A solid 66 kg cylinder has a radius of 0.10 m. What minimum work is required to get the cylinder rolling without slipping at a rotational speed of 20 s−1?

The minimum mass of hydrogen gas required is  641.64 grams.

Hydrogenation is a chemical reaction between molecular hydrogen and another compound or element, usually in the presence of a catalyst such as nickel, palladium, or platinum. This process is commonly used to reduce or saturate organic compounds.

2-butene = C4H8

maximum hydrogenation = C4H10

then we require 2 H, that is 1 mol ofH2

2-butene +H2 --> butane

MW of butene = 56.106

mol of butene = mass/MW = 18000/56.106 = 320.8213mol

then we require 1:1 ratio

320.8213 mol of H2

mass = mol*MW = 320.8213*2 = 641.64 g of H2

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In a photoelectric effect experiment at a frequency above the cut off frequency the number of electrons ejected is proportional to the number of photons that hit the sample per second.

The photoelectric current is measured in relation to the intensity of the incident radiation at a specific frequency and potential between the metal plate and collector. It demonstrates that incident radiation intensity and photoelectric current are inversely correlated. The photoelectric current shows how many photoelectrons are released each second.

The idea of light as a wave cannot be used to explain the photoelectric effect. However, the particle nature of light, which can be visualized as a stream of electromagnetic energy-containing particles, can provide an explanation for this phenomenon. These particles of light are called as photons.

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Based on the provided information, it can be predicted that the circadian rhythms for the astronauts would be drift toward a slightly longer cycle. (Option A)

A circadian rhythm, also known as circadian cycle, refers to a natural, internal process that regulates the sleep–wake cycle and is repeated roughly every 24 hours. It can refer to any process that originates within an organism and responds to the environment. These natural processes respond primarily to light and dark and affect most living things. A zeitgeber refers to any external cue or environmental cue that synchronizes an organism's biological rhythms such as circadian rhythm, usually naturally occurring and serving to entrain to the Earth's 24-hour light/dark and 12-month cycles. Circadian rhythms that are expressed in the absence of any 24-hour signals from the external environment are called free running, which are slightly longer cycle than usual. Hence, in the absence of external cue, the circadian rhythms for the astronauts would drift toward a slightly longer cycle.

Note: The question is incomplete as it is missing options which are a. They would drift toward a slightly longer cycle. b. They would become sporadic and show no definite pattern. c. They would stay synchronized with a 24-hour cycle. d. They would become synchronized with the light pattern around Mars.

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Due to the dependence of gas volume on temperature and pressure, gases are not commercially marketed by volume.

The space occupied by the gaseous particles under typical pressure and temperature circumstances is referred to as the volume of gas.

It has the symbol "V."

The symbol for volume in the SI is "litres," or "L".

When the gas is at normal temperature, a mole has a volume of 24 m3, or 24 000 cm3.

The molar volume of a gas is this quantity.

The body of lecture 18 is included in the material that follows. The Gas Laws, including the Ideal and Combined Gas Laws, as well as Charles', Boyle's, Avagadro's, and Gay Lussacs', are covered in this lecture.

The four primary characteristics of gases are related to one another by four main principles.

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The relationship between light frequency and wavelength is inverse. No matter how powerful, yellow light simply lacks the necessary energy per photon to excite any electron sufficiently to liberate it from the metal.

Since yellow and red light have longer wavelengths than green light and lower frequencies than green light, when yellow or red light strikes metal, no photoelectrons are produced. Yellow light makes a green thing appear green. Under cyan light, a red object seems to be black. Cyan light makes a blue thing appear blue. Red and green light are also present in yellow light, which likewise reflects both colors.

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The reversible process is the one that can be reverted back and an reversible process is the one that cannot back towards initial state.

In the field of thermodynamics the processes are defined as reversible or Irreversible.

Practically speaking, process is that one which occurs slowly slowly and reversible process is the one which occurs suddenly. Irreversible processes cannot be reverted back and reversible processes can be reverted back.

An example of reversible process is the change of state of water and an example of Irreversible process is the change in colour often iodine containing sample at the addition of starch.

