if a star located 45 light years away from us exploded today, how long would it take before we can see the explosion?

The largest value of I_max that the breaker can carry is approximately 21.21 A.

Given a circuit breaker rated for 15 A RMS at 240 V RMS, we want to find the largest value of Imax (maximum current) that the breaker can carry. To do this, we'll use the following formula:

I_max = √2 * I_RMS

Where I_RMS is the rated current in RMS, which is 15 A in this case.

Substitute the value of I_RMS into the formula:
Imax = √2 * 15 A

Calculate the value of Imax:
Imax ≈ 21.21 A

Therefore approximately 21.21 A is the largest value of Imax that the breaker can carry.

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Answer:

C.

Explanation:

When Venus surface get bit cold when weather hits the planet gets soupy clouds and etc.

The law of conservation of energy states that energy is neither created nor destroyed but is transformed from one form to another.

The law of conservation of energy is the law that states that energy is neither created nor destroyed but is transformed from one form to another.

Examples of activities of everyday life that shows the conservation of energy include the following:

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An example of the law of conservation of energy is a roller coaster.

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

A roller coaster car gains kinetic energy as it moves down the track, but it also loses potential energy. At the bottom of the track, the car has the most kinetic energy and the least potential energy, while at the top of the track, it has the most potential energy and the least kinetic energy. However, the total amount of energy in the system remains constant.

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A) The magnitude force required to give a helicopter of mass M an acceleration of 0.10 g upward is F = 0.981 M N.

B) The work done by the force as the helicopter moves a distance h upward is W = 0.981 Mh N.

A) The force required to give a helicopter of mass M an acceleration of 0.10 g upward can be calculated using Newton's Second Law of Motion, which states that the force applied to an object is equal to the object's mass multiplied by its acceleration. The acceleration given is 0.10g, which can be converted to meters per second squared (m/s²) as follows:

0.10 g = 0.10 × 9.81 m/s² = 0.981 m/s²

Thus, the force required can be calculated as:

F = M × a

F = M × 0.981 N

B) To calculate the work done by the force as the helicopter moves a distance h upward, we can use the formula for work done by a constant force, which is:

W = F × d × cos(θ)

where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and the displacement vectors. In this case, the displacement is upward and the force is also upward, so θ = 0 and cos(θ) = 1.

The work done by the force as the helicopter moves a distance h upward is:

W = F × h × cos(θ)

W = F × h

Substituting the value of F from Part A, we get:

W = 0.981 M N × h

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The complete question is:

A) What magnitude force is required to give a helicopter of mass M an acceleration of 0.10 g upward? Express your answer in terms of the variable M and appropriate constants.

B) What work is done by this force as the helicopter moves a distance h upward? Express your answer in terms of the variables M,h, and appropriate constants.

The coils in the spring will move farther apart when a current is passed through it because of the solenoid effect.

The solenoid effect describes the way a loose spiral spring expands when a current is fed through it. An electric current flows through a coil of wire to create a solenoid, a type of electromagnet. A magnetic field is produced when current passes through the coil, and the magnetic field lines are parallel to the axis of the coil. The amount of current flowing through the coil and the number of wire turns within the coil determines how strong the magnetic field is.

Because a loose spiral spring behaves like a coil of wire, the solenoid effect is seen in this situation. The magnetic field that is created around a spring when a current is sent through it has lines that are parallel to the spring's axis. The interaction between the magnetic field and the spring's current produces a force that pushes the coils apart.

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Color: Both the bromine gas and steak have a brownish color.

Bromine gas is a reddish-brown, nonflammable, and highly toxic gas with a very strong, unpleasant odor. It is composed of two heavy, diatomic, halogen molecules, Br2, and is the only nonmetal element that exists as a liquid at room temperature. Bromine gas is denser than air and is soluble in water and organic solvents.

