The shaft has a diameter of 40 mm and is made of steel for which 75 GPa, 250 MPa.
a. Determine the angle of twist of wheel B with respect to wheel A.
b. Determine if yielding occurs using the maximum distortion energy theory

Answer: In hookes law K represents the constant of proportionality, also known as the spring constant. 

Explanation:

The resultant displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C is -0.0012 m.

When a metal is heated, it tends to expand, and when cooled, it tends to contract.

The coefficient of linear expansion for a metal determines how much the metal changes in length per unit of temperature change.

The amount of change in length (L) per unit length (Lo) per unit of temperature change (∆T) is given by

∆L=αL ∆T, where α is the coefficient of linear expansion.

We'll use the following formula to calculate the resulting displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C:

ΔL = LαΔT

where L is the length of the metal rod

α is the coefficient of linear expansion

ΔT is the temperature difference.

Let us first calculate the coefficient of linear expansion for aluminum and steel.

ALUMINUM:α (aluminum) = 24 × 10-6 /°C

STEEL:α (steel) = 12 × 10-6 /°C

Now, let's calculate the change in length of the rods as a result of the temperature change.

ΔLA = αA

LΔT= 24 × 10-6/°C × 1.0 m × (25°C − 15°C)

LΔT= 0.0024 m

ΔLB = αB

LΔT= 12 × 10-6/°C × 1.0 m × (25°C − 15°C)

LΔT= 0.0012 m

Now we may calculate the resultant displacement of the free end of rod B from its present location.

ΔLresultant = ΔLB - ΔLA

ΔLresultant = (0.0012 m) - (0.0024 m)

ΔLresultant = -0.0012 m

Therefore, the resultant displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C is -0.0012 m.

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The correct expression for the natural frequency of oscillation of a stick of length (l) oscillating around one end is given by :[tex]\sqrt{g/l}[/tex].

The correct answer is option A.

To derive this expression, let's go through the calculation:

The restoring force acting on the stick is provided by the gravitational force, which is proportional to the displacement of the stick. The gravitational force is given by F = mg, where m is the mass of the stick and g is the acceleration due to gravity.

For a stick oscillating around one end, the effective length of the pendulum is l. The torque acting on the stick is given by τ = Iα, where I is the moment of inertia of the stick about the pivot point and α is the angular acceleration.

For small angular displacements, we can use the approximation α = θ'', where θ'' is the second derivative of the angular displacement with respect to time.

Using the torque equation, we have Iθ'' = mglθ, where θ represents the angular displacement.

Dividing both sides of the equation by θ and rearranging, we get θ'' + (g/l)θ = 0, which is a differential equation for simple harmonic motion.

The solution to this differential equation is of the form θ = A sin(ωt), where A is the amplitude and ω is the angular frequency.

Comparing this solution to the differential equation, we find that ω² = g/l.

The natural frequency of oscillation is given by f = ω/(2π), so substituting the value of ω, we have f = [tex]\sqrt{(g/l)/(2}[/tex]π).

Therefore, the correct expression for the natural frequency of oscillation is [tex]\sqrt{g/l}[/tex] which corresponds to option A.

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8 μC written in scientific notation is 8 × 10⁻⁶ C.

Scientific notation is a way to express numbers that are either very large or very small in a concise and standardized format. It consists of two parts: a coefficient and a power of 10.

In the case of 8 μC (8 microcoulombs), the prefix "micro" represents a factor of 10⁻⁶ (1 micro = 10⁻⁶)).

So, we can rewrite 8 μC as 8 × 10⁻⁶ C.

The coefficient, in this case, is 8, which is a single-digit number. The power of 10 is -6, indicating that the decimal point needs to be moved 6 places to the left to obtain the actual value.

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What is 8 μC written in scientific notation?

