JAMB UTME - Physics - 2024

If a body in linear motion changes from point P to Q, the motion is 

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

Let's break down the other options:

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


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


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

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

The fourth overtone of a closed pipes is 900Hz, its fundamental frequency is 

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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.

In electrolysis, when same quantity of electricity is passed through different electrolytes, mass of substances deposited is proportional to 

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In electrolysis, when the same quantity of electricity is passed through different electrolytes, the mass of substances deposited is proportional to their chemical equivalent. The reason for this lies in Faraday's laws of electrolysis. Faraday's second law states that the amounts of different substances deposited or liberated by the same quantity of electricity are proportional to their chemical equivalents.

Chemical equivalent refers to a measure of a substance's ability to react or be deposited during electrolysis, and it is calculated as the molar mass divided by valency (n). This is why it is sometimes also referred to as equivalent weight.

In essence, for a given charge (equal number of electrons or electricity), a substance with a lower chemical equivalent will deposit more mass because it requires fewer electrons to undergo the chemical change.

A body is pulled on a horizontal surface with a rope inclined at 30º to the vertical. If the effective force pulling the body along the horizontal surface is 15N, calculate the tension on the rope.

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In this problem, the tension in the rope results in a force that acts to pull the body along the horizontal surface. The rope is inclined at 30º to the vertical, which means it makes an angle of 60º with the horizontal since the total angle between vertical and horizontal is 90º.

To find the tension in the rope, we first understand that the component of the tension force acting along the horizontal surface is given by the formula:

F_horizontal = Tension * cos(θ)

Where:

• F_horizontal is the effective force pulling the body along the horizontal, given as 15N.
• Tension is the total tension in the rope that we need to find.
• θ is the angle of inclination with respect to horizontal = 60º (since the rope is 30º to the vertical, it's 60º to the horizontal).

Given that F_horizontal = 15N, we substitute into the equation:

15N = Tension * cos(60º)

We know that cos(60º) = 0.5, therefore:

15N = Tension * 0.5

To find the Tension, divide both sides of the equation by 0.5:

Tension = 15N / 0.5

Tension = 30N

Therefore, the tension in the rope is 30N.

Calculate the quantity of heat for copper rod whose thermal capacity is 400Jk−1 ${}^{-1}$ for a temperature change of 60ºC to  80ºC

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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.

In the diagram above, the galvanometer is converted to 

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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.

An air force jet flying with a speed of 335m/s went past an anti-aircraft gun. How far is the aircraft 5s later when the gun was fired?

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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.

Inbreeding is highly discouraged in humans because it may 

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Inbreeding is the process where closely related individuals, like cousins or siblings, mate and produce offspring. **This practice is highly discouraged in humans for several reasons, but a significant concern is the potential for an outbreak of hereditary diseases.**

Here’s why inbreeding is problematic:

• Humans carry genes in pairs, and some of these genes might be recessive, meaning they only show their effects if an individual inherits two copies of the same gene (one from each parent). These genes might cause diseases or other health issues.
• When two closely related individuals mate, the chance of both carrying the same recessive genes is **higher**. This increases the likelihood that their offspring will inherit these genes, leading to hereditary diseases. **This genetic similarity can result in a higher risk of disorders such as cystic fibrosis, sickle cell anemia, and Tay-Sachs disease**.
• While some may argue that inbreeding could lead to other issues, such as dwarfism or higher death rates in newborns, the primary scientific concern backed by genetics is the increased susceptibility to hereditary diseases.

Therefore, **to promote genetic diversity and reduce the risk of hereditary diseases in offspring, inbreeding is discouraged in human populations**. This way, offspring are less likely to inherit harmful genetic combinations that can lead to health problems.

When a bus is accelerating, it must be 

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When a bus is accelerating, it is primarily changing its velocity. This is because velocity is a vector quantity, which means it includes both the speed and the direction of the object's movement. Acceleration refers to any change in this velocity. Therefore, the bus could be increasing its speed, decreasing its speed (which is also known as deceleration), or changing its direction. All these aspects involve a change in velocity.

Let's break it down further:

Changing its Speed: If the bus is speeding up or slowing down, it results in a change in the magnitude of its velocity, contributing to acceleration.

Changing its Direction: Even if the bus maintains a constant speed, if it changes direction (like taking a turn), its velocity is altered because direction is a part of velocity. This results in acceleration.

Changing its Position: While a change in position happens during acceleration, it is not the defining feature of acceleration. An object can change its position even if it is moving with constant velocity and not accelerating.

So, the key component here for acceleration is the change in velocity, which encompasses changes in speed, direction, or both.

A wheelbarrow inclined at 60º to the horizontal is pushed with a force of 150N. What is the horizontal component of the applied force

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

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

F_horizontal = F_applied \times \cos(\theta)

Where:

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

Substitute the values into the formula:

F_horizontal = 150N \times \cos(60º)

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

Therefore:

F_horizontal = 150N \times 0.5 = 75N

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

An effort of 40N is applied on a machine to lift a mass of 60kg. Determine the mechanical advantage of the machine [ g = 10ms2 ${}^2$ ]

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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.

A boy standing 408m from a wall blew a trumpet and heard the echo 2.4s later. Calculate the speed of the sound

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To calculate the speed of sound, we need to understand that an echo involves a sound wave traveling to a surface and back. In this case, the sound travels from the boy to the wall and then returns.

