What would be the linear velocity of a boy's toes doing a cartwheel who is 2.1 m long from the tip of his toes to the end of his fingers and who is experiencing a centripetal force of 5.0 m/s2?

Answer:

Explanation: Correct on Edg 2020/2021 for my school.

Answer:

John applied a force of approximately \(795\; {\rm N}\) (on average, rounded) on Lucy.

John slows down to a stop after approximately another \(5.37\; {\rm s}\).

(Assuming that \(g = 9.81\; {\rm N\cdot kg^{-1}}\).)

Explanation:

Assuming that the surface is level. The normal force on Johnny will be equal to the weight of Johnny: \(N(\text{John}) = m(\text{John})\, g\). Similarly, the normal force on Lucy will be equal to weight \(N(\text{Lucy}) = m(\text{Lucy})\, g\).

Multiply normal force by the coefficient of kinetic friction to find the friction on each person:

\(f(\text{John}) = \mu_{k}\, N(\text{John}) = \mu_{k}\, m(\text{John})\, g\).

\(f(\text{Lucy}) = \mu_{k}\, N(\text{Lucy}) = \mu_{k}\, m(\text{Lucy})\, g\).

Again, because the surface is level, the net force on each person after the first \(1.0\; {\rm s}\) will be equal to the friction. Divide that the net force on each person by the mass of that person to find acceleration:
\(\displaystyle a(\text{John}) = \frac{\mu_{k}\, m(\text{John})\, g}{m(\text{John})} = \mu_{k}\, g\).

\(\displaystyle a(\text{Lucy}) = \frac{\mu_{k}\, m(\text{Lucy})\, g}{m(\text{Lucy})} = \mu_{k}\, g\).

(Note that the magnitude of acceleration is independent of mass and is the same for both John and Lucy.)

\(a = \mu_{k}\, g= (0.2)\, (9.81\; {\rm m\cdot s^{-2}}) = 1.962\; {\rm m\cdot s^{-2}}\).

In other words, after the first \(1\; {\rm s}\), both John and Lucy will slow down at a rate of \(1.962\; {\rm m\cdot s^{-2}}\).

To find the speed of Lucy immediately after the first \(1.0\: {\rm s}\), multiply this acceleration by the time \(t = 8.0\; {\rm s}\) it took for Lucy to slow down to \(0\; {\rm m\cdot s^{-1}}\):

\(\begin{aligned}& (8.0\; {\rm s})\, (1.962\; {\rm m\cdot s^{-2}}) \\ =\; & (8.0)\, (1.962)\; {\rm m\cdot s^{-1}} \\ =\; & 15.696\; {\rm m\cdot s^{-1}}\end{aligned}\).

Thus, in the first \(1.0\; {\rm s}\), Lucy accelerated (from \(0\; {\rm m\cdot s^{-1}}\)) to \(15.696\; {\rm m\cdot s^{-1}}\).

The average acceleration of Lucy in the first \(1.0\; {\rm s}\) would be \((15.696) / (1) = 15.696\; {\rm m\cdot s^{-2}}\). Multiply this average acceleration by the mass of Lucy to find the average net force on Lucy during that \(1.0\; {\rm s}\):

\(\begin{aligned}F_{\text{net}}(\text{Lucy}) &= m(\text{Lucy})\, a \\ &= (45)\, (15.696)\; {\rm N} \\ &= 706.320\; {\rm N}\end{aligned}\).

This net force on Lucy during that \(1.0\; {\rm s}\) is the combined result of both the push from Johnny and friction:

\(F_{\text{net}}(\text{Lucy}) = F(\text{push}) - f(\text{Lucy})\).

Since \(f(\text{Lucy}) = \mu_{k}\, N(\text{Lucy}) = \mu_{k}\, m(\text{Lucy})\, g\):

\(\begin{aligned}F(\text{push}) &= F_{\text{net}}(\text{Lucy}) + f(\text{Lucy}) \\ &= F_{\text{net}}(\text{Lucy}) + \mu_{k}\, m(\text{Lucy})\, g \\ &= (706.320) \; {\rm N}+ (0.2)\, (45)\, (9.81)\; {\rm N} \\ &= 706.320\; {\rm N} + 88.290\; {\rm N} \\ &=794.610\; {\rm N}\end{aligned}\).