● 8 x 103 C

• 8 × 10-3 C

8 × 106 C

O 8 × 10-6 C

Answer: So, just as the blood enters the blocked portion of the vessel, its speed is approximately 7.31 times its initial speed v0

Explanation: The flow rate of a fluid is given by the equation Q = A * v, where Q is the flow rate, A is the cross-sectional area of the vessel, and v is the speed of the fluid. Since the blood is incompressible, its flow rate must remain constant. Therefore, if the cross-sectional area of the vessel decreases, the speed of the blood must increase to maintain a constant flow rate.

The cross-sectional area of a cylinder is given by the equation A = πr^2, where r is the radius of the cylinder. If the diameter of the vessel decreases by 63.0%, then its radius decreases by 63.0% as well. Therefore, the new radius of the vessel is r_new = r_old * (1 - 0.63) = 0.37 * r_old.

Substituting this into the equation for the cross-sectional area, we get:

A_new = π * (0.37 * r_old)^2

A_new = (0.37^2) * π * r_old^2

A_new = 0.1369 * A_old

Since the flow rate must remain constant, we have:

Q = A_old * v0 = A_new * v_new

Substituting in the values for A_old and A_new, we get:

v_new = (A_old / A_new) * v0

v_new = (1 / 0.1369) * v0

v_new ≈ 7.31 * v0

So, just as the blood enters the blocked portion of the vessel, its speed is approximately 7.31 times its initial speed v0.

Given:A 1-ton object at 1AU from the sun will experience a gravitational force of 6N. Newton’s Law of Universal Gravitation states that the force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically,F ∝ (M1M2/d²)Where,F = Force of gravitational attraction between two objectsM1 = Mass of object 1M2 = Mass of object 2d = Distance between the centers of mass of two objects.Given,Mass of the first object, M1 = 1 tonMass of the second object, M2 = 220 tons Distance of the first object from the sun, d1 = 1 AU

Distance of the second object from the sun, d2 = 2 AUForce experienced by the first object, F1 = 6 NWe can use the formula to calculate the force experienced by the second object.

F1/F2 = (M1/M2) * (d2/d1)²F2 = F1 * (M2/M1) * (d1/d2)²

Putting the values,M1 = 1 ton

M2 = 220 tons

d1 = 1 AUd2 = 2 AUF1 = 6 N

Thus,F2 = 6 N * (220 tons/1 ton) * (1 AU/2 AU)²

F2 = 6 N * 220 * (1/4)

F2 = 330 NAnswer:

Therefore, the 220-ton object would experience a gravitational force of 330 N at a distance of 2 AU from the sun

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Answer:

The Correct answer is A

to the right

Answer:

50 Hz

Explanation:

Frequency is oscillations per second.

50/1 = 50

The name of my community service is “Feed the Homeless”. The aim of this program is to provide nutritious food and basic necessities to the homeless community in my city. The homeless community faces various challenges and difficulties in their everyday life.

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Explanation:

You are given   J    and   kg   and want    J/kg

so

8.2 x 10^7 J / 38.6 kg =~ 2.12 x10^6  J/kg

[tex]{\underline{\tt{Answer 1}}}[/tex]

For a fixed pulley alone, the resistance force is equal to the effort force, and the mechanical advantage is 1. When a movable pulley is added to the fixed pulley, the resistance force is reduced by half, the effort force is reduced, but the distance the effort force must be applied over is doubled. The mechanical advantage for a fixed and movable pulley is 2, and the slope of the line for each pulley represents the mechanical advantage.

[tex]{\underline{\tt{Answer 2}}}[/tex]

The work output for the pulleys is equal to the weight of the object multiplied by the distance it was lifted. The work input is equal to the force applied to the rope multiplied by the distance it was pulled. Since the weight of the object and the force applied to the rope are equal, the work output is equal to the work input. However, the pulleys allow the force to be applied over a greater distance, which means that less force is required to lift the object, but the force must be applied over a longer distance.

[tex]{\underline{\tt{Answer 3}}}[/tex]

Pulleys allow the effort force to be reduced while increasing the effort distance, and they allow the resistance force to be reduced while increasing the resistance distance. The advantages of using pulleys include the ability to lift heavy objects with less effort, the ability to change the direction of the force, and the ability to increase the distance that the force can be applied over.

