If the electron were replaced with a proton moving with the same velocity, how would the resulting acceleration of the particle change?.

If a 2d system has a stable equilibrium point that is located somewhere outside a limit cycle, a trajectory starting inside the limit cycle will not reach the equilibrium point.

A trajectory starting inside a limit cycle will at some point reach the limit cycle. But, even t = ∞, the trajectory will still be in the limit cycle. For the trajectory, there is no possible way to leave the limit cycle. So if a stable equilibrium point is located outside a limit cycle, a trajectory starting inside the limit cycle cannot reach that point.

In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity.

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If the human body typically contains 5.1 L of blood of density 1060 kg/m³, there are 5 kilograms 406 ounce of blood in the body.

The density of blood plаsmа is аpproximаtely 1025 kg/m³ аnd the density of blood cells circulаting in the blood is аpproximаtely 1125 kg/m³. Blood plаsmа аnd its contents are known аs whole blood. The аverаge density of whole blood for а humаn is аbout 1060 kg/m³.

e = 1.060 kg/liter ⇒ change to m³

e = 1.060 × [tex]10^{-3}[/tex]

Blood is in the body (m):

m = e × v

m = 1.060 × 5.1 × [tex]10^{-3}[/tex]

m = 5.406 × [tex]10^{-3}[/tex] kg

m = 5 kg 406 ounce

The аverаge density of whole blood for а humаn is 1.060 kg/liter. So, 5.1 liters of аverаge blood will weigh 5 kg 406 ounce.

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The standard way to express an order of magnitude is as 10 to the nth power where q/h is 0.01.

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Yes, she breaks the record.

Given

distance of track = 1000 feet = 304.8 m

S(t) = t² + 30t

After differentiating we get,

S'(t) = 2t + 30

S''(t) = 2

The time taken by racer = 65 feet per second.

Time taken to for 1000 feet,

1000/65 = 15 second.

Time taken by Sam = S''(t) = 2 by which we can know that the time taken by Sam is less than that of the racer.

Therefore, with differentiating equation, she can surpass the racer and break the record.

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The speed of the private jet and the commercial jet were 200mph and 400mph respectively.

The private jet flies the same distance in 10 hour that the commercial jet cover in 6 hours.

The speed of the commercial jet is 200mph less than 3 time of the speed of private jet.

Now, if we assume the speed of Private jet to be X mph then the speed of the commercial jet will be (3X - 200) mph.

If the distance cover is D, then, for the private jet,

D = 10X

For commercial jet,

D = (3X-200)6

Now, we can write,

10X = 18X - 1200

6X = 1200

X = 200 mph.

So, the speed of the private jet was 200mph and the speed of the commercial jet was 400mph.

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In order for the wicked duo's plot to work, a small black hole with a mass of 38634.83 kg must exist.

Science has a specific definition for the term "force." At this point, describing a force as being pushed or pulled is quite acceptable. A strength is not something that something "contains" or "has in it." A force is applied to one thing by another. The idea of such a force encompasses either living and non-living things.

To overcome this issue, you should be aware of Isaac Newton discovered an equation that expresses the gravitational effect of two mass-bearing things at a distance r. The formula is as follows:

where,

G = It is the universal gravitational constant = 6.67 x 10⁻¹¹ Nm²/kg²

m₁ = mass of the moon=7.36 × 10²² kg

m₂ = mass of the mini black hole

r = distance=7.33 × 10⁶ m

F = force=3530N

solving for m;

(F)(r²)/m₁(G) = m₂

3530*[(7.33 × 10⁶)²]/(7.36 × 10²²) (6.67 x 10⁻¹¹) = m₂

m₂ = 38634.83 kg

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Let's first create our working equation. Everyone is aware that pressure is a force applied to a specific area of space. That would be P = F/A in an equation. According to Newton's Second Law of Motion, force equals mass times gravity, or F = mg. So, we can change the first equation to read P = mg/A by substituting F.

Now, the force that a fluid applies to a surface may also be used to calculate pressure. The volume of this fluid can be calculated. The density parameter, p = m/V, is used to relate volume and mass. Volume is the product of the cross-sectional area and the height, to further simplify things in terms of height. So, V = A*h. Following that, the working equation will be derived to be

P = pgh

The pressure that a fluid exerts over a specified height is referred to as hydrostatic pressure. We then locate the density of seawater data from the literature. According to research, saltwater has a density between 1,020 and 1,030 kg/m3. Let's stick with 1.020 kg/m3. Making the units consistent while substituting the values:

P = (1,020 kg/m³) (9.81 m/s2)(11 km)*(1,000 m/1km)

P = 110,068,200 Pa or 110.07 MPa

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The length of rotating string having 47 revolutions is 2m.

