europa, one of the moons of jupiter, was discovered by galileo in 1610. europa has a circular orbit of radius 6.708 105 km and period 3.551 days. find the mass of jupiter.

The period of a mass-spring oscillating system undergoing SHM with a period t, when the amplitude is doubled, is still t.

The period of a mass-spring oscillating system undergoing simple harmonic motion (SHM) is determined by the spring constant and mass of the system.

When the amplitude of the system is doubled, the period of the system remains the same, regardless of the amplitude. This means that the period of a mass-spring oscillating system undergoing SHM with a period t, when the amplitude is doubled, is still t.
To understand why the period remains the same, consider the equation for simple harmonic motion:

x(t) = A cos (2πft).

This equation describes the displacement of an object over time and is based on the principle that any system undergoing SHM oscillates about a fixed point at a constant frequency.

The frequency of the system is inversely proportional to the period, and is determined by the spring constant and mass of the system.

Increasing the amplitude of the system does not affect the frequency or period of the oscillations.

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An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. the heavier fragment slides 7.90 m before stopping 0.1612 m does the lighter fragment slide.

When a heavy object explodes into two pieces, the momentum before and after the explosion is conserved. As a result, after the explosion, the momentum is conserved, and each fragment acquires a velocity.

The velocity of the smaller mass is more significant than that of the larger mass since they have the same momentum. The momentum is equal to the sum of the product of mass and velocity of the fragments.

Since the momentum is conserved, we can say that:

mu*vu = [tex]m_1\times v_1 + m_2 \times v_2[/tex]

where mu is the momentum before the explosion, and [tex]v_1[/tex] and [tex]v_2[/tex] are the velocities of the lighter and heavier mass respectively.

mu x vu = [tex]m_1 \times v_1 + m_2 \times v_2[/tex]

Since one of the fragments is seven times as massive as the other, we may express the total mass as

[tex]m = m_1 + m_2[/tex], and [tex]m_2 = 7m_1[/tex]

Therefore, the expression for the total momentum is:

mu x vu = [tex]m_1\times v_1 + 7m_1 \times v_2m_1(7v_2 - v_1)[/tex] = mu x vu ........(1)

We'll now apply the law of conservation of energy to determine the distance traveled by the fragments.

Let [tex]m_1 = m_2/7[/tex], and rewrite equation (1) as:

[tex]m_2(v_2 - v_1/7) = mu*vu\\ m_2(v_2 - v1/7) = 1/2 \times m_2 \times (v_2^2 + v_1^2)[/tex] ........(2)

We will substitute (v2 - v1/7) into equation (2).

[tex]7m_1(7v_2 - v_1) = 1/2 \times 7m_1 \times (49v_2^2 + v_1^2)v_1^2 + 49v_2^2 = 98v_2^2v_1^2 = 49v_2^2v_1 = 7v_2[/tex]

The distance traveled by the lighter mass is proportional to the square of the velocity.

As a result, since [tex]v_1 = 7v_2[/tex], the distance traveled by the lighter mass is 49 times less than the distance traveled by the heavier mass.

Light fragment distance = 7.90/49 = 0.1612 m

Therefore, the lighter fragment slides 0.1612 m before stopping.

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The surface charge density on the belt is 2 A/cm.

The surface charge density on the belt can be computed by dividing the charge flow rate (100 A) by the width of the belt (50 cm). This yields a surface charge density of 2 A/cm.

Charge is the basic physical property of matter that allows it to produce and experience electrical and magnetic effects. Charge carriers are particles which are free to move, and in this case, they are moving along the belt.

The belt acts as a conductor and carries the charge with it. As the belt moves, it carries the charge into the sphere, where the charge accumulates and produces a surface charge density.

The surface charge density is a measure of the electric charge per unit area on the surface of a conductor, and in this case, it is 2 A/cm.

Charge carriers move in response to electric and magnetic fields. In this case, the charge is moving from the source to the sphere due to the electric field created by the source.

As the charge moves, the electric field changes, resulting in the charge carriers picking up speed.

This explains why the belt is travelling at 30 m/s - the electric field is strong enough to propel the charge carriers at this speed.

The surface charge density on the belt is 2 A/cm, and this is the result of the charge carriers travelling along the belt due to the electric field created by the source of charge.