If a third movable pulley were added to the pulley system, the mechanical advantage would be increased. Specifically, the mechanical advantage would be equal to 3, since the resistance force would be divided by three and the effort force would be equal to one-third of the resistance force.

Answer:

The relationship between the resistance force and the effort force for the fixed pulley alone is that they are equal in magnitude.

Explanation:

The relationship between the resistance force and the effort force for the fixed pulley alone is that they are equal in magnitude. In other words, the effort force needed to lift a certain weight is the same as the weight itself. However, when a movable pulley is added to the fixed pulley, the resistance force is halved compared to the effort force. This means that the effort force required to lift a certain weight is only half of the weight itself. The mechanical advantage of a pulley system can be determined by the slope of the line on a force vs. distance graph. The steeper the slope, the greater the mechanical advantage. In this case, the mechanical advantage is higher for the system with the movable pulley compared to the fixed pulley alone, as the slope is steeper for the former.

The work output relates to the work input for the pulleys based on the principle of work conservation. In an ideal scenario with no energy losses, the work input should be equal to the work output. However, due to friction and other factors, there might be some energy losses in the pulley system, resulting in a slightly lower work output compared to the work input.

Pulleys provide a mechanical advantage by reducing the amount of effort force required to lift a heavy object. As more pulleys are added, the mechanical advantage increases further. With respect to changes in effort force and effort distance compared to resistance force and resistance distance, pulleys allow for a trade-off between the two. By applying a smaller effort force over a longer distance, a greater resistance force can be overcome over a shorter distance. This is advantageous as it enables the lifting of heavy loads with less effort. Adding a third movable pulley would further increase the mechanical advantage, making it easier to lift heavier objects with even less effort force.

Mass over density is a mathematical expression that represents the ratio of mass to density. It is calculated by dividing the mass of an object or substance by its density. Mathematically, it can be represented as:

The equation relating mass (m) and density (ρ) is given by:

m = ρ * V

where:

m is the mass of the object or substance,

ρ is the density of the object or substance, and

V is the volume of the object or substance.

This equation states that the mass of an object is equal to the product of its density and volume. It shows that mass is directly proportional to density and volume.

To create a resonant circuit with a 1H inductor at 100Hz, a capacitance of 0.0159 microfarads (uF) should be used.

1. Determine the frequency of the resonant circuit, which is given as 100Hz.

2. The formula for calculating the resonant frequency of an LC circuit is: f = 1 / (2π√(LC)), where f is the frequency, L is the inductance, and C is the capacitance.

3. Rearrange the formula to solve for C: C = 1 / (4π²f²L).

4. Substitute the given values into the formula: C = 1 / (4π² * 100² * 1).

5. Calculate the capacitance using a calculator or mathematical software: C ≈ 1.5915 × 10^(-5) farads.

6. Convert the capacitance to microfarads for convenience: 1 farad = 1,000,000 microfarads, so C ≈ 15.915 uF.

7. Round the capacitance to an appropriate number of significant figures, resulting in a capacitance of 0.0159 uF (or 15.9 nF).

Therefore, to produce a resonant circuit with a 1H inductor at 100Hz, a capacitance of approximately 0.0159 microfarads (uF) should be used.

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Answer:

Explanation:

The three physical characteristics of a sound stimulus and their corresponding perceptual characteristics are as follows:

1. Frequency: Frequency refers to the number of vibrations or cycles per second that occur in a sound wave. It is measured in hertz (Hz). Frequency gives rise to the perception of pitch. Pitch is the subjective perception of how high or low a sound is. Higher frequencies are perceived as higher pitches, while lower frequencies are perceived as lower pitches. For example, a sound wave with a higher frequency would be perceived as a higher-pitched sound, like a whistle, whereas a sound wave with a lower frequency would be perceived as a lower-pitched sound, like a deep bass note.