In other words, Johnny would have applied a force of \(794.610\; {\rm N}\) on Lucy.

By Newton's Laws of Motion, when Johnny exerts this force on Lucy in that \(1.0\; {\rm s}\), Lucy would exert a reaction force on Johnny of the same magnitude: \(794.610\; {\rm N}\).

Similar to Lucy, the net force on Johnny during that \(1.0\; {\rm s}\) will be the combined effect of the push \(F(\text{push})\) and friction \(f(\text{John}) = \mu_{k}\, m(\text{John})\, g\):

\(\begin{aligned}F_{\text{net}}(\text{John}) &= F(\text{push}) - f(\text{John}) \\ &= F(\text{push}) - \mu_{k}\, m(\text{John})\, g\\ &= 794.610\; {\rm N} - (0.2)\, (65)\, (9.81)\; {\rm N} \\ &= 667.080\; {\rm N}\end{aligned}\).

Divide net force by mass to find acceleration:

\(\begin{aligned}\frac{667.080\; {\rm N}}{65\; {\rm kg}} \approx 10.2628\; {\rm m\cdot s^{-2}}\end{aligned}\).

In other words, Johnny accelerated at a rate of approximately \(10.5406\; {\rm m\cdot s^{-2}}\) during that \(1.0\; {\rm s}\). Assuming that Johnny was initially not moving, the velocity of Johnny right after that \(1.0\; {\rm s}\!\) would be:

\((0\; {\rm m\cdot s^{-1}}) + (10.2628\; {\rm m\cdot s^{-2}})\, (1.0\; {\rm s}) = 10.2628\; {\rm m\cdot s^{-1}}\).

After the first \(1.0\; {\rm s}\), the acceleration of both John and Lucy (as a result of friction) would both be equal to \(a = \mu_{k}\, g= (0.2)\, (9.81\; {\rm m\cdot s^{-2}}) = 1.962\; {\rm m\cdot s^{-2}}\). Divide initial velocity of Johnny by this acceleration to find the time it took for Johnny to slow down to a stop:

\(\displaystyle \frac{10.2628\; {\rm {m\cdot s^{-1}}}}{1.962\; {\rm m\cdot s^{-2}}} \approx 5.23\; {\rm s}\).

Answer:

John applied a force of approximately \(795\; {\rm N}\) (on average, rounded) on Lucy.

John slows down to a stop after approximately another \(5.37\; {\rm s}\).

(Assuming that \(g = 9.81\; {\rm N\cdot kg^{-1}}\).)

Explanation:

Assuming that the surface is level. The normal force on Johnny will be equal to the weight of Johnny: \(N(\text{John}) = m(\text{John})\, g\). Similarly, the normal force on Lucy will be equal to weight \(N(\text{Lucy}) = m(\text{Lucy})\, g\).

Multiply normal force by the coefficient of kinetic friction to find the friction on each person:

\(f(\text{John}) = \mu_{k}\, N(\text{John}) = \mu_{k}\, m(\text{John})\, g\).

\(f(\text{Lucy}) = \mu_{k}\, N(\text{Lucy}) = \mu_{k}\, m(\text{Lucy})\, g\).

Again, because the surface is level, the net force on each person after the first \(1.0\; {\rm s}\) will be equal to the friction. Divide that the net force on each person by the mass of that person to find acceleration:
\(\displaystyle a(\text{John}) = \frac{\mu_{k}\, m(\text{John})\, g}{m(\text{John})} = \mu_{k}\, g\).

\(\displaystyle a(\text{Lucy}) = \frac{\mu_{k}\, m(\text{Lucy})\, g}{m(\text{Lucy})} = \mu_{k}\, g\).

(Note that the magnitude of acceleration is independent of mass and is the same for both John and Lucy.)

\(a = \mu_{k}\, g= (0.2)\, (9.81\; {\rm m\cdot s^{-2}}) = 1.962\; {\rm m\cdot s^{-2}}\).

In other words, after the first \(1\; {\rm s}\), both John and Lucy will slow down at a rate of \(1.962\; {\rm m\cdot s^{-2}}\).