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Greenhouse gases are capable of absorbing: infrared radiation

Infrared radiation is a type of radiation affected by greenhouse gases. Greenhouse gases are capable of absorbing infrared radiation. Water vapor, carbon dioxide, and methane are the primary greenhouse gases. When the Earth receives energy from the sun, some of it is reflected and some is absorbed by the Earth.

The absorbed energy heats up the Earth's surface, which then radiates energy back out into the atmosphere in the form of infrared radiation. Greenhouse gases absorb some of this outgoing infrared radiation, which warms the atmosphere. This warming is known as the greenhouse effect.

The more greenhouse gases there are in the atmosphere, the more radiation they can absorb, and the warmer the Earth's surface will become. As a result, climate change can be caused by increases in greenhouse gases. As greenhouse gas levels rise, they absorb more of the outgoing radiation and the greenhouse effect becomes stronger. This causes the Earth's surface temperature to rise, leading to changes in the Earth's climate.

In summary, greenhouse gases are capable of absorbing infrared radiation, and as the concentration of greenhouse gases in the atmosphere increases, they become more effective at trapping heat and warming the Earth's surface, leading to changes in the Earth's climate.

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Answer:

igneous rock is produced when magma exits and cools above (or very near) the Earth's surface. These are the rocks that form at erupting volcanoes and oozing fissures.

Answer:

Explanation

What exactly do you need? More context to this problem would help me in helping you!

Answer:

Explanation:

Durante as aulas, os estudantes da 3ª série deveriam escolher uma entre as três atividades físicas possíveis, sendo elas: natação, futsal e dança. Na turma, 25% escolheram dança, 15% escolheram natação, e os outros 24 estudantes escolheram futsal. Podemos afirmar que, nessa turma, existe um total de:

A) 64 alunos

B) 55 alunos

C) 48 alunos

D) 45 alunos

E) 40 alunos

If a Tesla Model S P100D in "ludicrous mode" is pushed to its limit, the first 3.0 seconds of acceleration can be modeled as `a = 15.7 m/s²`.

The acceleration of the Tesla Model S P100D in "ludicrous mode" is known to be 15.7 m/s² for the first 3.0 seconds. Ludicrous mode is a high-performance mode that Tesla introduced in 2015 to increase the power output of the Model S P90D sedan. It was then carried over to the Tesla Model X and Model S P100D Ludicrous. It is a high-performance mode that raises Tesla's acceleration to an absurd level. This is made possible by the maximum power output of the car's battery pack, which can be increased in ludicrous mode.

Hence, If a Tesla Model S P100D in "ludicrous mode" is pushed to its limit, the first 3.0 seconds of acceleration can be modeled as `a = 15.7 m/s²`.

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The time taken by both balls to be at the same height is 1.02 seconds.

The time taken by two balls to be at the same heightGiven,Initial speed of the ball that is thrown upward from the ground, u = 35 m/s,Initial height of the ball that is dropped from a building, h = 5.0 m,Finding out the time taken by both balls to be at the same height,Time taken by ball that is thrown upward from the ground, t = ?

For the first ball (that is thrown upward from the ground), the acceleration, a = -9.8 m/s² (negative because it's going against the gravity).Using the formula of motion,S = ut + 1/2 at²where,S = height of the ball above the ground, t = time taken by the ball to reach that height, and u = initial speed of the ball that is thrown upward from the ground.

Here, h = S and u = 35 m/s, and a = -9.8 m/s². Then putting the values we get,h = ut + 1/2 at²5 = (35)t + 1/2 (-9.8)t²5 = 35t - 4.9t²----------------(1)Also, for the second ball (that is dropped from a building), the time taken to reach the ground can be found using the formula, h = 1/2gt². Here, h = 5.0 m.

Therefore,5 = 1/2 × (-9.8) × t²5 = -4.9t²t² = -5/-4.9t² = 1.02t = √1.02

Therefore, the time taken by both balls to be at the same height is 1.02 seconds.

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If the polar ice caps melted and increased the Earth's moment of inertia by 1.1, the angular velocity of the planet would decrease. The exact change in angular velocity would depend on the initial angular velocity and the magnitude of the moment of inertia increase.

The melting of the polar ice caps would result in a transfer of mass from the poles towards the equator. This would cause a redistribution of the Earth's mass, resulting in an increase in the moment of inertia of the planet.

Assuming no other external forces act on the Earth, the conservation of angular momentum dictates that an increase in moment of inertia leads to a decrease in angular velocity.