2. Amplitude: Amplitude is the magnitude or intensity of a sound wave and is usually measured in decibels (dB). It represents the amount of energy carried by the sound wave. Amplitude gives rise to the perception of loudness. Loudness is the subjective perception of the strength or intensity of a sound. Greater amplitudes are perceived as louder sounds, while smaller amplitudes are perceived as quieter sounds. For instance, a sound wave with a higher amplitude would be perceived as a louder sound, like a thunderclap, whereas a sound wave with a lower amplitude would be perceived as a softer sound, like a whisper.

3. Timbre: Timbre refers to the quality or tone color of a sound. It is the characteristic that allows us to distinguish between sounds with the same pitch and loudness. Timbre is influenced by the complex combination of different frequencies, amplitudes, and waveforms present in a sound wave. It gives rise to the perception of the unique "sound signature" of an instrument or voice. For example, a guitar and a piano playing the same note at the same loudness would still sound different due to their distinct timbres. Timbre enables us to identify and differentiate between various musical instruments and voices.

In summary, frequency determines the pitch perception of a sound, amplitude influences the perception of loudness, and timbre defines the unique quality or tone color of a sound. These physical characteristics directly relate to the corresponding perceptual characteristics, providing us with a rich and diverse soundscape in our auditory experience.

The volumetric flow rate of the oil is 2.37 m³/s.

In order to calculate the volumetric flow rate of the oil, we need to use the formula for volumetric flow rate.Q = vA Where,Q = volumetric flow rate v = velocity of fluid A = cross-sectional area of the pipe

First, we need to calculate the cross-sectional area of the pipe. Since the thickness of the pipe is not given, we will use an approximate value for the inner diameter of the pipe, which is equal to the nominal diameter minus twice the wall thickness.

This is given by:Di = N.D. - 2e

For Schedule 80 pipes, the wall thickness is given by:

e = 0.0153D - 0.0153

For N.D. = 450 mm,

e = 0.0153(450) - 0.0153= 6.885 mm

= 0.006885 m.

Hence,Di = 0.45 - 2(0.006885)= 0.43623 m

Now, we can calculate the cross-sectional area of the pipe:

A = π/4 D²

= π/4 (0.43623)²

= 0.15015 m²

Finally, we can calculate the volumetric flow rate using the formula:

Q = vA

Q= 15.8 × 0.15015

Q= 2.37207 m³/s≈ 2.37 m³/s (to two decimal places).

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Answer:

electric charges

dielectric substance

metal plates

Charge

electric charges

Charge

other charge

potential difference between them

Farad or F

Answer:

Capacitors are devices that store (electrical)energy. They usually consist of an insulating material inserted between two conductive plates. When a voltage is applied across the plates, electric charge builds up on the plates. The ratio of charge on one plate to the voltage across the plates is called the capacitance. The SI unit for capacitance is the farad (F).

Additional Information:

A capacitor is an electronic device that stores electrical energy. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, one plate accumulates a positive charge while the other plate accumulates an equal and opposite negative charge. This charge separation creates an electric field between the plates.

The capacitance of a capacitor, denoted by the symbol "C," determines its ability to store charge. It is defined as the ratio of the magnitude of charge stored on one plate (Q) to the potential difference (V) across the plates: C = Q/V. The unit of capacitance is the farad, F.

Capacitors store electrical energy in the electric field created between the plates. The amount of energy stored in a capacitor is given by the equations:

[tex]U=\dfrac{1}{2}QV= \dfrac{1}{2}CV^2=\dfrac{Q^2}{2C}[/tex]

Where:

The initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track: H = h + d.

To determine the initial height H of the boy in terms of h and d, we can use the principle of conservation of energy. The total mechanical energy of the system remains constant throughout the motion.

At the top of the slide, the boy has gravitational potential energy given by mgh, where m is the mass of the boy, g is the acceleration due to gravity, and h is the height of the slide above the ground.

As the boy slides down the slide, there is no friction or other dissipative forces, so there is no change in mechanical energy. At the bottom of the track, the gravitational potential energy is converted entirely into kinetic energy.