To find the speed of Lucy immediately after the first \(1.0\: {\rm s}\), multiply this acceleration by the time \(t = 8.0\; {\rm s}\) it took for Lucy to slow down to \(0\; {\rm m\cdot s^{-1}}\):

\(\begin{aligned}& (8.0\; {\rm s})\, (1.962\; {\rm m\cdot s^{-2}}) \\ =\; & (8.0)\, (1.962)\; {\rm m\cdot s^{-1}} \\ =\; & 15.696\; {\rm m\cdot s^{-1}}\end{aligned}\).

Thus, in the first \(1.0\; {\rm s}\), Lucy accelerated (from \(0\; {\rm m\cdot s^{-1}}\)) to \(15.696\; {\rm m\cdot s^{-1}}\).

The average acceleration of Lucy in the first \(1.0\; {\rm s}\) would be \((15.696) / (1) = 15.696\; {\rm m\cdot s^{-2}}\). Multiply this average acceleration by the mass of Lucy to find the average net force on Lucy during that \(1.0\; {\rm s}\):

\(\begin{aligned}F_{\text{net}}(\text{Lucy}) &= m(\text{Lucy})\, a \\ &= (45)\, (15.696)\; {\rm N} \\ &= 706.320\; {\rm N}\end{aligned}\).

This net force on Lucy during that \(1.0\; {\rm s}\) is the combined result of both the push from Johnny and friction:

\(F_{\text{net}}(\text{Lucy}) = F(\text{push}) - f(\text{Lucy})\).

Since \(f(\text{Lucy}) = \mu_{k}\, N(\text{Lucy}) = \mu_{k}\, m(\text{Lucy})\, g\):

\(\begin{aligned}F(\text{push}) &= F_{\text{net}}(\text{Lucy}) + f(\text{Lucy}) \\ &= F_{\text{net}}(\text{Lucy}) + \mu_{k}\, m(\text{Lucy})\, g \\ &= (706.320) \; {\rm N}+ (0.2)\, (45)\, (9.81)\; {\rm N} \\ &= 706.320\; {\rm N} + 88.290\; {\rm N} \\ &=794.610\; {\rm N}\end{aligned}\).

In other words, Johnny would have applied a force of \(794.610\; {\rm N}\) on Lucy.

By Newton's Laws of Motion, when Johnny exerts this force on Lucy in that \(1.0\; {\rm s}\), Lucy would exert a reaction force on Johnny of the same magnitude: \(794.610\; {\rm N}\).

Similar to Lucy, the net force on Johnny during that \(1.0\; {\rm s}\) will be the combined effect of the push \(F(\text{push})\) and friction \(f(\text{John}) = \mu_{k}\, m(\text{John})\, g\):

\(\begin{aligned}F_{\text{net}}(\text{John}) &= F(\text{push}) - f(\text{John}) \\ &= F(\text{push}) - \mu_{k}\, m(\text{John})\, g\\ &= 794.610\; {\rm N} - (0.2)\, (65)\, (9.81)\; {\rm N} \\ &= 667.080\; {\rm N}\end{aligned}\).

Divide net force by mass to find acceleration:

\(\begin{aligned}\frac{667.080\; {\rm N}}{65\; {\rm kg}} \approx 10.2628\; {\rm m\cdot s^{-2}}\end{aligned}\).

In other words, Johnny accelerated at a rate of approximately \(10.5406\; {\rm m\cdot s^{-2}}\) during that \(1.0\; {\rm s}\). Assuming that Johnny was initially not moving, the velocity of Johnny right after that \(1.0\; {\rm s}\!\) would be:

\((0\; {\rm m\cdot s^{-1}}) + (10.2628\; {\rm m\cdot s^{-2}})\, (1.0\; {\rm s}) = 10.2628\; {\rm m\cdot s^{-1}}\).

After the first \(1.0\; {\rm s}\), the acceleration of both John and Lucy (as a result of friction) would both be equal to \(a = \mu_{k}\, g= (0.2)\, (9.81\; {\rm m\cdot s^{-2}}) = 1.962\; {\rm m\cdot s^{-2}}\). Divide initial velocity of Johnny by this acceleration to find the time it took for Johnny to slow down to a stop:

\(\displaystyle \frac{10.2628\; {\rm {m\cdot s^{-1}}}}{1.962\; {\rm m\cdot s^{-2}}} \approx 5.23\; {\rm s}\).

The shift in fringes is equal to 1. This means that the position of the fringes has shifted by one full fringe.