The exact change in angular velocity would depend on the magnitude of the moment of inertia increase and the initial angular velocity of the Earth. However, assuming the moment of inertia increases by 1.1, which is a significant change, we can expect a noticeable decrease in the Earth's angular velocity.

In summary, if the polar ice caps melted and increased the Earth's moment of inertia by 1.1, the angular velocity of the planet would decrease. The exact change in angular velocity would depend on the initial angular velocity and the magnitude of the moment of inertia increase.

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1 - Since electrοns can be transferred frοm οur hair tο the ballοοn , electrοns cannοt be transferred frοm ballοοn tο οur hair because. This is an illustratiοn οf  charging by cοnductiοn.

2 - Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.

3 - Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.

A charged οbject must cοme intο cοntact with a neutral οbject tο cοnduct electricity. As a result, when twο charged cοnductοrs cοme intο cοntact, the charge is split between the twο cοnductοrs, charging the uncharged cοnductοr.

When twο neutral οbjects are rubbed against οne anοther, electrοns are transferred. The οbject that has a strοnger affinity fοr electrοns will take electrοns frοm the οther οbject, and the twο becοme charged in οppοsitiοn. In this instance, the electrοns frοm the hair are taken up by the ballοοn , which nοw has an excess οf electrοns and a negative charge cοmpared tο the hair's current electrοn shοrtage and pοsitive charge.

2- Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.

3- Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.

4-Insulating materials may becοme electrically charged when they cοme intο cοntact with οne anοther. Negatively charged electrοns can "rub οff" οne material and "rub οn" tο anοther. After bοth things have the same quantity οf οppοsite charges, the substance that gets electrοns becοmes negatively charged, and the material that lοses electrοns becοmes pοsitively charged.

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The magnitude of acceleration is 7.44 m/s²

Given data:

Radius of the circle, r = 26 m,

Speed of the particle, v = 14 m/s.

Acceleration of the particle is given by the formula: a = v²/r

Where, v is the velocity of the particle and r is the radius of the circle on which the particle is moving.

Substitute the given values in the formula of acceleration.

a = v²/r

= (14 m/s)²/26 m

= 7.44 m/s² (rounded off to two decimal places)

Therefore, the magnitude of acceleration is 7.44 m/s².

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Explanation:

Nonmetals tend to gain electrons and become anions. For example, in Fig. 2.22 A, a neutral oxygen atom (O), with eight protons and eight electrons, gains two electrons. This gives it two more negative charges than positive charges and an overall charge of 2–.

The amount of tension a rope must withstand if it is used to accelerate a 1410 kg car horizontally along a frictionless surface at 1.40 m/s² is 1974 N.

Tension is the force that stretches or pulls something tightly. In physics, the term "tension" refers to the force that is transmitted through a string, cable, chain, or wire when it is pulled taut by forces acting on either end. The acceleration of the car is given as 1.40 m/s². This means that the force required to move the car is given as F = m × a. Where, F = force acting on the car M = mass of the car = 1410 kg.a = acceleration = 1.40 m/s²Therefore, F = 1410 × 1.40= 1974 N. The rope or cable used to pull the car must generate enough force to overcome the weight of the car and move it forward. The force of tension in the rope or cable required to move the car at the given acceleration is Ft = F= 1974 N.

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The magnitude of the resultant force acting on the shot is 1000 N, and its direction is approximately 59.5 degrees above the horizontal.

The resultant force acting on the shot can be found using vector addition of the two forces applied on the shot.

The two forces can be represented as vectors in the xy-plane, with the horizontal force of 500 N pointing in the positive x-direction and the vertical force of 866 N pointing in the positive y-direction. We can use the Pythagorean theorem and trigonometry to find the magnitude and direction of the resultant force vector.

The magnitude of the resultant force vector F is given by:

|F| = [tex]\sqrt{(500 N)^2 + (866 N)^2)}[/tex]

|F| = 1000 N

The direction of the resultant force vector is given by the angle θ it makes with the positive x-axis:

tan θ = (866 N) / (500 N)

θ = tan⁻¹(866/500)

θ ≈ 59.5 degrees

Therefore, the magnitude of the resultant is 1000 N, and its direction is approximately 59.5 degrees.

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If the absorbance for a sample is large, then the intensity of light as it passes through the sample will be: low.

The light is absorbed by the sample, resulting in a lower intensity of light. Absorbance is the measure of the amount of light absorbed by a sample, and it is proportional to the concentration of the absorbing substance. If the concentration of the absorbing substance is high, the absorbance will be high, indicating that more light is being absorbed by the sample.