A string trimmer is a tool for cutting grass and weeds; it makes use of a length of nylon "string" that rotates around an axis perpendicular to one end of the string. The string's tangential speed at its tip is 54 m/s, and its angular speed is 47 rev/s.

[tex]Z=dc+CvdT+\pi (d^2L)/dT^2+\alpha \\\\Z=dc+CvdT\\\\Z=\left \{ {{\neq 1} \atop {=1}} \right.[/tex]

For ideal situations Z needs to be unity.

Mathematically, function tends to reduce to negligible.

This is due to its inverse relation with order of the derivative.

[tex]Cv\geq 1[/tex]

The linear speed of any object moving along a circular path at any given moment is known as tangential speed or tangential velocity. For any two instants of time for a given object in circular motion, the direction of tangential speed can never be the same.

[tex]\frac{d^2L}{y}+S=0\\ \\\frac{d^2L}{y}=0\\\\s\neq 0[/tex]

[tex]speed= \frac{47\pi }{54}\\ \\=12.38m/s[/tex]

Length of string=12.38 /2π

=1.97m approx to 2m

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(1) In the first day after the materials were placed in the system, the temperature of the water would probably increase.

(2) As time passes, the total energy in the system will be conserved.

The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.

Based on the law of conservation of energy, when equal masses of copper, granite, air and water  are in a perfectly insulated container, there will be heat transfer from one object to another.

After several hours, all the objects in the perfectly insulated container, will attain equilibrium temperature.

The equilibrium temperature attained by the objects will be greater than the initial temperature of water, lower than the initial temperature of copper, granite, and air.

Conclusively, we would say that the temperature of water will increase in the first day after the materials were placed in the system.

As time passes, the total energy in the system will be conserved since it is a perfectly insulated container, and no heat energy will be lost.

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The light from the bicycle have a velocity of 3.00x 10^8 m/s.

Explain Einstein's two postulates.

Einstein's two postulates form the foundation of modern relativity. The idea that the rules of physics are the same and can be expressed in their most basic form in all inertial frames of reference is the first postulate of special relativity. The assumption that the speed of light, or c, is a constant regardless of the source's relative motion is known as the second postulate of special relativity.

How several observers see the same event is the subject of relativity.

The theory of special relativity states that, in an inertial frame of reference, an object's velocity is relative to the frame from which it is observed or measured.

A body in motion moves in a straight path at a constant speed unless acted upon by an outside force in an inertial frame of reference, and a body at rest remains at rest.

According to einstein’s second postulate, speed of light from bike is equal to normal normal speed of light i.e. 3*10^8m/s

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The emf induced in the outer solenoid by the changing current in the inner solenoid is: 3.93 x [tex]10^{-2}[/tex] Volt .

Given that -

Number of turns in inner solenoid = N1 = 300

Number of turns in outer solenoid = N2 = 30

Length of inner solenoid = L= 24.0 cm = 0.24 m

Radius of inner solenoid = r = diameter/2 = 2.5/2=1.25 cm = 0.0125 m

The current in the inner solenoid = i = 0.140 A

Rate of increasing of current =di/dt = 1700 A/s.

(A) The average magnetic flux through each turn of the inner solenoid. =B.A

Put the values,

The average magnetic flux through each turn of the inner solenoid:

= 1.08 x [tex]10^{-7}[/tex] Wb

(B) Mutual inductance of the two solenoids, M = N2 x (average flux) / current= = 2.314 x [tex]10^{-5}[/tex]H

(C) The emf induced in the outer solenoid by the changing current in the inner solenoid.= M×di/dt

                         = 3.93 x [tex]10^{-2}[/tex] Volt

What is a solenoid?

A solenoid is a type of electromagnet consisting of a helical coil of wire whose length is much greater than its diameter, creating a controlled magnetic field. A uniform magnetic field can be generated in a certain space by passing an electric current through the coil. The term solenoid was coined by André-Marie Ampère in 1823.

The electromagnet's coil does not necessarily have to rotate about a linear axis. For example, William Sturgeon's his 1824 electromagnet consisted of a solenoid bent into a horseshoe shape (similar to an arc spring).

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It is likely critical to understanding the surface temperatures of each planet to understand the overall amount of gases that compose its atmosphere.

What are planets ?

Large natural objects called planets orbit or move around stars. The Sun is a star that is orbited by eight planets. These planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, starting with those that are nearest to the Sun.