Therefore, we can equate the initial potential energy to the final kinetic energy:

mgh = 1/2 m[tex]v^{2}[/tex],

where v is the horizontal velocity of the boy when he leaves the track.

Since the boy leaves the track horizontally, the vertical component of his velocity is zero. Therefore, we can use the relationship between horizontal distance d and horizontal velocity v:

d = vt.

Solving these equations, we can express the initial height H in terms of h and d:

H = h + d.

So the initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track.G

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Answer:

Explanation:

The correct shutter speed for f/2.8 is 1/15 sec.

The aperture and shutter speed are two of the three factors that determine the exposure of a photograph. The third factor is the ISO sensitivity of the camera.

The aperture is a hole in the lens that allows light to pass through. The smaller the aperture, the less light that passes through. The shutter speed is the amount of time that the shutter is open, allowing light to hit the sensor.

In this case, we are changing the aperture from f/5.6 to f/2.8. This means that we are letting in twice as much light. To compensate for this, we need to halve the shutter speed.

So, the correct shutter speed for f/2.8 is 1/60 * 1/2 = 1/15 sec.

Here is the formula for calculating the correct shutter speed when changing the aperture:

shutter_speed_2 = shutter_speed_1 * aperture_1 / aperture_2

Answer:

[tex]s_{avg}= \dfrac{2 \pi}{3} \approx 2.09 \ m/s[/tex]

[tex]v_{avg}=\frac{4}{3} \approx 1.33 \ m/s[/tex]

Explanation:

To find the girl's average speed and average velocity, we can use the following formulas:

[tex]s_{avg}= \dfrac{\pi r}{t} \\\\ \\v_{avg}= \dfrac{2r}{t}\\\\\\ \hrule[/tex]

(A) - Finding the average speed.

[tex]\Longrightarrow s_{avg}= \dfrac{\pi(10.0)}{15.0}\\\\\\\therefore \boxed{s_{avg}= \dfrac{2 \pi}{3} \approx 2.09 \ m/s}[/tex]

(B) - Finding the average velocity.

[tex]\Longrightarrow v_{avg}= \dfrac{2(10.0)}{15.0}\\\\\\\therefore \boxed{v_{avg}=\frac{4}{3} \approx 1.33 \ m/s }[/tex]

Thus, the problem is solved.

Temperature of iron (Ti) = 415 °C Temperature of water (Tw) = 15.0 °CTemperature at equilibrium (Te) = 100 °CMass of water (m) = 0.625 kgMass of steam evaporated (ms) = 0.144 kgHeat lost by iron (Q1) = Heat gained by water (Q2) + Heat required to evaporate steam .

Heat lost by iron  = (mass of iron (m) x specific heat capacity of iron (c) x change in temperature of iron (ΔT1))Heat gained by water = (mass of water (m) x specific heat capacity of water (c) x change in temperature of water (ΔT2))Heat required to evaporate steam  = (mass of steam (ms) x specific latent heat of vaporization of water (L))Now, using the above formula we can calculate the mass of the iron block as:

Q3m x c x ΔT1 = m x c x ΔT2 + ms x L

Let's calculate the value of Q1 first.

Q1 = m x c x ΔT1m = Q1 / (c x ΔT1)

We know that

c = 450 J/kg °C and ΔT1 = Ti - Te = 415 - 100 = 315°CQ1 = m x c x ΔT1= m x 450 J/kg

°C x 315°C= 141750 m Jm = Q1 / (c x ΔT1)= 141750 / (450 x 315)= 1.002 kg

Now, let's calculate the value of Q3.Q3 = ms x L= 0.144 kg x 2.26 x 10^6 J/kg= 325440 J

Now, let's calculate the value of Q2

.Q2 = m x c x ΔT2m = (Q2 + Q3) / (c x ΔT2)

We know that ΔT2 = Te - Tw = 100 - 15 = 85°CQ2 = m x c x ΔT2= 0.625 kg x 4186 J/kg °C x 85°C= 276981.25 JNow, let's calculate the mass of the iron block.m =

(Q2 + Q3) / (c x ΔT2)= (276981.25 + 325440) / (450 x 85)= 1.003 kg

Hence, the mass of the iron block is 1.003 kg rounded off to 3 significant figures.