To measure the concentration of a substance in a sample, absorbance is often used. A sample is irradiated with light of a known intensity and a known wavelength, and the intensity of the transmitted light is measured. The intensity of the transmitted light is compared to that of the incident light, and the percentage of light absorbed by the sample is calculated based on the difference between the two.

A high absorbance value means that a lot of light is being absorbed by the sample, which indicates a high concentration of the absorbing substance in the sample.

Therefore, when the absorbance for a sample is large, the intensity of light as it passes through the sample will be low.

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(a) The speed of the alpha particle is 1.37 x 10⁶ m/s.

(b) Time taken for the alpha particle is 1.03 x 10⁻⁵ s.

(c) The kinetic energy of the alpha particle is 1.02 x 10⁻¹³ J.

(d) The potential difference is 5.09 x 10⁻¹⁴ V.

An alpha particle is a type of nucleus particle composed of two protons and two neutrons.

(a) The speed of the alpha particle can be calculated using the equation v = (Bqr)/m,

where B is the magnetic field strength,

q is the charge,

r is the radius of the circular path,

and m is the mass of the particle.

Substituting the given values, we get:

v = (1.20 T x 2e x 4.50 cm) / (4.00 u x 1.661 x 10⁻²⁷ kg)

= 1.37 x 10⁶ m/s.

(b) The period of revolution is the time taken for the alpha particle to make one complete rotation around the circle and can be calculated using the equation T = 2πr/v,

where r is the radius of the circular path and v is the speed.

Substituting the given values, we get:

T = (2π x 4.50 cm) / (1.37 x 10⁶ m/s)

= 1.03 x 10⁻⁵ s.

(c) The kinetic energy of the alpha particle can be calculated using the equation EK = ½mv2,

where m is the mass and v is the speed. Substituting the given values, we get:

EK = (½ x 4.00 u x 1.661 x 10⁻²⁷ kg x (1.37 x 10⁶ m/s)2)

= 1.02 x 10⁻¹³ J.

(d) The potential difference through which the alpha particle would have to be accelerated to achieve this energy can be calculated using the equation V = EK/q,

where EK is the kinetic energy and q is the charge.

Substituting the given values, we get:

V = (1.02 x 10⁻¹³ J) / (2e)

= 5.09 x 10⁻¹⁴ V.

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The resistance of the resistor is 2.8 ohms.

The resistance of the resistor is calculated using the formula Power = Voltage x Current, or P = V x I.

Plugging in the given values, we get:

1.47 J = 12 V x I x 6.50 hours

Rearranging to solve for I, we get:

I = 1.47 J / (12 V x 6.50 hours)

Then, using Ohm's law (V = I x R) we can solve for R:

R = 12 V / I

Substituting in the value of I, we get:

R = 12 V / (1.47 J / (12 V x 6.50 hours))

Therefore, the resistance of the resistor is 2.8 ohms.

Resistance is the opposition that a substance offers to the flow of electric current

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When you hold a box of books with flat hands and press harder, the friction force applied by your hands onto the sides of the box will increase.

The force causes motion because if an object is at rest, it remains at rest until acted upon by a force. If the object is in motion, it remains in motion unless acted upon by a force to slow it down, speed it up, or change its direction. So, we have to look at the direction of the force and the motion to understand how the force will affect it. In general, the frictional force opposes motion.

The force of friction is proportional to the force pressing the two surfaces together. In this case, the force pressing the box onto your hands will be greater if you press harder, resulting in a greater frictional force applied by your hands onto the sides of the box, according to Coulomb's laws. Therefore, the friction force will increase when you press harder.

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Answer:

The relative density of the liquid is 1.5

Explanation:

The relative density of a liquid is defined as the ratio of the density of the liquid to the density of water. We can use the principle of buoyancy to find the relative density of the liquid.

When the body is immersed in water, it experiences an upthrust equal to the weight of water displaced. Therefore, the weight of water displaced = weight of the body in air - weight of the body in water = 0.5 kg - 0.3 kg = 0.2 kg.

Similarly, when the body is immersed in the liquid, it experiences an upthrust equal to the weight of liquid displaced. Therefore, the weight of liquid displaced = weight of the body in air - weight of the body in the liquid = 0.5 kg - 0.2 kg = 0.3 kg.