We study the reversible processes in order to understand the thermodynamical perspective of the process and the energy change associated with the system.

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An Electromagnet can be best described as a temporary magnet.

An Electromagnet is called a non permanent magnet or a temporary magnet.

It is called so because of its property of getting magnetized and demagnetized.

Electromagnet behaves like a magnet only in the presence of the electric current their magnetic properties disappear as soon as the current in them stops.

Electromagnet are used in various devices like headphones and loudspeakers,  induction cookers, data storage devices MRI machines and magnetic locks.

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The current of the resistor 2 from a circuit of four resistors is calculated to be 2 A.

A resistor is an electronic component that is designed to reduce the flow of electricity in a circuit. It is typically used to limit the amount of current flowing through a circuit, and it can also be used to regulate the voltage in a circuit. Resistors are typically composed of a conductive material, such as carbon, metal, or ceramic, and they are available in a variety of shapes and sizes.

I₂ is found using Ohm's Law. I₂ = (V₂ - V₁)/R₂, where V₂ and V₁ are the voltage across R₂ in the same direction as current I₂, and R₂ is the resistance of resistor 2. Substituting the given values gives

I₂ = (12 - 4)/200 = 8/200 = 0.04 A = 2 A.

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The differential gravitational force that one body exerts on opposite sides of another body is called gravitational torque.

Gravitational torque is a measure of the rotational force exerted by a gravitational field on an object. It is equal to the product of the gravitational force and the lever arm (the distance between the point of application of the force and the axis of rotation).

For example, consider a satellite orbiting a planet. The satellite experiences a gravitational force from the planet, which acts to pull it toward the planet. However, this gravitational force is not uniform over the surface of the satellite.

The side of the satellite closest to the planet experiences a stronger gravitational force than the side furthest from the planet. This differential gravitational force creates a gravitational torque on the satellite, which causes it to rotate about its axis.

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QCS=QC1+QC2+QC3. When we cancel the charge Q, we get the formula 1CS=1C1+1C2+1C3, which contains the equivalent capacitance, CS, of three capacitors connected in series.

Any number of capacitors in a series network can be included in the generalization of this formula. The polarity of an AC current alternates between positive and negative on a regular basis. As the polarity of the current changes, capacitors are continuously charged and discharged, allowing AC current to pass through. A capacitor, as contrast to a battery, is a component of a circuit that temporarily stores electrical energy by dispersing charged particles between (often two) plates to produce a potential difference. A capacitor may charge more fast than a battery and can discharge its whole stored energy in a matter of seconds.

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Yes, it is possible for a particle to be found within the barrier while undergoing tunneling.

This phenomenon is known as quantum tunneling. Quantum tunneling occurs when a particle tunnels through a barrier that is normally too high to be crossed by the particle's kinetic energy. This occurs due to the wave-like nature of particles, which allows them to go through barriers that are otherwise impenetrable.

The wave-like nature of particles allows them to penetrate the barrier, often with a probability greater than zero. This phenomenon is used in many applications in science and technology, such as in quantum computing, where quantum tunneling is used to tunnel qubits through the barrier of a logic gate.

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The maximum height reached by the ball thrown upwards with kinetic and potential energies specified is nearly 20 m.

Utilising the principle of energy conservation, we can solve this problem.

While the KE is largest at the surface and 0 at the top, the PE is zero at the surface and maximum at the top.

From the above data,

PE = mgh = 50 J ----(1)

m g* 10 = 50

m* g = 50/10

m* g = 5

The total energy at that point = PE + KE = 50 + 50 = 100 J

The PE will therefore be 100 J at the highest point.

m g H = 100 J , H is the needed height

Using the above-mentioned value of m* g, we have

H = 100/5

H = 20 m

So, the maximum height reached by the ball is 20 m.

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A particle has potential energy U(x)=x+sin ((2 rad/m) x) as a particle moves over the range 0 m \leq pi m The equilibrium positions in this range will be a=(pi/3), x=(2pi/3).

Potential energy and equilibrium are related in that the body's potential energy is lower in such an equilibrium.