Although there are obvious similarities between the atmospheres of the four terrestrial planets and the four gas giant planets, each of the planets has a unique atmosphere. The two main ones are size and separation from the Sun. Small planets and moons like Mars and the Moon have thin atmospheres because gravity helps planets and moons retain their atmospheres.

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The net force on the block at 0.89 s is zero Newtons.

What is net force?
The vector sum of the forces that act on a particle as well as object is known as the net force in mechanics. The original forces' impact on the motion of the particle is replaced by the net force, which is a single force. In accordance with Newton's second law of motion, it causes the particle to accelerate at a rate equal to the sum of all those actual forces. In order to keep the object's jets moving underneath the original system of forces, it is possible to calculate the torque connected to the point of application of the a net force. As with all actual forces combined, its corresponding torque, or net force, is becoming the resultant force and affects the object's rotational motion.

This is because the two forces acting on the block (the 10 Newton force to the right and the 10 Newton force to the left) are equal in magnitude, thus canceling each other out. Therefore, the net force on the block is zero Newtons.

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Effect it will have on its pull on mars will be twice as much

On average, the Sun is 93 million miles from Earth, but it is still essential to sustaining life as we know it.

If it were to decrease, grow, or change in any way, we would undoubtedly see significant changes in our lives.

The majority of people concur that the solar system's central star, the sun, is the source of the energy that powers planet Earth.

The light and heat that our star emits, which also contribute to the emergence of life on Earth, are used to build our climate and weather systems.

The length of a year is also influenced by the sun's gravitational pull, which is subject to our control.

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The resistance of the wire with a diameter of 4.3 mm and a length of 8.1 m is 9.14*10⁻³ Ω

Resistance is defined as a refusal to give up to something that prevents or slows down anything. A child fighting her abductor is an example of resistance. An example of resistance is the wind pushing up against an airplane's wings.

We can calculate the resistance as follows:

R = 1/σ . L / A, where:

l is the wire's length, σ is the electrical conductivity, and A is its cross-section (assumed circular).

By modifying the values, we may determine R as follows:

R = 1/6.1. 10⁷ (Ω.m) . 8.1 m. / π (0.0043)² m / 4

= 9.14 . 10⁻³ Ω

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The complete question is-

For a metal that has an electrical conductivity of 6.1 × 10⁷ (Ω∙m)⁻¹, what is the resistance of a wire that is 4.3 mm in diameter and 8.1 m long?

(A) 3.93 × 10⁻⁵ Ω

(B) 2.29 × 10⁻³ Ω

(C) 9.14 × 10⁻³ Ω

(D) 1.46 × 10¹¹ Ω

The magnitude of the net electric field at the origin is kq/a².

What is magnitude?
The magnitude as well as size of a statistical model determines whether it is bigger or smaller than some other objects of the same type in mathematics. Formally speaking, the magnitude of an object is the result of the group of objects it belongs to being ordered (or ranked) and displayed. Magnitude in physics can be interpreted as either a quantity or a distance.

The magnitude of the net electric field at the origin produced by this distribution of charge is given by the equation E = kq/a², where k is a constant, q is the charge, and a is the distance between the origin and the charge. Thus, the magnitude of the net electric field at the origin is kq/a².

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In case of node to node, the message travels faster. Our brain can exchange signals with our toes in a few thousandths of a second by jumping signals hundreds of times quicker than signals that travel along the surface of the axon.

The speed of nerve impulse conduction is accelerated by the presence of a myelin sheath. Similar unmyelinated axons conduct impulses about ten times slower than myelinated ones do.

Action potentials "jump" from node to node as they move down the axon. The term saltatory conduction, which means "to leap," describes this. Moving in an axon with myelin is slower than traveling along an axon through saltatory conduction.

E. myelinated neurons conduct impulses at the quickest speeds. A fatty layer called myelin surrounds the neuronal axon. When compared to continuous conduction on unmyelinated axons, saltatory conduction on myelinated axons is a faster and more energy-efficient type of impulse conduction.

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Discoveries that burning coal changes the climate by increasing the levels of carbon in the atmosphere provide evidence that a warming planet is related to human behavior, which causes global warming.

What is Global Warming?

The heating of the earth's surface is due to an increase in carbon content and another pollutant in the atmosphere that, traps the heat being radiated back by the earth's surface, which in turn increases the temperature.

What are pollutants?

Pollutants are a substance that increases the toxicity of something, such as air, water, land, etc., and thus contributes to pollution.

what is pollution?

Pollution is the contamination of the environment by toxic substances, such as nitrogen oxide, carbon monoxide, Ground level ozone, etc. that increase the toxicity of the environment and are hazardous for living organisms.

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The magnitude of the force of the person on the elevator floor is 435.2 N.

