JAMB UTME - Physics - 2024

Bile is a greenish alkaline liquid which is stored in the

Bayanin Amsa

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.

The device for measuring the angle of dip is 

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The device used for measuring the angle of dip is the dip circle.

Let me explain this in simple terms:

The angle of dip, also known as the magnetic inclination, is the angle made by the Earth's magnetic field lines with the horizontal plane. It varies depending on where you are on the Earth's surface. In some places, magnetic field lines are nearly vertical, while in others they are more horizontal.

A dip circle is a specialized scientific instrument used to measure this angle. It usually consists of a magnetic needle that is free to rotate in the vertical plane.

When using a dip circle, you align it so that its plane is parallel to the direction of the Earth's magnetic field. Then, you read the angle at which the magnetic needle stabilizes. This is the angle of dip. The instrument's mechanism allows for accurate measurement of this angle by compensating for any external influences or inclinations.

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.

Calculate the magnetic force on an electron in a magnetic field of flux density 10T, with a velocity of 3 x 107 ${}^7$m/s at 60º to the magnetic field (e = 1.6 x 10−19 ${}^{-19}$C)

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The magnetic force on an electron in a magnetic field (F) = q v Bsinθ $\theta$

B = 10T, q =  3 x 107 ${}^7$m/, θ $\theta$ = 60º and q =  1.6 x 10−19 ${}^{-19}$C

F =  1.6 x 10−19 ${}^{-19}$ x 3 x 107 ${}^7$ x 10 x sin 60º ≊ $\approxeq$ 4.162 × 10−11 ${}^{-11}$N

The gravitational force between two objects  masses 1024 ${}^{24}$kg and 1027 ${}^{27}$kg is 6.67N. Calculate the distance between them [ G = 6.6 x 10−11 ${}^{-11}$Nm2 ${}^2$kg−2 ${}^{-2}$ ]

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

F = (G * m1 * m2) / r²

Where:

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

We need to compute r by rearranging the formula:

r² = (G * m1 * m2) / F

Therefore, the distance r is:

r = √((G * m1 * m2) / F)

Substitute the given values into the equation:

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

Calculating inside the square root:

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

Then divide by the force:

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

Finally, calculate the square root:

r = √(0.99 x 10⁴⁰)

r ≈ 1.0 x 10²⁰ m

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

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.

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.

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.

Under which conditions is work done

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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 gravitational force between two objects is determined by Newton's Law of Universal Gravitation, which can be expressed by the formula:

F = G * (m1 * m2) / r²

where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the centers of the two objects.

In this problem, it is given that the initial gravitational force is 10N. According to the formula, the gravitational force is inversely proportional to the square of the distance between the two objects.

So, if the distance between the objects is halved (i.e., r becomes r/2), then the new gravitational force F' can be calculated based on the relationship:

F' = G * (m1 * m2) / (r/2)² = G * (m1 * m2) / (r²/4) = 4 * (G * m1 * m2 / r²) = 4 * F

Since the initial force F was 10N, the new force F' when the distance is halved is:

F' = 4 * 10 = 40N

Thus, the new value of the gravitational force is 40N.

Find the value of a capacitor with voltage 5V and 30C.

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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.

One main feature of trees in the savanna habitat is the possession of

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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.

The distance between two successive crests of a water wave is 0.25m. If a particle on the surface of the water makes four complete vertical oscillations in one second. Calculate the speed of the wave.

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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.

How much joules of heat are given out when a piece of iron, of mass 60g and specific heat capacity 460JKg−1 ${}^{-1}$K−1 ${}^{-1}$, cools from 75ºC to 35ºC

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

Q = mcΔT

Where:

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

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

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

Now, calculate the change in temperature:

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

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

Substitute these values into the heat transfer formula:

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

Q = 0.06 x 460 x -40

Q = -1104 Joules

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

Calculate the depth of a swimming pool if the apparent depth is 10cm. ( Refractive index of water = 1.33 )

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To calculate the real depth of a swimming pool given the apparent depth, we can use the concept of refraction of light. When light passes from one medium to a denser medium, it bends towards the normal. This bending effect causes objects submerged in water to appear closer to the surface than they actually are. The formula to relate these depths is given by:

Real Depth = Apparent Depth × Refractive Index

Given the problem:

• Apparent Depth = 10 cm
• Refractive Index of water = 1.33

Using the formula:

Real Depth = 10 cm × 1.33

Calculating the above:

• Real Depth = 13.3 cm

Therefore, the depth of the swimming pool is 13.3cm.