In this case, the state generates a force that does not resist the displacement when a little distance displaces the body.

When the body shifts from its initial posture in such a situation.

Potential energy is a form of stored energy that is dependent on the relationship between different system components.

When a spring is squeezed or extended, its potential energy increases.

If a steel ball is lifted above the ground as opposed to falling to the ground, it has higher potential energy.

A particle has potential energy u(x)=x+sin 2 x

Now differentiating with respect to x.

[tex]\Rightarrow \frac{d u}{d x}=1+2 \cos 2 x \\\\[/tex]

for equilibrium point  

[tex]\frac{d u}{d x}=0 \\\\\Rightarrow (1+2 \cos 2 x)=0 \\\\\Rightarrow \cos 2 x=-\frac{1}{2}[/tex]

[tex]$$\begin{aligned} \Rightarrow \cos 2 x=\cos \left(\pi-\frac{\pi}{3}\right) \\\Rightarrow 2 x=\frac{2 \pi}{3} \Rightarrow x=\frac{\pi}{3} \\\cos 2 x=\cos \left(\pi+\frac{\pi}{3}\right) \\\Rightarrow 2 x=\frac{4 \pi}{3} \Rightarrow x=\frac{2 \pi}{3}\end{aligned}$$[/tex]

Hence, a=(Pi/3), x=(2pi/3) is correct,

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The correct questions should be:

A particle has potential energy U(x)=x+sin ((2 rad/m) x) as a particle moves over the range 0 m [tex]\leq[/tex] pi m.

Where are the equilibrium positions in this range?

Check all that apply.

x=pi/6 m

x=pi m

x=(pi/2) m

x=(pi/3) m

x=(2/3) pi m

Archimedes, on the other hand, states that the amount of water (equal to 16000N) will be reduced by 3% since seawater has a specific gravity that is roughly 3% higher than freshwater.

900 000 metric tonnes of water are removed by it. 300,000 elephants would be the equal. The air inside a ship is significantly less dense than water. It floats because of that. The key concept is that the body "floats," which is the underlying presumption in this situation. According to the Archimedes Principle, for this body, vessel, or whatever it may be to float, it must move an equal amount of water.

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The work that has been done by air resistance during this time is 55800 k m²/s².

To determine the work done by air resistance during the skydiver's fall, we can use the equation:

W = F × d

where W is the work, F is the force of air resistance, and d is the distance traveled.

The force of air resistance on the skydiver is given by the equation:

F = k × v²

where k is the drag coefficient, which is a measure of the resistance of the air to the movement of the object, and v is the velocity of the skydiver.

To determine the work done by air resistance, we need to determine the distance traveled by the skydiver and the force of air resistance at each point in her fall. The skydiver falls from an altitude of 1500 m to an altitude of 425 m, a distance of 1075 m.

At an altitude of 1500 m, the skydiver is falling at a terminal velocity of 52 m/s. Plugging these values into the equation for the force of air resistance gives us:

F = k × v² = k × (52 m/s)²

To determine the work done by air resistance at this point in the skydiver's fall, we can plug the value of F and the distance traveled into the equation for work:

W = F × d = (k × (52 m/s)²) × 1075 m = 55800 k m²/s²

The work done by air resistance at this point in the skydiver's fall is 55800 k m²/s².

At an altitude of 425 m, the skydiver is falling at a terminal velocity of 52 m/s. Plugging these values into the equation for the force of air resistance gives us:

F = k × v² = k × (52 m/s)²

To determine the work done by air resistance at this point in the skydiver's fall, we can plug the value of F and the distance traveled into the equation for work:

W = F × d = (k × (52 m/s)²) × 1075 m = 55800 k m²/s²

The work done by air resistance at this point in the skydiver's fall is 55800 k m²/s².

To determine the total work done by air resistance during the skydiver's fall, we can add the work done at each point in the fall:

W_total = W_1500m + W_425m = 55800 k m²/s² + 55800 k m²/s² = 111600 k m²/s²

The total work done by air resistance during the skydiver's fall is 111600 k m²/s².