The total distance that the sound wave travels is twice the distance from the boy to the wall because it goes to the wall and back. Therefore, the total distance is:

Total Distance = 2 x 408m = 816m

The echo was heard 2.4 seconds after the sound was made. The speed of sound can be calculated using the formula:

Speed of Sound = Total Distance / Time

Plugging in the values, we have:

Speed of Sound = 816m / 2.4s

When you perform the division, you find:

Speed of Sound = 340 m/s

Thus, the speed of the sound is 340 m/s, which is the correct answer.

In a cross involving a heterozygous red flower plant (Rr) and a white flowered plant (rr). What is the probability that the offspring will be Rr?

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By crossing  Rr  x  rr

We obtain  Rr , rr , rr , Rr

⇒ 50% = 12

What will be the weight of a man of mass 60kg standing in a lift if the lift is descending vertically at 3ms2 ${}^2$?

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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.

An object is placed 25cm in front of a convex mirror has its image formed 5cm behind the mirror. what is the focal length of the convex mirror

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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.

Using the circuit above, at resonance 

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

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

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

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

A red shirt under a red light appears pale because red

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To understand why a red shirt appears pale under red light, we need to consider how colors are perceived. A shirt's color is due to the light it reflects. A red shirt reflects red light and absorbs other colors. This is why it looks red under normal white light, which is made up of many colors including red.

When you place a red shirt under red light, the only available light to reflect is red. Since the shirt is already designed to reflect red light, it reflects the red light and appears its vivid color. However, it might appear brighter or paler since no other colors are present to contrast against the red.

Therefore, the best explanation is that the red shirt absorbs other colours and reflects red.

An electron falls from an energy level of -5.44eV to another energy level, E. If the emitted photon is of wavelength 5.68 x 10−6 ${}^{-6}$m, calculate the energy change. [ Plank's constant = 6.63 x 10−34 ${}^{-34}$Js, emitted radiation speed = 3.0 x 108 ${}^8$ms−1 ${}^{-1}$]

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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.

I clear  II sharp  III poor IV dark

Which of the above happens when the hole of a pinhole camera is diminished?

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

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

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

Answer: II only (The image becomes sharper.)

The total number of ATP produced during glycolysis is

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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.

The process of adding impurities to a semiconductor material to increase its conductivity is 

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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.

Which of the following is not a part of model rocket?

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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.

A cell of internal resistance of 2Ω $\mathrm{\Omega }$ supplies current through a resistor, X if the efficiency of the cell is 75%, find the value of X.

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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.

Which of the following structures enables the exchange of gases in insects?

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

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

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

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

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

The acceleration of a free fall due to gravity is not a constant everywhere on the Earth's surface because

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

If the S.V.P of water vapour was 13.5mmHg at 33ºC and 7.3mmHg at 7ºC. Find the percentage relative of the air on a day when average air temperature was 33ºC and dew point was 7ºC.

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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%.

The power of a convex lens of focal length 20cm is 

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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.

A sonometer's fundamental note is 50Hz, what is the new frequency when the tension is four times the original?

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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.

288KJ is conducted across two opposite faces of a 3m cube of temperature gradient 90ºCm−1 ${}^{-1}$ in 7200s. Calculate the thermal conductivity.

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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.

What is the least possible error encountered when taking measurement with a metre rule?

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

If the velocity ratio of a machine is 4, what does it mean?

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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 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**.

An ideal transformer has

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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.

Rainbow is formed when sunlight undergoes 

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A rainbow is formed through a combination of three processes: reflection, refraction, and dispersion. Let's break down each process to understand how a rainbow forms:

1. Refraction: When sunlight enters a raindrop, it bends or changes direction. This bending of light is known as **refraction**. Different colors of sunlight bend by different amounts because they have different wavelengths.

2. Reflection: Once inside the raindrop, the light gets reflected off the inside surface of the drop. This reflection sends the light back out of the raindrop at different angles.

3. Dispersion: As the light exits the raindrop, it bends again (refraction). Because each color bends by a different amount, the sunlight is spread out into its component colors, creating a spectrum. This spreading into a spectrum is called **dispersion**.

All three processes contribute to the formation of a rainbow. The combination of **refraction, reflection, and dispersion** results in the beautiful arc of colors that we see in the sky.

A body is whirled in a horizontal circle at the rate of 800 revolutions per minute. Determine the angular velocity

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

Here’s how you can calculate it:

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

Now let's perform the conversion:

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

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

The food nutrient with the highest energy value is

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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.

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

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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.

The quantity of heat required to melt ice of 0.2 kg whose specific latent heat is 3.4 x 105 ${}^5$J/Kg is

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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.

When a charged ebonite rod is brought near a charged glass rod, there will be 

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When a charged ebonite rod is brought near a charged glass rod, there will be attraction. This is because charged objects obey the fundamental principle of electrostatics, which states that opposite charges attract each other while like charges repel each other.

An ebonite rod typically acquires a negative charge when rubbed with fur, as it gains electrons. In contrast, a glass rod usually acquires a positive charge when rubbed with silk, as it loses electrons. Therefore, when these two objects, one negatively charged and the other positively charged, are brought near each other, the opposite charges will attract.

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

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

f₀ = 1 / (2π√(LC))

At the resonant frequency:

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

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