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.

A practical application of total internal reflection is found in 

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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.

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.

Calculate the upthrust on a spherical ball of volume 4.2 x 10−4 ${}^{-4}$m3 ${}^3$ when totally immersed in a liquid of density 1028kgm−3

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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

An accumulator is 90% efficient. If it gives out 2700J of energy while discharging, how much energy does it take in?

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In order to find out how much energy the accumulator takes in, given that it is 90% efficient and gives out 2700J of energy, we can use the formula for efficiency:

Efficiency = (Useful Energy Output / Total Energy Input) × 100%

Given:

Efficiency = 90%

Useful Energy Output = 2700J

We need to calculate the Total Energy Input (how much energy the accumulator takes in). Rearranging the formula to solve for Total Energy Input, we get:

Total Energy Input = Useful Energy Output / Efficiency

Substitute the known values:

Total Energy Input = 2700J / 0.9

Calculate the input:

Total Energy Input = 3000J

Therefore, the accumulator takes in 3000J of energy.

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.

The part of the inner ear that is responsible for hearing is

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The part of the inner ear that is responsible for hearing is the cochlea.

The inner ear is a complex structure, and each of its components serves different functions. Let me break it down further:

• Cochlea: This is a spiral-shaped, fluid-filled structure that resembles a snail shell. It is the main organ responsible for hearing. Sound waves enter the ear, travel through the ear canal, and cause the eardrum to vibrate. These vibrations are then transmitted to the cochlea through tiny bones in the middle ear. Inside the cochlea, these vibrations create waves in the fluid, stimulating tiny hair cells. The movement of these hair cells converts the sound waves into electrical signals, which are sent to the brain through the auditory nerve, allowing us to perceive sound.


• Sacculus and Utriculus: These structures primarily deal with balance rather than hearing. They are part of the vestibular system, which helps the body maintain its balance and spatial orientation.


• Ampullae: These are located in the semicircular canals of the inner ear and also play a role in balance. They contain sensory hair cells that detect rotational movement of the head.

Thus, the cochlea is the crucial component of the inner ear responsible for converting sound vibrations into nerve signals, making it central to the process of hearing.

A blacksmith heated a metal whose cubic expansivity  is 3.9 x 10−6 ${}^{-6}$K−1 ${}^{-1}$. Calculate the area expansivity.

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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}**.

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 process by which plants loss water to the atmosphere is

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

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

Here's a simple breakdown of how transpiration works:

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

Transpiration is crucial for a number of reasons:

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

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

A hydrometer of mass y kg and volume 2y x 10−5 ${}^{-5}$m3 ${}^3$ floats in a fluid with 20% of its volume above the fluid, what is the density of the fluid?

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

Step 1: Understand the volume submerged

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

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

Step 2: Apply the principle of floatation

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

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

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

According to the principle of floatation:

y x g = ρ_fluid x 1.6y x 10^-5 m³ x g

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

y = ρ_fluid x 1.6y x 10^-5

Step 3: Solving for the density of the fluid

ρ_fluid = y / (1.6y x 10^-5)

The y on both numerator and denominator cancels out:

ρ_fluid = 1 / (1.6 x 10^-5)

ρ_fluid = 6.25 x 10⁴ kg/m³

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

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%.

In a solar panel, solar beam is concentrated by using 

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In a solar panel system, the type of mirror used to concentrate solar beams is the Concave Mirror.