Texture: The bromine gas is a gas and therefore has no texture, while the steak is solid and has a firm texture.
Temperature: The bromine gas is a gas and therefore has a lower temperature than the steak, which is at room temperature.
Bromine Gas and Juice:
Color: The bromine gas is brownish and the juice is a yellowish or orange color.
Texture: The bromine gas is a gas and therefore has no texture, while the juice is a liquid and has a smooth texture.
Temperature: The bromine gas is a gas and therefore has a lower temperature than the juice, which is at room temperature.

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The magnetic field inside the coil is 0.036 T.

As the area of the coil increases, the magnetic field strength increases, and as the length of the wire increases, the magnetic field strength decreases. Understanding the factors that affect the magnetic field inside a coil is important in designing and optimizing various devices that use electromagnetic fields, such as transformers, motors, and generators. The magnetic field inside a coil can be calculated using the formula:

B = (μ₀ * n * I * A) / L

where,

μ₀ = permeability of free space = 4π x 10^-7 T m/A

n = number of turns

I = current in amperes

A = area of the coil in square meters

L = length of the coil in meters

Substituting the given values,

B = (4π x 10^-7 T m/A * 636 turns * 0.487 A * (2.12 x 10^-2 m)^2) / (2.12 x 10^-2 m)

B = 0.036 T (Tesla)

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In order for a vehicle travelling at 18.0 m/s to negotiate  highway bend without sliding, curve must be banked (inclined). The radius of curve approximately 33.1 metres.

The coefficient of side friction is found to be 0.10, and the superelevation at one horizontal curve has been set at 6.0%.the formula for calculating a road curve's radiusFind the shortest curve radius necessary to ensure safe vehicle operation.

speed of the car v = 18.0 m/s

angle of banking of the curve θ = 37°

acceleration due to gravityg = 9.81 m/s²

radius of the curve = r

N = mg * cos(θ).........1

also

N = mv² / r...........2

from equation 1 and 2 we get

mg * cos(θ) = mv² / r

r = v² / (g * cos(θ))

r = (18.0 m/s)² / (9.81 m/s² * cos(37°)) ≈ 33.1 m

Therefore, radius of the curve is approximately 33.1 meters.

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Answer:

The answer is Continental Grip

The nonconservative work done on the surfer is 2845.5 J.

We can use the work-energy theorem to solve this problem. The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this case, we can calculate the initial and final kinetic energies of the surfer and find the difference, which will give us the net work done.

The initial kinetic energy of the surfer is:

[tex]K_i = (1/2) * m * v_i^2[/tex]

[tex]K_i = (1/2) * 73.2 kg * (1.44 m/s)^2[/tex]

K_i = 75.7 J

The final kinetic energy of the surfer is:

[tex]K_f = (1/2) * m * v_f^2[/tex]

[tex]K_f = (1/2) * 73.2 kg * (8.89 m/s)^2[/tex]

K_f = 2921.2 J

The change in kinetic energy is:

ΔK = K_f - K_i

ΔK = 2921.2 J - 75.7 J

ΔK = 2845.5 J

According to the work-energy theorem, this change in kinetic energy must be equal to the net work done on the surfer. Therefore, the nonconservative work done on the surfer is:

W_nc = ΔK

W_nc = 2845.5 J

So, the nonconservative work done on the surfer is 2845.5 J.

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First, we need to find the total mass of the system by adding the masses of the two objects: m_total = m1   m2 = 50.0 kg   75.0 kg = 125.0 kg  Next, we can plug in the given force and mass values into the equation: F = ma 40.0 N = 125.0 kg * a  Solving for a: a = 40.0 N

125.0 kg * a

Solving for a:

a = 40.0 N / 125.0 kg

a = 0.32 m/s^2

Therefore, the acceleration of the system is 0.32 m/s^2.

m_c (mass of cylinder)=50 kg

d=25 cm so r=12.5 cm = 0.125 m m_b

(mass of bucket)=20 kg

So using the equations: RT = � = I � RT= I � (m_b)g-T= (m_b)aR And from what I understand, this is the same as the tangential acceleration? (m_b)g-T=(m_b) � r = F T= ( i � ) / r (m_b)g -(( i � ) / r ) = m � r � ( ((m_b)r) + (I /R ) ) = (m_b)g Leaving us with the final : � = ((m_b)g)/(((m_b)r) + (I /r)) Using this equation, I found I = 0.390625 and the final answer would be 35 rad/s^2 Sorry for such a long post--this is my first time on the website and I read the rules so hopefully I've done everything correctly! Thank you all!