The magnitude of the force of the person on the elevator floor is calculated by applying Newton's second law of motion as shown below.

F(net) = ma

where;

For downward motion in an elevator, the force acting on the elevator's floor is given as;

F = mg - ma

F = m(g - a)

where;

F = 64 (9.8 - 3)

F = 435.2 N

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The installation of baghouse filters in exhaust systems is Particulate matter.

The exhaust system gathers the cylinder exhaust gases, filters out dangerous materials, lowers the noise level, and then releases the cleaned exhaust gases to an appropriate location of the vehicle away from the occupants. Depending on the engine, the exhaust system may have one or two channels.

The majority of people are aware that an exhaust system eliminates the dangerous gases your engine produces, however exhaust systems also perform a lot more functions! The four primary purposes of your vehicle's exhaust system are to reduce fuel consumption, move gases away, reduce noise, and increase engine performance.

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If a sample of an ideal monatomic gas is confined in a rigid 0.008 m3 container. if 40 joules of heat energy were added to the sample, how much would the pressure increase by 3,333 Pa only.

Correct option is (D) i.e., 3,333 Pa

At constant volume

∆U = Q = 3/2nR∆T

where in an isochoric process

nR∆T = ∆pV

so Q = 3/2 ∆pV

or

∆p = 2 × +40J/3 × 0.008 m3.

"monatomic" is a combination of the words "mono" and "atomic", and means "single atom". It is usually applied to gases: a monatomic gas is a gas in which atoms are not bound to each other.

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They estimate dates by counting the number of craters visible on the surface and comparing crater counts to other worlds.

Crater counting is a technique for determining the age of a planet's surface based on the suppositions that impact craters are absent from freshly formed planetary surfaces and that they collect through time at a known pace.

The density of craters on a planet's surface can be used to estimate the relative ages of various regions; the older the surface, the more craters it has accumulated.

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3.5*10^-5 N/m  is the magnitude of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A current and the force on each wire will be repulsive.

The number which shows or represents the strength  of the force is termed as the magnitude of that force.

Data given :

Two parallel wires

35 m long and 7.0 cm apart,

each carrying 35 A  current .

To find the magnitude and direction of current.

f=μ/4π*2[tex]I_{1}[/tex][tex]I_{2}[/tex]/d

f=[tex]10^{-7}[/tex]*2*35*35/7

f=3.5*10^-5

​Hence, 3.5*10^-5 N is the magnitude of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A current.

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A block moving due east collide with a block moving due west. The set of directions that is not possible after the collision is (c) One block travels northeast, and the other block travels northwest.

This problem can be solved using the law of conservation of momentum, which states the total momentums before and after collision of two objects are the same. Mathematically,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where:

m = mass

u = initial velocity

v = final velocity

In the given problem, one block is moving due east, and the other block is moving due west. Hence, before the collision, both objects only have velocity in horizontal components and no vertical components. Therefore, after the collision, the resultant of the velocity should also have only the horizontal component.

a. Both blocks are travelling east after the collision <---- it is possible since both objects only have horizontal component

b. Both blocks are traveling west after the collision.<---- it is possible since both objects only have horizontal component

c. One block travels northeast, and the other block travels northwest.  In this case, the components of northeast velocity is due north and due east, while the components of northwest velocity is due north and due west. The resultant of velocity will have vertical (north) component, hence this set of direction is not possible.

d. One block travels southwest, and the other block travels northeast. This is possible, since the north component can be cancelled out by the south component, resulting in horizontal component only.

e. One block travels southeast, and the other block travels northwest.

This is possible, since the north component can be cancelled out by the south component, resulting in horizontal component only.

Therefore, the set of directions that is not possible is (c) One block travels northeast, and the other block travels northwest.

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The average angular acceleration of a Ferris wheel with final angular speed 1.9 rad/s and angular displacement 4.9 rad  is 0.37 radians per square second.

What is angular displacement ?

The angle at which a point revolves around a particular axis or centre defines the angular displacement of a body. Because a body rotates about its axis, its motion cannot simply be analysed as a particle because it is constantly altering its speed and acceleration.