Explanation:

A concave mirror is a type of mirror that curves inward, like the inside of a bowl. This shape is very effective at focusing light. When sunlight hits a concave mirror, the mirror's shape causes the light beams to converge, or come together, at a single point known as the focus. This concentrated light can then be used to generate heat or electricity more efficiently.

Why not the others?

A convex mirror curves outward and disperses light beams rather than concentrating them.

A plane mirror has a flat surface and reflects light at the same angle it receives it, meaning it doesn't concentrate the beams.

A triangular mirror is not typically used in solar applications for concentrating light as its shape is not conducive to focusing beams effectively.

Therefore, a concave mirror is best suited for concentrating solar beams in solar panel systems.

I clear  II sharp  III poor IV dark

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

Bayanin Amsa

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.)

A rectifier is a device that changes 

Bayanin Amsa

A rectifier is a device that changes alternating current (A.C) to direct current (D.C). Alternating current is the type of electrical current that changes direction periodically, while direct current flows in a single, constant direction.

Rectifiers are essential in numerous electrical devices, particularly those that require a stable and consistent power supply. For example, most electronic devices like mobile phone chargers, laptop adapters, and televisions operate on D.C. power, and rectifiers convert the household A.C. power supply to D.C. so that these devices can function properly.

In summary, a rectifier converts A.C., which is alternating power supply, into D.C., which is a steady flow of electricity in one direction, making it usable for electronic devices and various applications that require direct current.

The major building block of an organism is...

Bayanin Amsa

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

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

Here's why Carbon is indispensable:

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

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

The energy stored in the above capacitor is 

Bayanin Amsa

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

Bayanin Amsa

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.

The formation of cilia and flagella in living cells is carried out with the help of

Bayanin Amsa

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.

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.

Bayanin Amsa

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.

The degree of precision of a vernier caliper is 

Bayanin Amsa

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

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

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

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

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

Which of these gas laws is equivalent to workdone

Bayanin Amsa

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

Let's consider the given gas laws:

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

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

What is the inductance reactance of a coil of 7H when connected to a 50Hz a.c circuit?

Bayanin Amsa

To determine the inductive reactance of a coil, we use the formula:

Inductive Reactance (X_L) = 2πfL

Where:

• X_L is the inductive reactance, measured in ohms (Ω)
• π is a constant approximately equal to 3.14159
• f is the frequency of the AC source, measured in hertz (Hz)
• L is the inductance of the coil, measured in henrys (H)

Given:

• Inductance (L) = 7 H
• Frequency (f) = 50 Hz

Substituting the given values into the formula:

X_L = 2 × π × 50 × 7

Calculating this:

X_L = 2 × 3.14159 × 50 × 7

X_L ≈ 2 × 3.14159 × 350

X_L ≈ 2 × 1099.557

X_L ≈ 2199.114

Therefore, the inductive reactance of the coil is approximately 2200Ω.

A red shirt under a red light appears pale because red

Bayanin Amsa

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.

A force of 10N extends a spring of natural length 1m by 0.02m, calculate the length of the spring when the applied force is 40N.

Bayanin Amsa

To solve this problem, we will use Hooke's Law. Hooke's Law states that the force needed to extend or compress a spring by some distance is proportional to that distance. Mathematically, it is represented as:

F = k * x

where:

• F is the force applied to the spring.
• k is the spring constant.
• x is the extension or compression of the spring from its natural length.

Firstly, we need to find the spring constant k. We know that a force of 10N extends the spring by 0.02m. Therefore, using Hooke's Law:

10N = k * 0.02m

From this, we can solve for k:

k = 10N / 0.02m = 500N/m

Now that we have determined the spring constant, let's calculate the extension caused by a force of 40N:

Using Hooke's Law again:

F = k * x

40N = 500N/m * x

Solving for x:

x = 40N / 500N/m = 0.08m

This means that the spring is extended by 0.08m when a force of 40N is applied. Therefore, the length of the spring (natural length plus extension) becomes:

1.00m + 0.08m = 1.08m

Thus, the **length** of the spring when the applied force is 40N is 1.08m.