The relative density of the liquid can be found as follows,

Relative density of liquid = Density of liquid / Density of water

= (Weight of liquid displaced / Volume of liquid) / (Weight of water displaced / Volume of water)

= (0.3 kg / Volume of liquid) / (0.2 kg / Volume of water)

= (0.3 kg / Volume of liquid) / (0.2 kg / 0.2 L) [since the density of water is 1 g/mL or 1 kg/L]

= 1.5 / Volume of liquid

Therefore, the relative density of the liquid is 1.5 divided by the volume of the liquid in liters.

Free fall is the motion of an object in a gravitational field, where gravity is the only force acting upon it. It is different from movement in the y-direction because in free fall, the object's speed and direction of motion is constantly changing, whereas in the y-direction the object moves at a constant speed. It is also different from movement in the x-direction because the object experiences no acceleration in the x-direction. Examples of free fall include an apple falling from a tree, or a person skydiving from an airplane.

Free fall refers to the motion of an object that is falling due to gravity with no other forces acting on it except for the force of gravity. The movement in the y-direction refers to the vertical movement of an object. Movement in the x-direction refers to the horizontal movement of an object. The following are the differences between free fall and movement in the y and x directions.

Free fall vs movement in y-direction

In free fall, the object falls freely with no other force acting on it except gravity. However, in the movement in y-direction, the object can either be rising, falling, or staying still due to the presence of other forces like air resistance or thrust. For instance, when a ball is thrown into the air, it moves in the y-direction, but eventually, it stops rising and starts falling due to the force of gravity.

Free fall vs movement in x-direction

In free fall, the object falls vertically with no horizontal movement. However, in movement in the x-direction, the object moves horizontally with no vertical movement. For example, when a ball is thrown horizontally, it moves in the x-direction but does not experience any vertical movement.  

Examples

A few examples of free fall are an apple falling from a tree, a skydiver falling from a plane, and a stone falling from a cliff.

A few examples of movement in the y-direction are an airplane taking off, a rocket launching into space, and a ball thrown into the air.

A few examples of movement in the x-direction are a car moving along a straight road, a roller coaster moving along a straight track, and a person walking in a straight line.

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The property of objects that is best measured by their capacitance is c) the ability to store charge.

Capacitance is a measure of an object's ability to store an electric charge. It is defined as the ratio of the magnitude of the electric charge on each conductor to the potential difference between them. A capacitor is a device that stores electrical energy in an electric field between two conductive plates. The larger the capacitance of a capacitor, the more chance it can store for a given potential difference.

While objects that can conduct electric current or distort an external electrostatic field can also exhibit capacitance, these properties are not directly measured by capacitance

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What property of objects is best measured by their capacitance?

a) ability to conduct electric current

b) ability to distort an external electrostatic field

c) ability to store charge

Answer:

Q = I t        definition of current

Q = .32 Coul/sec * 82 sec = 26.2 coul

More work was done on the box by the 5.4 n force when: it was supported and carried 1.9 m horizontally across the room.

The 5.4 N vertical force did more work on the box when it was supported and carried 1.9 m horizontally across the room. This is because work is the product of force and distance, meaning more work is done when the force is greater and the distance is longer. In this case, the force remained the same, but the distance traveled was greater, so more work was done.

When the box was pushed 1.9 m horizontally across the smooth table by a 5.4 N horizontal force, less work was done on the box. This is because although the force remained the same, the distance traveled was shorter. As a result, less work was done by the 5.4 N force.

To summarize, more work was done on the box by the 5.4 N force when it was supported and carried 1.9 m horizontally across the room. This is because work is the product of force and distance, and the distance was greater in this case.

Conversely, less work was done on the box when it was pushed 1.9 m horizontally across the smooth table by the 5.4 N force since the distance traveled was shorter.

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The value of  uncharged capacitor in series with a 10.0-microfarad capacitor, given that each capacitor has a voltage of 3.00 volts, can be calculated using the formula for equivalent capacitance in series and  formula for charge on a capacitor. The value of c is approximately 4.00 microfarads.

To determine the value of c, which is [tex]1/Ceq = 1/C1 + 1/C2[/tex] . Initially, the 10.0-microfarad capacitor has a charge of [tex]Q = CV = (10.0 * 10^{-6 }F) * 12.0 V = 1.20 * 10^{-4} C[/tex].