Note that this calculation assumes that the drag coefficient k is constant throughout the skydiver's fall. If the drag coefficient changes during the fall (for example, if the skydiver deploys a parachute), additional calculations will be needed to determine the total work done by air resistance.

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The velocity is 6.52 m/s, and the velocity in component vector form is vcos.

"The pace at which an item changes its location" is described by a vector number known as velocity. Consider someone walking swiftly, one step ahead, one step back, and beginning each stride in the same place. Velocity is measured as a vector quantity. As a result, velocity is aware of direction. When calculating an object's velocity, the direction must be considered. A speed of 55 miles per hour does not provide enough information. To accurately represent the velocity of an object, the direction must be taken into account. Simply simply, the direction of the velocity vector describes the object's motion.

velocity in vector form

= vcos vector form

=18cos53 v

=16.52 m/s

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The pressure exerted by the person is found to be  3 N/cm².

The physical force applied to an object is referred to as pressure. It is the force that is dispersed over a unit area per unit of time perpendicular to the surface of an object. The formula used to calculate pressure is P=F/A where P is the pressure, F is force, and A is the area.

Given the force is 600 N and the area is 200 cm².

Then, the pressure is calculated as follows,

P = F/A

P = 600 N/200 cm²

P = 3 N/cm²

The answer is 3 N/cm².

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A ray diagram is a tool used by physicists to explain or predict the behavior of beams of light as they pass through objects such as glass blocks or lenses.

A ray diagram is a diagram that strains the route that light takes so as for a person to view a factor in the photograph of an object. In the diagram, rays are drawn for the incident ray and the meditated ray.

Ray diagrams help us hint at the course of the light for the man or woman to view a point on the photograph of an object. The Ray diagram makes use of lines with arrows to symbolize the incident and reflected ray. It also helps us trace the direction in which the mild travels.

A mild ray is a line that is perpendicular to the mild's wavefronts; its tangent is collinear with the wave vector. light rays in homogeneous media are instant. They bend at the interface between two distinctive media and may be curved in a medium wherein the refractive index modifications.

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The spring's compressed length before halting frictionless  is therefore 0.40m.

(m2) (s–1) (s–1)

2 N kg m s2 (kg m-1) Take a test. 5. Scalars: mass, distance, and the labour required to extend the spring out of its equilibrium position are stored as elastic potential energy; vectors: displacement, velocity, acceleration, and force; The work required to extend the spring away from equilibrium is equal to the change in kinetic energy of the box. The spring is extended until the box stops moving; hence, the box's final kinetic energy is zero. The elastic potential energy used to compress the spring can be equated to the initial kinetic energy of the box to find the expression to compute the compressed distance using the law of conservation of energy frictionless.

The force required to create

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Workers expect inflation to fall from 4% to 1% next year. as a result, this should Shift the short-run aggregate supply curve to the right.

Option (B) is the correct choice.

The SRAS curve demonstrates that the amount of real GDP that will be generated in an economy grows as the price level rises as you move along the SRAS.

A movement to the right indicates an increase in the SRAS.

In the near run, decreasing wages, increasing the stock of physical resources, lowering inflation, and advances in technology would move the aggregate supply curve to the right.

The short term aggregate supply will move to SRAS2 on the left if businesses and labour anticipate price increases.

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The complete question may be:

Workers expect inflation to fall from 4% to 1% next year. As a result, this should

A) shift the short-run aggregate supply curve to the left.

B) shift the short-run aggregate supply curve to the right.

C) move the economy up along a stationary short-run aggregate supply curve.

D) move the economy down along a stationary short-run aggregate supply curve.

The ratio of their radius [tex]\frac{r_A}{r_B}[/tex] = 1/4 .

Escape velocity is the speed at which the sum of kinetic and gravitational potential energy of an object equals 0.