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Answer:

V = 108 km/hr = 108 * 1000  m / 3600 s = 30 m/s

V = speed of train = 30 m/s

(L + 120) m / 7 sec = 30 m/s

When front of train reaches station, back of train must travel L + 120 m to clear the station

S = V / t

(L + 120) / 7 = 30

L = 210 - 120 = 90 m    length of train

We can calculate the time taken by the compass to hit the ground by using kinematic equations of motion. The motion of the compass is a free-fall motion since it is only under the influence of gravity. When the compass is dropped, it is initially at rest.

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Answer: velocity

Explanation:

A form of energy released from the nucleus, the core of atoms, made up of protons and neutrons.

Saturation of colors in light waves is determined by the amplitude or intensity of the light, affecting color vibrancy and purity.

The saturation of colors in a light wave is determined by the amplitude or intensity of the light wave. Saturation refers to the purity or intensity of a specific color, indicating how vibrant or dull the color appears. In the context of light waves, it specifically refers to the degree to which a color appears vivid and free from a mixture of other colors.

The perception of color saturation is closely related to the amplitude of the light wave. Amplitude represents the maximum displacement of particles in the medium through which the wave is propagating. In the case of light waves, the amplitude corresponds to the intensity or brightness of the light. A higher amplitude leads to a more intense light wave, resulting in brighter and more saturated colors.

To understand this concept further, we can consider the RGB color model commonly used in digital displays. In this model, colors are produced by combining varying intensities of red, green, and blue light. The saturation of a particular color is determined by the amplitude of the corresponding light wave. Higher amplitudes result in more intense primary colors and, therefore, greater saturation.

However, it's important to note that color perception is also influenced by factors such as the color spectrum, the human visual system, and individual preferences. Additionally, factors like ambient lighting conditions, color mixing, and color reproduction technologies can affect the perceived saturation of colors.

In summary, the saturation of colors in a light wave is primarily determined by the amplitude or intensity of the light. Higher amplitudes result in more vibrant and saturated colors, while lower amplitudes lead to duller or desaturated colors. However, other factors can also influence color perception, and the specific color model or context may further affect how saturation is perceived.

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Explanation:

You have to 'balance' the vertical and horizontal forces with an equal but opposite third force .....

vertical   :     100 sin60 + 200 sin (120)  = 259.8 N

Horizontal  100 cos 60 + 200 cos 120 = -50 N

Magnitude = sqrt ( 259.8^2 + (-50)^2) = 264.57 N

The vertical and horizontal components will be opposite the ones found above :

       angle = arc tan  -259.8 / (50) = 280.9 degrees

The force of gravity between two objects can be calculated using the equation:

F = (G * m1 * m2) / r^2

where:

F is the force of gravity

G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)

m1 and m2 are the masses of the two objects

r is the distance between the centers of the two objects

Plugging in the values given:

m1 = 37,000,000 kg

m2 = 36,000,000 kg

r = 13 m

G = 6.67430 × 10^-11 N m^2/kg^2

Calculating the force of gravity:

F = (6.67430 × 10^-11 N m^2/kg^2 * 37,000,000 kg * 36,000,000 kg) / (13 m)^2

F ≈ 9.804 N

Therefore, the force of gravity between the two objects is approximately 9.804 Newtons.

The force of gravity acting on the plane is directly proportional to the mass of the plane, which is 4,300kg. Therefore, the weight of the plane is given by the formula:Fg = mgwhere Fg represents the force of gravity, m represents the mass of the plane and g is the acceleration due to gravity, which is 9.8 m/s².The force of gravity acting on the plane is:Fg = 4,300 × 9.8Fg = 42,140 N The plane needs to be traveling at least 101 m/s in order to take off. The engines of the plane can produce a thrust of 16,000 N.

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Answer:

It is incredibly difficult to sustain fusion reaction.

Explanation: