JAMB UTME - Physics - 2024

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.

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 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.

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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.

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 unit of impedance is 

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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 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.

The energy stored in the above capacitor is 

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

Where C = 2F, q = 3C

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

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.

An example of a non-rechargeable cell is 

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

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

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

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

The efficiency of a cell with internal resistance of 2Ω $\mathrm{\Omega }$ supply current to a 6Ω $\mathrm{\Omega }$ resistor is 

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

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

Let's break it down step by step:

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

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

The value of R in the above circuit to make the galvanometer measure 2A is 

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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

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.

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.

The velocity ratio of an inclined plane at 60º to the horizontal is 

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The concept of an inclined plane is all about simplifying the forces involved in moving or holding a load. The **velocity ratio (VR)** for an inclined plane is defined as the ratio of the distance moved by the effort to the distance moved by the load. This can also be expressed in terms of the lengths involved in the triangle made by the inclined plane.

For an inclined plane placed at an angle **θ** to the horizontal, the velocity ratio is given by the formula:

VR = 1/sin(θ)

Given that the inclined plane is at an angle of **60º**:

First, find the sine of 60º:

sin(60º) = √3/2 (approximately 0.866)

Now, substitute this value into the formula for VR:

VR = 1/sin(60º) ≈ 1/0.866 ≈ 1.155

The **velocity ratio** for an inclined plane at **60º** to the horizontal is **approximately 1.155**.

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).

Use the diagram above to answer the question that follows

The diagram above is

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

Main Parts of the Urinary System:

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

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

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

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

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

The energy in a moving car is an example of 

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The energy in a moving car is an example of kinetic energy.

To explain simply, **energy** is the ability to do **work** or cause **change**. There are different forms of energy, and **kinetic energy** is one of them. It is defined as the energy possessed by an object due to its motion.

When a car is moving, it possesses **kinetic energy** because its components are in **motion**. This motion energy allows the car to do tasks, such as transporting people or goods from one place to another. The faster the car moves, the greater its **kinetic energy**, and thus it can make a larger impact or do more work.

In contrast, energy forms like **mechanical energy** is a combination of both kinetic and potential energy; **electrical energy** is associated with electrical charge movement, while **potential energy** is related to the position or condition of an object (like a car parked on a hill). Therefore, the specific type of energy from a moving car is **kinetic energy**.

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.

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 capacitance of a capacitor, C, is inversely proportional to

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The capacitance of a capacitor is primarily determined by three key factors: the area of the plates, the distance between the plates, and the dielectric material used between the plates.

Capacitance (C) is calculated using the formula:

\(C = \frac{\varepsilon A}{d}\)

Where:

• A is the area of one of the plates.
• d is the distance between the two plates.
• &varepsilon is the permittivity of the dielectric substance between the plates.

Let's analyze the relationship:

• The area of the plates (A): The larger the area, the greater the capacitance. This means capacitance is directly proportional to the area.
• The distance between the plates (d): The greater the distance, the lower the capacitance. Therefore, capacitance is inversely proportional to the distance between the plates.
• The dielectric substance: Different materials have different permittivity values. The capacitance is directly proportional to the permittivity of the dielectric substance.
• The direction of the plate has no effect on the capacitance.

In summary, the capacitance of a capacitor is inversely proportional to the distance between the plates. Hence, you increase capacitance by decreasing the distance between the plates.

The dimension of power is 

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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

When a cell of e.m.f 3.06V is connected, the balance of a potentiometer is 75cm, Calculate the new balance of a cell of e.m.f  2.295V

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

Let's denote:

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

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

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

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

The basic relationship for a potentiometer is given by:

\( V_1 / V_2 = l_1 / l_2 \)

Substituting the given values:

\( 3.06 / 2.295 = 75 / l_2 \)

We need to solve for \( l_2 \):

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

Now, calculating the above expression:

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

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

Infra-red thermometers work by detecting the 

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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.

The stress experienced by a wire of diameter 

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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.

In a Hare's apparatus, the height of water and a liquid X are 0.3m and 0.5m respectively. The relative density of x is?

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For Hare's apparatus

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

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

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

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

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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.

The friction due to air mass can be reduced by 

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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.

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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.

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.