A Michelson interferometer is a type of interferometer that divides a wavefront by splitting a beam of light into two perpendicular paths.

By combining these waves, interference occurs, resulting in a pattern of bright and dark fringes known as an interferogram.

Therefore, let’s find the shift in fringes when the mirror of Michelson Interferometer is moved a length equal to the wavelength of the incident light.

First, it is important to note that the number of fringes observed in an interferometer depends on the wavelength of light being used, as well as the path difference between the two beams.

The following equation is used to calculate the number of fringes shifted:ΔN = ΔL/λwhere:ΔN = number of fringes shiftedΔL = distance moved by the mirrorλ = wavelength of light.

When the mirror is moved a distance equal to the wavelength of the incident light, the path difference between the two beams is equal to one wavelength.

Thus, there will be a shift of one fringe as a result.

Substituting the values into the equation, we have:ΔN = (1λ)/λΔN = 1

Therefore, the shift in fringes is equal to 1.

This means that the position of the fringes has shifted by one full fringe.

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Answer:s

Explanation:

Answer:

78.34

Explanation:

1.3/30=78.3m

Answer:

A.

Explanation:

Because your throwing something or adding force to it to make it go somewhere.

it takes a light from a flash camera to reach a subject 6.0 meters across a room in scientific notation is 2.0 *10^-8 seconds.

we apply the  equation shown below:

v=d/t

where t= time

d = distance

v = velocity

Therefore  time =distance /velocity

distance =6m

v=3*10^8 m/s

time =6m/3*10^8 m/s

time =2*10^-8 seconds

Therefore,  the time it takes light from a flash camera to reach a subject 6.0 meters across a room in scientific notation is 2.0 *10^-8 seconds

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Within 20 nanoseconds, photo subjects standing at a distance of 6.0 metres receive the flash from the camera.

The speed of light, a rate equal to an estimated 3 x 10^8 meters per second, determines the amount of time it takes for light to travel from the flash camera's source to a subject standing six meters away.

Employing the formula

Speed = distance / time

Then

time = distance / speed

where

distance  = 6.0 meters and

speed = 3 x 10^8

time = 6.0 / 3 x 10^8

time = 2 x 10^-8

time = 20.0 nanoseconds

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Answer:

70 km/h

Explanation:

70 divided by 2 = 35

In the case,  the mass and buoyant force acting on the balloon is 35260 N, the acceleration of the balloon is 3.4 m/s², and minimum volume the balloon can have before it goes downward instead of upward is 421 m³.

The parameters are:

Density of normal air = 1.22 kg/m3

Density of hot air in balloon = 0.95 kg/m3

Total volume of the hot air balloon = 3000 m3

Mass of basket and riders = 400 kg

Part (A)

First, we need to find the mass of the air inside the balloon. We can find it by multiplying the density by volume.

m = ρV

Now, let's calculate the mass of air inside the balloon using the given parameters.

m = (0.95 kg/m3) (3000 m3) = 2850 kg

Now, let's find the buoyant force acting on the balloon. We can find it by subtracting the weight of the air displaced by the balloon from the weight of the balloon and air inside it.

Buoyant force = weight of balloon + weight of air inside balloon - weight of air displaced by balloon

Buoyant force = (m + M)g - Mg

where, m = mass of air inside balloon

M = mass of basket and riders

g = acceleration due to gravity

Mg = weight of basket and riders

Buoyant force = (2850 + 400) (9.8) - (2850) (9.8) = 35260 N

Part (B)

The net force acting on the balloon is given by

Net force = buoyant force - weight of balloon - weight of basket - weight of riders

Net force = 35260 - (3000) (1.22) (9.8) - (400) (9.8) = 11762 N

Now, let's find the acceleration of the balloon. We can use the formula,

F = ma

or

a = F/m

where,

F = net force acting on the balloon

a = acceleration

m = total mass of the balloon and riders

a = (11762) / (2850 + 400) = 3.4 m/s2

Therefore, the acceleration of the balloon is 3.4 m/s².

