 9

f_1 = 100 Hz

Therefore, the fundamental frequency is 100 Hz.

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.

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.

The diaphragm in a camera is similar to the iris in the human eye.

Here's a simple explanation:

• Both the diaphragm in a camera and the iris in the eye control the amount of light that enters. The diaphragm adjusts the size of the aperture, which is the opening that allows light to hit the camera's sensor.
• Similarly, the iris adjusts the size of the pupil, which is the opening that allows light to enter the eye and reach the retina.
• The camera's diaphragm is responsible for creating different aperture sizes, just as the iris changes the size of the pupil in different lighting conditions.
• In bright light, both the diaphragm and the iris make their respective openings smaller to reduce the amount of light entering, protecting the camera's sensor and the eye's retina respectively.
• Conversely, in low light conditions, both open wider to allow more light in, enhancing clarity and visibility.

In summary, the iris acts like a natural diaphragm, regulating the light that passes through the eye, much like the diaphragm does in a camera.

Friction due to air mass, also known as air resistance or drag, can be reduced by a concept called **streamlining**.

**Streamlining** refers to the shaping of an object in such a way that it allows air to flow smoothly around it, minimizing turbulence and reducing drag. When air flows smoothly over an object without much disturbance, there is less resistance, and the object can move more easily through the air.

Think of it like how a bullet or a fast-moving car is designed. They have a sleek, smooth shape that cuts through the air with minimal effort. This principle is applied in designing cars, airplanes, and even boats to enhance their efficiency and speed by reducing the friction with the air or water they move through.

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

To derive the dimension of power:

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

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

Thus, the dimensional formula for power is:

M L² T^-3

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

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

To understand this, let's break it down:

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

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

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

At absolute zero temperature, which is defined as 0 Kelvin or -273.15 degrees Celsius, the energy of molecular motion ceases. This means that the molecules theoretically have minimal energy, and hence, their motion stops entirely. Therefore, the average velocity of the molecules is zero. In reality, absolute zero is a theoretical limit, and it is practically unreachable, but it serves as a concept to help in understanding the behavior of molecules at extremely low temperatures. Thus, under this theoretical condition, the average motion of molecules would be nonexistent. In summary, the average velocity of the molecules at absolute zero is zero.

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

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

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

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

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

r = (yπ)/2

So, the area (A) is:

A = π[(yπ)/2]²

Simplifying the area:

A = π(y²π²/4)
A = y²π³/4

Stress (σ) is given by the formula:

σ = F/A

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

σ = (y²) / (y²π³/4)

By simplifying the expression:

σ = (4y²) / (y²π³)

Cancel out y² from numerator and denominator:

σ = 4/π² Nm⁻²

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

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.

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.

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.

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.

To determine what the galvanometer is converted to in the described scenario, let’s first understand how a galvanometer can be transformed into different measuring devices:

1. Galvanometer to Voltmeter: To convert a galvanometer into a voltmeter, a high resistance (known as a multiplier) is connected in series with the galvanometer. This high resistance ensures that the voltmeter can measure a wide range of voltages without drawing significant current from the circuit.

2. Galvanometer to Ammeter: To convert a galvanometer into an ammeter, a low resistance (called a shunt) is connected in parallel with the galvanometer. This allows the majority of the current to pass through the shunt, enabling the ammeter to measure high currents without damaging the galvanometer.

Since the problem statement does not specify any additional details, a general observation is that a galvanometer is commonly converted into an ammeter using a shunt, especially in basic electrical circuits where current measurement is necessary. Therefore, from the options provided, **the galvanometer is most likely converted to an ammeter**.

**In summary**, if a low resistance is added in parallel with the galvanometer, it becomes an ammeter, while adding a high resistance in series would convert it into a voltmeter. Since the context commonly involves conversion for current measurement, the provided diagram likely represents a galvanometer converted into an ammeter.

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.

The formation of cilia and flagella in living cells is primarily carried out with the help of **centrioles**.

Here's a simple explanation:

Centrioles are cylindrical structures made up of microtubules. They are found in eukaryotic cells and play a critical role in cell division and the organization of the cell's cytoskeleton. However, their role extends beyond this to the formation of the basal bodies which seed the growth of cilia and flagella.

Cilia and flagella are microscopic, hair-like structures that protrude from the surface of certain eukaryotic cells. They are primarily involved in movement. Cilia often work like tiny oars, moving fluid across the cell's surface or propelling single-celled organisms. Flagella are typically longer and move in a whip-like fashion to propel cells, such as sperm cells.

Here's how centrioles contribute to the formation of these structures:

1. **Basal Body Formation**: Each cilium or flagellum grows out from a structure known as a basal body. The basal body is derived from the centrioles. During this process, a centriole migrates to the cell's surface and acts as a nucleation site for the growth of microtubules, which in turn form the structural core of cilia and flagella.

2. **Microtubule Organization**: The centrioles help organize microtubules in a "9+2" arrangement, which is characteristic of cilia and flagella. This refers to nine pairs of microtubules forming a ring around two central microtubules, giving these structures both stability and flexibility for movement.

Thus, centrioles are crucial as they provide the groundwork for the formation and proper functioning of cilia and flagella. They ensure that these structures are assembled correctly and are able to carry out their roles in cell movement and fluid transport.

Infra-red thermometers work by detecting the radiation from the body and converting it to temperature. These thermometers are designed to measure the infrared radiation, also known as heat radiation, emitted by objects. All objects with a temperature above absolute zero emit infrared radiation. The thermometer's sensor captures this radiation and converts it into an electrical signal that can be read as a temperature measurement. This method allows for quick, non-contact temperature readings, which is why infrared thermometers are often used in medical settings, industrial applications, and more.

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.

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.

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%.

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

Let's break down the other options:

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


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


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

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

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

To determine the effective force pushing the object forward at an angle of 60º, we need to resolve the given force into its components. Specifically, we are interested in the horizontal component of the force, as this is the part that effectively pushes the object forward.

The general formula to calculate the horizontal component of a force (F_x) when the force is applied at an angle (θ) is:

F_x = F * cos(θ)

Where:

• F is the magnitude of the force applied.
• θ is the angle at which the force is applied, in this case, 60º.
• cos(θ) is the cosine of the angle.

Assuming the magnitude of the force applied (F) is 50N, then the effective forward force can be calculated as follows:

F_x = 50N * cos(60º)

Using the trigonometric value:

cos(60º) = 0.5

Therefore:

F_x = 50N * 0.5

F_x = 25N

Hence, the effective force pushing it forward at an angle of 60º is 25.00N. Therefore, the correct answer is 25.00N.

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.

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.

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