When it is connected in series with uncharged capacitor with capacitance c,  charge is shared between the two capacitors. The charge on  10.0-microfarad capacitor is also equal to the charge on  uncharged capacitor, which is given by [tex]Q = (3.00 V) * C[/tex] .

Equating the two expressions for Q and solving for c, we get [tex]C = Q/3.00[/tex] [tex]V = (1.20 * 10^{-4 C}) / (3.00 V) = 4.00 * 10^{-5 F}[/tex]. Therefore,  value of c is approximately 4.00 microfarads.

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The number of electrons per second that enter the positive end of a battery can be calculated by the current flowing through the circuit and the time for which it flows.

Therefore, The formula of current is as

I = Q/t

where I is the current,

Q is the charge passing through the circuit, and

t is the time for which the current flows.

Since one electron carries a charge of -1.6 x 10⁻¹⁹Coulombs, we can calculate the number of electrons passing through the circuit using the following formula:

n = Q/e

where n is the number of electrons and

e is the charge on an electron (-1.6 x 10⁻¹⁹ Coulombs).

If we know the current flowing through the circuit and the time for which it flows, we can calculate the number of electrons per second using the following formula:

n/s = I/e

where n/s is the number of electrons per second.

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Answer:

The type of pressure that prevents a white dwarf from collapsing is the electron degeneracy pressure.

A white dwarf is a stellar remnant of a low or medium-mass star that has died, formed by a white dwarf supernova.

How does a white dwarf stay stable?

The white dwarf's stability is maintained by electron degeneracy pressure, which is the result of electrons being packed so tightly in the star's core that they are forced to behave like a gas, rather than a collection of individual particles.

The quantum mechanical Pauli exclusion principle governs the behavior of these electrons, which prohibits two fermions from occupying the same quantum state at the same time.

As a result, each electron is forced into a higher-energy state, resulting in a pressure that resists gravitational compression.

Therefore, the type of pressure that prevents a white dwarf from collapsing is the electron degeneracy pressure.

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When resistors are connected in series, the current flowing in each is the same.

Thus, the correct option is A.

When resistors аre connected in series, the current through eаch resistor is the sаme. In other words, the current is the sаme аt аll points in а series circuit.

When resistors аre connected in series, the totаl voltаge (or potentiаl difference) аcross аll the resistors is equаl to the sum of the voltаges аcross eаch resistor. In other words, the voltаges аround the circuit аdd up to the voltаge of the supply. The totаl resistаnce of а number of resistors in series is equаl to the sum of аll the individuаl resistаnces.

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To determine g, you must graph distance vs. time squared. When you draw a straight line that passes through the origin of this graph, you can use the slope of the line to determine the acceleration due to gravity g.

To yield a straight line whose slope could be used to calculate a numerical value for the acceleration due to gravity g, the quantity that should be graphed on the vertical axis is the distance (d) and the quantity that should be graphed on the horizontal axis is the time (t). Gravity acceleration, denoted by the letter "g," is the rate at which a falling object increases its speed. A constant acceleration is generated by gravity acceleration, and it is used to describe falling bodies. In any experiment to determine the acceleration due to gravity g, the distance an object travels over a period of time must be measured, recorded, and plotted.

The equation to use for measuring the distance d is: d = 1/2gt^2. The above equation shows that distance d depends on the time t and gravity acceleration g. We can rewrite the equation to give the acceleration due to gravity g by dividing both sides by t^2:g = 2d/t^2. Therefore, to determine g, you must graph distance vs. time squared.

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The rotational kinetic energy of a flywheel increases by 80% when its rotational speed increases by 40%. This is because the rotational kinetic energy of a flywheel is directly proportional to the square of its angular velocity.

The rotational speed of a flywheel increases by 40%. The percentage increase in its rotational kinetic energy is approximately 96.8%. Suppose the initial rotational speed of the flywheel is n1 and the initial rotational kinetic energy is K.E.1. After the speed of the flywheel is increased by 40 percent, the new speed is n2 = n1 + 0.4n1 = 1.4n1.

Then the new kinetic energy K.E.2 of the flywheel is given by K.E.2 = (1/2)I(n2^2)where I is the moment of inertia of the flywheel.Since n2 = 1.4n1, we have [tex]K.E.2 = (1/2)I(1.96n1^2) = 0.98I(n1^2).[/tex].

Therefore, the percentage increase in the rotational kinetic energy of the flywheel is approximately 96.8%.

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