A medium texture soil with high organic matter is

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A medium texture soil with high organic matter is best described as loamy soil. Here's why:

Loamy soil is a type of soil that is characterized by a balanced mixture of sand, silt, and clay particles. Because of this blend, loamy soil is not too coarse like sandy soil, nor is it too compact and dense like clay soil, making it a medium texture.

Moreover, loamy soil is renowned for its high organic matter content. This means that it contains a significant amount of decomposed plant and animal residues, which enrich the soil and provide essential nutrients for plant growth. This high organic content enhances the soil's fertility and structure, enabling it to retain moisture yet drain well, making it ideal for farming and gardening.

In conclusion, due to its balanced texture and richness in organic matter, loamy soil is the best fit for a medium-textured soil with high organic matter.

The tangential force acting on an object that opposes it from sliding freely on the adjacent surface is called

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The tangential force acting on an object that opposes it from sliding freely on the adjacent surface is called the friction force.

Let me explain each of the options to clarify why friction force is the correct answer:

• Normal force: This is the force exerted by a surface perpendicular (at a right angle) to the object resting on it. It supports the weight of the object, stopping it from passing through the surface. It is not tangential and does not oppose sliding; rather, it acts perpendicular to the surface.
• Friction force: This is the force that acts parallel to the surface contact between two objects or surfaces. It arises when one object tries to move over another. The friction force acts to oppose that movement, providing the necessary resistance to prevent sliding.
• Weight: This is the gravitational force acting downwards due to the mass of an object. It does not act tangentially on the surface but directly downwards towards the center of the Earth.
• Upthrust: Also known as buoyant force, this is the upwards force experienced by an object when it is immersed in a fluid (liquid or gas). It is responsible for the object floating or being pushed up, and is not related to tangential force or friction.

In summary, friction force is the force that acts to oppose sliding between surfaces in contact and acts tangentially, making it the correct answer.

The major building block of an organism is...

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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.

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?

Maelezo ya Majibu

By crossing  Rr  x  rr

We obtain  Rr , rr , rr , Rr

⇒ 50% = 12

A red shirt under a red light appears pale because red

Maelezo ya Majibu

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 ${}^{-1}$]

Maelezo ya Majibu

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.

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

Maelezo ya Majibu

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.

The dimension of young's modulus,E is given by 

Maelezo ya Majibu

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

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

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

Stress = Force / Area

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

The dimension of area is length × length = L².

Therefore, the dimension of stress is:

Stress = (MLT^-2) / (L²) = ML^-1T^-2

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

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

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

ML^-1T^-2

Using the diagram above, the effective force pushing it forward at an angle 60º is 

Maelezo ya Majibu

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.

A thick glass tumbler cracks when boiling water is poured into it because

Maelezo ya Majibu

When boiling water is poured into a thick glass tumbler, the inner surface of the glass is suddenly exposed to a much higher temperature compared to the outer surface. Glass is a poor conductor of heat, which means it does not transfer heat quickly. As a result, the inside of the tumbler becomes hot and attempts to **expand quickly**, while the outside remains cooler and does not expand at the same rate.

**This uneven expansion** creates tension between the inner and outer layers of the glass. The inner surface tries to expand but is constrained by the cooler, rigid outer surface, which isn't expanding as much or as quickly. This stress and tension can lead to cracking.

Therefore, the correct reason a thick glass tumbler cracks when boiling water is poured into it is because **the inside expands more rapidly than the outside.**

Maelezo ya Majibu

When you insert a sheet of an insulating material between the plates of an air capacitor, the capacitance will increase.

Here's why:

• Capacitance is a measure of a capacitor's ability to store charge per unit voltage across its plates.
• The formula for capacitance (C) is:

C = ε₀ * (εr) * (A/d)

• Where:
  • ε₀ is the permittivity of free space (a constant).
  • εr is the relative permittivity (also known as the dielectric constant) of the material between the plates.
  • A is the area of one of the plates.
  • d is the separation between the plates.
• When an insulating material (also known as a dielectric) is inserted between the plates, its εr is greater than that of air (which is 1).
• This increases the overall capacitance of the capacitor since the product of ε₀ and εr is larger than ε₀ alone.

Therefore, inserting an insulating material as a dielectric enhances the capacitor's ability to store charge, ultimately resulting in an increase in capacitance.