[tex]v_e_s_c[/tex] = [tex]\sqrt{\frac{2GM}{r} }[/tex]

where [tex]v_e_s_c[/tex] is escape velocity G is universal gravitational constant and M is mass of the object and r is distance of object.

let [tex]v_A[/tex] and [tex]v_B[/tex] be the escape velocity of the of planet A and planet B

so [tex]v_A = \sqrt{\frac{2GM}{r_A} }[/tex]  -----(i)

and [tex]v_B=\sqrt{\frac{2GM}{r_B} }[/tex]   ----(ii)

given [tex]\frac{v_A}{v_B}[/tex] = 2

=>  [tex]\frac{v_A^2}{v_B^2}[/tex]  = 4

=> [tex]\frac{r_B}{r_A}[/tex] = 4

so [tex]\frac{r_A}{r_B}[/tex]  = 1/4

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The tension in the cord when the object is at the lowest point of its swing is 3 mg.

The complete question is in the attachment. The small object moves from point A to point B. According to the law of conservation of energy

KE a + PE a = KE b + PE b

0.5 m₁ v₁² + m₁ g h₁ + 0.5 m₂ v₂² + m g h₂

(0.5 × m × 0²) + (m × g × r) = (0.5 × m × v₂²) + (m × g × 0)

0 + mgr = 0.5 mv₂² + 0

v₂² = 2gr

[tex]v_2 \:=\: \sqrt{2gr}[/tex]

The object moves according to uniform circular motion. There is the centripetal force that works in the system. The forces acting on the object are weight force and tension force. According to Newton's second law for circular motion

Fc = mα

T - w = mv²/R

T - mg = mv²/R

T = mv₂²/r + mg

T = (m × 2gr ÷ r) + mg

T = 2mg + mg

T = 3 mg

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Answer:

10.347

Explanation:

The magnitude of the radial acceleration of the car 10m/sec²

Given Velocity v = 50m/sec

Diameter D = 500m

Radius r = 250m

Acceleration a = [tex]v^{2}[/tex]/r = 2500/250 = 10m/sec²

The rate of change in an object's velocity with respect to time is known as acceleration in mechanics. In vector quantities, accelerations exist (in that they have magnitude and direction). [1] [2] The direction of the net force that is acting on an object determines its acceleration. Newton's Second Law[3] states that the sum of the effects of two causes determines the size of an object's acceleration:

The net balance of all external forces acting on that thing — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is built — magnitude is inversely proportional to the object's mass.

Meter per Second Squared (m/s2) is the SI unit for acceleration. displaystyle, mathrm, tfrac, ms2, and

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The engine's thermal efficiency if the gas volume is halved during the adiabatic compression is 24%

Any thermal cycle's efficiency is expressed as

[tex]$$\eta=1-\frac{T_c}{T_h}$$[/tex]

We know that for an adiabatic process

[tex]$$p V^\gamma=\text { const }$$[/tex]

From the first law, we may express pressure in terms of temperature.

[tex]$$\begin{aligned}& p V=n R T \\& \Rightarrow p=\frac{n R T}{V} \propto T V^{-1}\end{aligned}$$[/tex]

As a result, we have the following for an adiabatic process:

[tex]$$T V^{\gamma-1}=\text { const } .$$[/tex]

Let us now calculate a temperature ratio based on the volume ratio:

[tex]$$T_c V_c^{V-1}=T_h V_h^{\gamma-1}$$[/tex]

We get that

[tex]\frac{T_c}{T_h}=\frac{V_h^{\gamma-1}}{V_c^{\gamma-1}}=\left(\frac{V_h}{V_c}\right)^{\gamma-1}$$[/tex]

The Efficiency will be,

[tex]$$\begin{array}{r}\eta=1-\left(\frac{V_h}{V_c}\right)^{\gamma-1} \\\eta=1-\left(\frac{1}{2}\right)^{1.40-1}=24 \% .\end{array}$$[/tex]

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If an object doubles its luminosity in 10 hours, emitting source of light can be about 10 light hours across.

Luminosity, L, is a measure of the total amount of energy radiated by a star or other celestial object per second. This is therefore the power output of a star. A star's power output across all wavelengths is called its bolometric luminosity. A star's luminosity can be determined from two stellar characteristics: size and effective temperature. The difference between luminosity and apparent brightness depends on distance.

Since, the luminosity of the object doubles in 10 hours, emitting source of light can be about 10 light hours across.