/

The equivalent gradient updates as momentum 0.9 with batch size B = 32 in the simplified SGD update equation.

The relationship between momentum and batch size in the simplified version of SGD update is that increasing the batch size leads to a decrease in the effective learning rate, which in turn requires an increase in momentum to maintain the same level of stability.

If we train a model with momentum and a batch size of B, and now have a GPU with more memory and can use a batch size of B', we should increase the momentum by a factor of sqrt(B/B') to maintain the same level of stability.

To find the equivalent momentum for the simplified SGD update equation, we can use the formula:

momentum' = momentum * sqrt(B/B')

For example, if we initially trained with momentum = 0.9 and batch size B = 32, and now have a GPU with enough memory to use batch size B' = 64, we would calculate:

momentum' = 0.9 * sqrt(32/64) = 0.9 * 0.7071 = 0.64 (rounded to two decimal digits)

Therefore, using a momentum of 0.64 with batch size B' = 64 would lead to equivalent gradient updates as momentum 0.9 with batch size B = 32 in the simplified SGD update equation.

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The range of capacitance needed for the capacitor to be 99.3% charged within 10 ms of turning the voltage source on is greater than or equal to 56.3 times the resistance in ohms.

To calculate the range of capacitance needed for the capacitor to be 99.3% charged within 10 ms of turning the voltage source on in an RC circuit, we can use the following formula:

Vc(t) = Vmax * (1 - e^(-t/RC))

where Vc(t) is the voltage across the capacitor at time t, Vmax is the maximum voltage of the source, e is the mathematical constant approximately equal to 2.718, R is the resistance in ohms, C is the capacitance in farads, and t is the time in seconds.

When the capacitor is 99.3% charged, the voltage across it is 0.993 * Vmax. Substituting this value into the formula and solving for C, we get:

C >= t / (R * ln(1 / (1 - 0.993)))

C >= 10 ms / (R * ln(1 / 0.007))

C >= 56.3 * R

Therefore, the range of capacitance needed for the capacitor to be 99.3% charged within 10 ms of turning the voltage source on is greater than or equal to 56.3 times the resistance in ohms.

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Answer:

The type of collision, whether elastic or inelastic, can be determined by observing the behavior of the colliding objects before and after the collision. Here are some key characteristics that can help identify whether a collision is elastic or inelastic:

Conservation of Kinetic Energy: In an elastic collision, kinetic energy is conserved, while in an inelastic collision, some of the kinetic energy may be converted into other forms of energy.

Objects' Motion After Collision: In an elastic collision, objects bounce off each other and move independently, while in an inelastic collision, objects may stick together, deform, or move as a single mass.

Restitution Coefficient: In an elastic collision, the restitution coefficient is close to 1, indicating high bounce-back, while in an inelastic collision, the restitution coefficient is less than 1, indicating less bounce-back.

Conservation of Momentum: In both elastic and inelastic collisions, momentum is conserved, but the change in velocity of the objects after the collision can indicate whether the collision is elastic or inelastic.

The peak electric field 10 km from the transmitter is approximately 15.435 mV/m.

To find the peak electric field 10 km from the transmitter, we can use the inverse square law.

This law states that the intensity of a wave (such as the electric field in this case) is inversely proportional to the square of the distance from the source.

Here's a step-by-step explanation:

1. Note the initial distance (d1) and electric field (E1):

d1 = 2.1 km, E1 = 350 mV/m.

2. Convert d1 to meters:

d1 = 2100 m.

3. Note the final distance (d2):

d2 = 10 km.

4. Convert d2 to meters:

d2 = 10,000 m.