Part (C)

To find the minimum volume of the balloon, we can use the formula,

Buoyant force = weight of balloon + weight of air inside balloon - weight of air displaced by balloon

Buoyant force = 0

We know that when buoyant force is zero, the balloon starts moving downward. So, to find the minimum volume, we need to find the volume of the balloon when the buoyant force is zero. Let's assume that the mass of the basket and riders remains the same

m = ρV

Now, let's find the volume of air inside the balloon that will cause the buoyant force to become zero.

m = ρVV = m / ρV = 400 / 0.95V = 421 m3

Therefore, the minimum volume of the balloon when it starts moving downward is 421 m³.

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Answer:

Distance, S = 13m

Explanation:

Given the following data;

Initial velocity, u = 4m/s

Final velocity, v = 9m/s

Time, t = 2 seconds

To find the distance, S;

First of all, we would determine the acceleration of the shark.

Acceleration = (v - u)/t

Acceleration = (9 - 4)/2

Acceleration = 5/2

Acceleration = 2.5m/s²

Now, to find the distance we would use the second equation of motion

S = ut + ½at²

Substituting into the equation, we have

S = 4(2) + ½*2.5*2²

S = 8 + 1.25*4

S = 8 + 5

Distance, S = 13m

did you end up getting the answer- im struggling

Answer:

I would think human error could cause differences like not pressing the stop watch on time.

Explanation:

Answer:

The strength of a magnet is determined by various factors such as the material used, shape and size of the magnet, distance between the magnet and the object it attracts, temperature, and external magnetic fields. The type of material used greatly affects its strength, with materials like neodymium and samarium cobalt being some of the strongest magnets available. Shape and size of the magnet also play a role, with larger magnets having greater strength. The distance between the magnet and the object it attracts affects the strength of attraction, as does temperature. External magnetic fields can also weaken a magnet's strength by altering its alignment.

Explanation:

Answer:

1.It allows for movement.

2.t controls the breathing rate.

4. It controls the heart rate.

Explanation:

Answer:

1629 metres

Explanation:

Given that Carlos runs with velocity v = (5.6 m/s, 29o north of east) for 10 minutes.

To the north, the velocity will be:

V = 5.6 × sin 29

V = 2.715 m/s

Convert the time to second

Time = 10 × 60 = 600

Using the formula below

Velocity = distance/ time

Substitute all the parameters into the formula

2.715 = distance/600

Distance = 2.715 × 600

distance = 1629 m

Any ellipse is drawn that connects the poles and is used to measure angular distance east and west is the definition of a meridian.

The definition you are referring to is that of a meridian, an imaginary great circle on the Earth's surface that passes through the North and South Poles and any point on the Earth's surface.

The meridian is used as a reference for measuring longitude, which is the angular distance east or west of the Prime Meridian. This meridian passes through the Royal Observatory in Greenwich, England.

A meridian is an imaginary line or circle that passes through the North and South Poles and any point on the Earth's surface. A meridian is used as a reference line for measuring longitude, the angular distance east or west of the Prime Meridian. This meridian passes through the Royal Observatory in Greenwich, England.

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Answer:

The parallel plate capacitor is the simplest form of capacitor. ... The property of a capacitor to store charge on its plates in the form of an electrostatic field is called the Capacitance of the capacitor. Not only that, but capacitance is also the property of a capacitor which resists the change of voltage across it.

Explanation:

credits :- adultsscience

Explanation:

Capacitance exists wherever conductive material is separated by insulating material. 

Capacitive structures have the ability to store energy as an electric field;

when a capacitive structure has been designed as an electrical component that has a specified amount of capacitance, it is called a capacitor.

Capacitance symbol is C

you can get a meter for Capacitance

Capacitance formula is C = ε(A/d) where ε represents the absolute permittivity of the dielectric material being used.

simple piece of wire has very low capacitance

Answer:

aye son yall think if i keep answering these questions incorrectly.. they'll find out what im doing and take my li points back?

Explanation:

The final volume of water in the container after increasing the temperature is 203.8 m³.

From the given,

The initial volume of water (Vο) = 200 cm³

Initial temperature = 4°C = 4+273 = 277K

Final temperature = 95°C = 273+95 = 368 K

Volume expansion co-efficient = 210×10⁻⁶(°C)⁻¹

Final volume =?

β = 1/Vο (ΔV/ΔT),  β represents the volume expansion coefficient, ΔV change in volume, ΔT is the change in temperature, and Vο is the initial volume.