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[tex]B_{f}[/tex] = - 4T  is the magnetic field strength on the front surface for the given details  B1 = 2 T, B2 = 2 T .

 In terms of direction, we know that by convention, the flux entering the surface is negative and the flux leaving the surface is positive.

Apply the following formula to all of the box's surfaces:

3T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) =6* [tex]10^{-6}[/tex]T[tex]m^{2}[/tex] on the left surface

3T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = 6* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] for the right surface

-2T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = -4* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] top surface

-1T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = -2* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] bottom surface

-2T(2 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = -2* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] back surface

Assume that the magnetic field strength on the front surface is [tex]B_{f}[/tex]

[tex]B_{f}[/tex]T(1 * [tex]10^{-6}[/tex] [tex]m^{2}[/tex]) = [tex]B_{f}[/tex]* [tex]10^{-6}[/tex] T[tex]m^{2}[/tex] front surface

The net flux through all of the box's surfaces should be zero.

(6T +6T-4T-2T+BfT)([tex]10^{-6}[/tex][tex]m^{2}[/tex]) = 0

When we divide [tex]10^{-6}[/tex][tex]m^{2}[/tex] on both sides, we get:

12T-8T+[tex]B_{f}[/tex]=0

4T+[tex]B_{f}[/tex] = 0

[tex]B_{f}[/tex]= - 4T

On the front surface, the magnetic field strength is [tex]B_{f}[/tex] = - 4T.

Because it is negative, it indicates that the magnetic field is entering the front surface.

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The inductance that must be connected to a capacitor is 5* 10⁻²¹ H.

If f is the frequency and λ is the wavelength of an electromagnetic wave, we know the relation between them as v = f * λ

The frequency is same as the frequency of oscillation of the current in the LC circuit of the generator.

f = 1/(2π* √LC)

where, C is the capacitance

L is the inductance

So, λ/(2π* √LC) = c

Given that, λ = 550* 10⁻⁹ m

C = 17 * 10⁻² F

c is the speed of light

Making L as subject, we have

L = λ²/(4π² C* c²) = (550* 10⁻⁹)² / [4π²(17 * 10⁻²) (3* 10⁸)²] = 5* 10⁻²¹ H

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the wavelength of this electromagnetic radiation is 12.2cm.

Calculation :

The frequency, speed of light, and wavelength are interrelated with each other as:

fλ=c

f is 2.45GHz or 2.45∗10⁹Hz

λ=3∗10⁸/2.45∗10⁹

So, the wavelength of this electromagnetic radiation is 12.2cm.

Wavelength is the distance between identical points (adjacent peaks) in adjacent cycles of a waveform signal propagating in space or along a line. For wireless systems, this length is usually specified in meters (m), centimeters (cm), or millimeters (mm).

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4.23 m is the height the crate can move in 3s.

At t = 0,

force F = 100 N.

the time taken to move upward is 3s

Since at this moment,

2 F = 200 N > W = 20(9.81) = 196.2 N2F=200N>W=20(9.81)=196.2N,

the crate will move at that moment force F is applied. Referring to the Free body diagram of the crate,

[tex]m(v_y)_1 + \sum\int\limits^{t_2}_{t_1} {F_y} \, dt=m(v_y)_2[/tex]

=>  [tex]0+2\int\limits^t_0 {100+5t^2} \, dt-20(9.81)t=20v[/tex]

=>[tex]2(100t+\frac{5}{3} t^3)-196.2t =20v[/tex]

=> v={0.1667[tex]t^3[/tex] + 0.19 t} m/s

The displacement of the crate can be calculated by integrating

ds = v dt with the primary condition s = 0 at t = 0.

[tex]\int\limits^s_o \, ds =\int\limits^t_o {0.1667t^3+0.19t} \, dt[/tex]

=> s={0.04167[tex]t^4[/tex]+0.095[tex]t^3[/tex]}m

At time  t = 3 s,

s=0.04167 ( [tex]3^4[/tex] ) + 0.095 ( [tex]3^3[/tex])

=> s = 4.23 m

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