5. Use the inverse square law formula:

E2 = E1 * (d1²) / (d2²).

6. Plug in the values:

E2 = 350 * (2100²) / (10,000²).

7. Calculate E2:

E2 ≈ 15.435 mV/m.

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The melting of methane hydrates on the seafloor can lead to a sharp rise in global temperatures because methane is a powerful greenhouse gas. The statement is true.

Methane is a powerful greenhouse gas, with a global warming potential that is estimated to be about 25 times greater than that of carbon dioxide over a 100-year time horizon. Methane hydrates are solid, crystalline compounds that contain a large amount of methane gas trapped within water molecules. These hydrates are stable under certain temperature and pressure conditions, but if they become destabilized, they can release large amounts of methane into the atmosphere.

The melting of methane hydrates on the seafloor is a concern because it has the potential to release vast amounts of methane into the atmosphere, which could significantly contribute to global warming and climate change. This process could be triggered by rising ocean temperatures, changes in ocean currents, or other factors that alter the stability of the hydrates. While the exact extent and impact of this phenomenon are still uncertain, it is an area of active research and concern among climate scientists.

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The option A is  best representation of the path that the ball would take after the string breaks.

When the string of a pendulum breaks, the ball's path will follow the laws of motion, specifically the law of conservation of energy. As the ball was halfway to its highest position, it had a certain amount of potential energy.

When the string broke, this potential energy would convert to kinetic energy, causing the ball to move in a straight line tangent to the point where the string broke.

Therefore, the path that the ball would take after the string breaks would be a straight line away from the pivot point of the pendulum, as shown in option A. The other paths shown do not follow the laws of motion and do not account for the conservation of energy. Option (A) is the correct answer.

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Note the full question is

A pendulum is swinging upward and is halfway toward its highest position, as shown, when the string breaks. which of the paths shown best represents the one that the ball would take after the string breaks?

A) A

B) B

C) C

D) D

E) E

The standing wave's fundamental frequency is the frequency of the first harmonic, which has one node and two antinodes, whereas the number of nodes determines the standing wave's harmonic number.

A 4.35 metre long, 137 gramme wire is being pulled at 125 newtons of force. With seven nodes total, including the endpoints, a standing wave has developed.

A collection of dots and dashes can be used to represent the wave pattern. The relationship between wave speed and wavelength is used to compute the standing wave's frequency. The tension in the wire and its linear mass density are used to calculate the wave speed.

The standing wave's fundamental frequency is the frequency of the first harmonic, which has one node and two antinodes, whereas the number of nodes determines the standing wave's harmonic number.

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The kinetic energy in Schrödinger's equation for the H2 molecule includes contributions from both electrons and nuclei. Thus the correct option is C.

The kinetic energy term in Schrödinger's equation for the H2 molecule refers to the energy involved in the motion of the particles. The H2 molecule comprises two hydrogen nuclei and two electrons, therefore the electrons and the nuclei both contribute to the kinetic energy.

The nuclei contribute to the kinetic energy by their mobility, whereas the electrons do so through their wave-like behaviour. The H2 molecule's kinetic energy term in Schrödinger's equation includes contributions from both electrons and nuclei, making option C the right response.

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The kinetic energy in Schrödinger's equation for the H2 molecule includes contributions from both electrons and nuclei. Thus the correct option is C

explanation - For Schrödinger's equation of the H2 molecule, the kinetic energy has contributions from both electrons and nuclei. This is because the kinetic energy term in the equation accounts for the motion of all particles in the system, which in this case includes both the electrons and nuclei of the H2 molecule. Therefore, options a, b, and d are incorrect.

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A spaceship is traveling at 0.7c when a laser beam is turned on, directed in the direction the ship is traveling.

According to the theory of relativity, the speed of light in a vacuum is always the same for all observers, regardless of their relative velocities.

The speed of the laser light is always c, which is the speed of light in a vacuum, approximately 3.0 x 10^8 meters per second. This is because the speed of light is constant and does not depend on the speed of the source (in this case, the spaceship).