According to the given information

Angular speed = 1.9 rad/s

Angular displacement= 4.9 rad

Let the Ferris wheel accelerates at constant rate,then

[tex]w^{2} = w{o} ^2 + 2.\alpha .[/tex] (θ - θo)

given that

[tex]w_{0 }[/tex] = 0 rad/s

[tex]w[/tex] = 1,.9 rad/s

θ - θo = 4.9 rad

α = [tex](1.9 rad/s)^{2} - (0 rad/s)^{2} / 2. (4.9 rad )[/tex]

α = 0.37 [tex]rad/s^{2}[/tex]

The time needed to accelerate the Ferris wheel uniformly is given by-

[tex]w = w_{0} + \alpha .t[/tex]

t = [tex]1.9 - 0 / 0.37[/tex]

t = 5.13 sec

now average angular velocity = [tex]\frac{w - w_{0} }{t}[/tex]

[tex]\alpha _{avg}[/tex] = 1.9- 0/ 5.13

= 0.37 [tex]rad/s^{2}[/tex]

The average angular acceleration of the ferris wheel is = 0.37 [tex]rad/s^{2}[/tex].

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Answer:How many moles of water are in one mole of the substance?

Explanation:

Mole measure the number of elementary entities of a given substance that are present in a given sample. Therefore, "How many moles of water are in one mole of the substance".

The SI unit of amount of substance in chemistry is mole. The mole is used to measure the quantity or amount of substance. We know one mole of any element contains 6.022×10²³ atoms which is also called Avogadro number.

Mathematically,

mole =given mass ÷ molar mass

A student finds the mass of a pure sample of a metal chloride hydrate. the student heats the sample several times, reaching a constant mass that contains 0.100 mole of anhydrous metal chloride. The most important question that can be asked from this experiment is "How many moles of water are in one mole of the substance".

Therefore, "How many moles of water are in one mole of the substance".

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It is only necessary to know the direction of two of the three rays in order to graphically depict the formation of an image in a thin lens with virtual image.

(i)  The one that strikes the lens perpendicular to the optical axis of the lens is one of them. When this is refracted in the lens, the image focus will not be affected. Its trajectory won't be altered by this.

(ii)  The third and final one is the one that crosses the object focus (or its extension does), which, following refraction, will move in a direction parallel to the optical axis of the lens.

Accordingly, depending on how an object or body is positioned in relation to the lens, one type of image will generally be formed in the lenses. The image will always be virtual, smaller than the body, and to the right in divergent lenses.

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The time it takes the clock's minute hand to make one revolution on the moon is (1.631.63/9.8)^2 * 60 minutes, or roughly 1.4 hours.

What is revolution?
When the populace rebels against the government, usually because of perceived oppression (ideological, social, or economic), or political incompetence, a revolution is defined in political science as a fundamental and comparatively unexpected change in political politics and influence organisation.

The period of a pendulum is determined by the equation T = 2π√(L/g), where T is the time it takes for the pendulum to make one complete oscillation, L is the length of the pendulum, and g is the acceleration due to gravity. Thus, on the moon, the period of the pendulum is T = 2π√(L/1.631.63 m/s2).

On Earth, the period of a pendulum is T = 2π√(L/9.8 m/s2). Thus, the ratio between the period on the moon and the period on Earth is T_moon/T_Earth = (2π√(L/1.631.63 m/s2))/(2π√(L/9.8 m/s2)) = sqrt(1.631.63/9.8).

Since the period of the pendulum is related to the time it takes for the clock's minute hand to make one revolution, the ratio between the time it takes the clock's minute hand to make one revolution on the moon and the time it takes the clock's minute hand to make one revolution on Earth is (T_moon/T_Earth)^2 = (1.631.63/9.8)^2.

Therefore, the time it takes the clock's minute hand to make one revolution on the moon is (1.631.63/9.8)^2 * 60 minutes, or roughly 1.4 hours.

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The circuit containing the inductor experiences the greatest increase in current.

A passive electrical component known as an inductor stores energy as a magnetic field. An inductor is basically just a coil or loop of wire. The number of turns in the coil directly relates to the inductance. The radius of the coil and the kind of material it is looped around both affect inductance.

An inductor is distinguished by its unique inductance, which is defined as the ratio of voltage to current change rate. The magnetic field that is induced on the coil causes inductance.

The following are the main uses of inductors in electrical power and electronic equipment: In electrical circuits, choking, blocking, attenuating, or smoothing out high frequency noise are all possible solutions. using power converters to store and move energy (dc-dc or ac-dc).

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Neither, the spheres reach the floor at the same time.

Why does mass not matter during freefall?

After a period of time spent in free fall, the object will achieve terminal velocity, at which point the force propelling it through the atmosphere towards the ground will be equal to the air friction, which grows with speed. Given that both objects accelerate in the same manner (assuming equal forms), we can infer that the heavier object's terminal velocity will be higher than that of a lighter object because it must reach a higher speed for the air friction to catch up with the heavier weight (G) (same shape). The heavier object will still strike the ground first if there is enough time because it will accelerate for a longer period of time and maintain a higher speed.

Hence, the answer is, Neither, the spheres reach the floor at the same time.

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