Explanation:

In this scenario, the spaceship is traveling at 0.7c, which means that it is moving at a speed that is 0.7 times the speed of light. When a laser beam is turned on in the direction of the spaceship's motion, the speed of the laser light is still c, as measured by an observer on the spaceship. This is because the speed of light is always the same, regardless of the motion of the source or observer.

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A laser beam is activated and pointed in the direction of a spaceship that is moving at 0.7c.

The speed of light in a vacuum is constant for all observers, regardless of their relative velocities, according to the theory of relativity.

The speed of the laser light is always c, or around 3.0 x 108 metres per second, the speed of light in a vacuum. This is due to the fact that the speed of light is independent of the source's (in this example, the spacecraft's) speed and is always constant.

In this scenario, the spaceship is traveling at 0.7c, which means that it is moving at a speed that is 0.7 times the speed of light. When a laser beam is turned on in the direction of the spaceship's motion, the speed of the laser light is still c, as measured by an observer on the spaceship. This is because the speed of light is always the same, regardless of the motion of the source or observer.

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Thermal energy is absorbed each hour is  13.53 x 10¹² J  and thermal energy lost per hour  is  7.092 x 10¹² J.

a technique of isothermal gas expansion that is reversible. In this process, the ideal gas in the system receives  amount heat from a heat source at a high temperature Thigh, expands and does work on surroundings. a technique of adiabatic gas expansion that is reversible. The system is thermally insulated throughout this process.

Temp_cold = 20°C + 273.15 = 293.15 K

Temp_hot = 425°C + 273.15 = 698.15 K

efficiency = 1 - (Temp_cold / Temp_hot)

                     = (698.15 K * 293.15 K) / (698.15 K)² - (293.15 K)²

efficiency = 0.524 or 52.4%

thermal energy absorbed/ hour = power output / efficiency

= 197 kW / 0.524

= 375.95 MJ/h  x 3.6 x 10⁶ J/kWh = 13.53 x 10¹² J

thermal energy is lost per hour

W = power output x time = 197 kW x 1 h = 197 kWh

W = 197 kWh x 3.6 x 10⁶ J/kWh = 7.092 x 10¹²1J

Since the engine is running in a cycle, the system's internal energy is equal to zero, hence U = 0.

Q = ΔU + W

hence, thermal energy lost per hour = Q = W = 7.092 x 10^11 J

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is a wheel with a concave edge for supporting a moving rope that is changing direction.

A sheave is a wheel with a concave edge for supporting a moving rope that is changing direction. A sheave helps to reduce friction and increase efficiency when managing ropes in various applications.

The term you are looking for is "pulley". A pulley is a simple machine that consists of a wheel with a grooved rim or concave edge, which is designed to support a moving rope or cable and change its direction of motion. Pulleys are commonly used in various applications, such as lifting heavy objects, moving loads, and transmitting power between machines.

They can also be combined with other pulleys and mechanical systems to create complex machines that perform a wide range of tasks.

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The magnitude of the force is 25 Newtons.

We can use Newton's second law, which states that the net force (F_net) acting on an object is equal to its mass (m) times its acceleration (a):

[tex]fnet = m*a[/tex]

The final velocity can be calculated using the formula:

[tex]v = d/t[/tex]

where d is the distance travelled and t is the time taken. Plugging in the values, we get:

v = 32 m / 8.0 s

v = 4.0 m/s

Therefore, the acceleration is:

a = Δv / Δt

a = 4.0 m/s / 8.0 s

a = 0.5 m/s^2

Now we can use Newton's second law to find the magnitude of the force:

F_net = 50 kg * 0.5 m/s^2

F_net = 25 N

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The technique of interferometry allows two or more telescopes to obtain the angular resolution of a single telescope much larger than any of the individual telescopes.

This is achieved by combining the signals received by the telescopes to create a single image with a higher resolution. Interferometry is especially useful for studying objects with small angular sizes, such as stars and planets.

Additionally, interferometry allows astronomers to make astronomical observations without interference from light pollution, as it can separate the signals from the object being observed from the background light.

However, interferometry does not directly determine the chemical composition of stars, although it can provide information about their temperature and other physical properties.

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Answer:

P (momentum) = M * V

V = (2.95^2 + 3.97^2)^1/2 = 4.95 m/s

P = 2.99 kg * 4.95 m/s = 14.8 kg-m/sec      total momentum

tan θ = Vy / Vx = -3.97 / 2.95 = -1.35

θ = 53.4 deg below positive x-axis

To find the distance at which the centripetal acceleration of an orbiting space station around a planet is equal to Earth's gravitational acceleration, we need to set up an equation involving the planet's mass (M), gravitational constant (G), and Earth's gravitational acceleration (g).

Given:
M = 8.00 × 10²³ kg
G = 6.67 × 10^(-11) m³·kg^(-1)·s^(-1)
g = 9.81 m/s² (Earth's gravitational acceleration)

Centripetal acceleration (a_c) is given by the formula:

a_c = (G * M) / r²

where r is the distance from the planet's center.

We want the centripetal acceleration to be equal to Earth's gravitational acceleration, so we can set them equal:

g = (G * M) / r²

Now, we need to solve for r:

r² = (G * M) / g

r² = (6.67 × 10^(-11) m³·kg^(-1)·s^(-1) * 8.00 × 10²³ kg) / 9.81 m/s²

r² ≈ 5.42 × 10¹² m²

Now, take the square root of both sides to find r:

r ≈ 2.33 × 10^6 m

So, at a distance of 2.33 x 10^6 meters from the planet's center, the centripetal acceleration of an orbiting space station will be equal to the gravitational acceleration on Earth's surface.

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The following formula can be used to determine the distance from the planet's centre at which the centripetal acceleration of an orbiting space station equals the gravitational acceleration on Earth's surface:

[tex]r = (GM/g)^(1/3)[/tex]

where the gravitational constant, G, equals 6.67 1011 m3 kg-1 s-1.

M is equal to 8.00 1023 kg (the planet's mass).

Gravitational acceleration on Earth's surface is equal to 9.81 m/s2.

When we change the values, we obtain:

[tex]r = [(6.67 × 10^-11) × (8.00 × 10^23) / 9.81]^(1/3)[/tex]

[tex]r = 2.33 × 10^6 m[/tex]

Therefore, 2.33 x 106 m is the necessary distance.

F = G (m1m2 / r2), where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them, can be used to express the gravitational force between two objects. When a planet and a satellite are involved, the centripetal force that holds the satellite in orbit around the planet is produced by the gravitational force. As a result, we may compare the centripetal force to gravity and find r. This results in the formula above, which we can use to calculate the necessary distance.

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Answer: hope it helps

Explanation:

A protostar becomes a main sequence star when its core temperature exceeds 10 million K. This is the temperature needed for hydrogen fusion to operate efficiently.

The stability of the nucleus is maintained through the combined effects of the strong force and neutrons.

Although protons repel each other due to their positive charge, they are stable in a nucleus because of the strong force, which is a fundamental force that binds the particles together.

The strong force is the strongest force in nature and overcomes the electromagnetic force that causes the protons to repel each other. Neutrons, which have no charge, also play a significant role in stabilizing the nucleus.

The neutrons act as a buffer between the positively charged protons, separating them from each other and reducing the electrostatic repulsion. Electrons, which have a negative charge, are not involved in stabilizing the nucleus as they are located outside the nucleus in orbitals around the nucleus.

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Potable water is fit for drinking. Option E

Potable water is water that is safe for human consumption and considered fit for drinking. It is free from harmful bacteria, viruses, chemicals, and other contaminants that can cause health problems.

Potable water can come from different sources such as groundwater, surface water, or treated wastewater, and it is typically treated and disinfected to ensure its safety before being distributed to consumers.

Portable water isn't known as industrial wastewater, irrigation water, groundwater and sewage.

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