ΔV = β×Vο×ΔT

     = 210×10⁻⁶×200×(368-277)

    =  210×10⁻⁶×200×91

ΔV = 3.83 m³

ΔV = final volume - initial volume

final volume = ΔV + 200

                    = 3.82 +200

                    = 203.82 m³

Final volume = 203.82 m³.

Thus, the final volume of the water is 203.82 m³.

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Answer:

High current flow

Explanation:

Generally , the measuring instruments used by technician also have some resistance, though its value is very low  . So when high current is present in the circuit , that current also passes through the instrument which creates a good potential drop across the instrument . So the external voltage used in the circuit measures less voltage .

The factors that affect the flow of electric charge will be Voltage and resistance.

The flow of the charge depends upon the voltage because the voltage is responsible to push or it applies the force on the particles to flow.

For example, whenever your battery gets discharged what happens is the potential difference of voltage becomes zero.

So there will not be enough force remaining in the battery to flow the charge but when we charge the battery then it regains its voltage and again pushes the charges to flow.

Now the resistance acts just opposite to the voltage because it restricts the flow of the charges so if the resistance is more then more voltage is required to flow the charge.

Thus the factors that affect the flow of electric charge will be Voltage and resistance.

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This question involves the concepts of projectile motion.

The maximum height to which the ball rose is "3.14 m".

The motion of an object in both x and y axes simultaneously is known as projectile motion. The total time of flight of the projectile is given by the following formula:

\(T=\frac{2v_oSin\theta}{g}\\\\v_oSin\theta=\frac{Tg}{2}\)

where,

Therefore,

\(v_oSin\theta = \frac{(1.6\ s)(9.81\ m/s^2)}{2}\\\\v_oSin\theta = 7.848\ m/s\\\)

Now, using the formula for the maximum height of the projectile, we get:

\(H=\frac{v_o^2Sin^2\theta}{2g}\\\\H= \frac{(7.848\ m/s)^2}{2(9.81\ m/s^2)}\)

H = 3.14 m

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Answer:

We have the position vector given in terms of time t. r(t) = t^3*i + t^2*j

To find the velocity vector we have to differentiate r(t) with respect to time.

r'(t) = 3t^2*i + 2t*j

The vector representing acceleration is the derivative of the position vector

r''(t) = 6t*i + 2*j

When time t = 2.

The velocity vector is 3*2^2*i + 2*2*j

=> 12*i + 4*j

The speed is the absolute value of the velocity vector or sqrt(12^2 + 4^2) = sqrt (144 + 16) = sqrt 160

The acceleration vector is 6*2*i + 2*j

=> 12*i + 2*j

The required acceleration at t=2 is 12*i + 2*j and the speed is sqrt 160.

Explanation:

Can I have thx and brainliest?

Answer:

The law of gravity

Explanation:

The correct answer is C. The magnitude of the magnetic field at the center of a circle wire with a linear charge density rotating at a constant angular speed is B = μ₀ωλ/2R.

To understand why this is the correct answer, we can analyze the situation using the Biot-Savart Law. The Biot-Savart Law states that the magnetic field created by a small segment of current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.

In this case, the circular wire is rotating at a constant angular speed, which means there is a current flowing through it. The linear charge density (λ) represents the charge per unit length of the wire. As the wire rotates, each point on the wire moves with the same angular speed, resulting in a circular current distribution.

When we calculate the magnetic field at the center of the circle wire, we find that it is directly proportional to the angular speed (ω), the linear charge density (λ), and the permeability of free space (μ₀), and inversely proportional to the radius of the wire (R). The factor of 1/2 arises from the geometric distribution of the current around the circle.

Therefore, the correct answer is C. B = μ₀ωλ/2R, which represents the magnitude of the magnetic field at the center of the rotating circle wire.

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(a)The maximum uncertainty in the horizontal position is 1.75 m / 2 = 0.875 m.(b)The minimum uncertainty in the horizontal velocity of the marble is approximately 2.38 x 10^-33 m/s.(c)it does not provide information about the actual velocity of the marble. (d)the longest time the marble could remain on the table is 7.35 x 10^32 seconds.

The Heisenberg uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously. Let's address the questions based on this principle:

(a) To determine the maximum uncertainty in the horizontal position of the marble, we need to consider the width of the tabletop. The maximum uncertainty in position can be estimated as half the width of the tabletop, since the marble can be anywhere within that range. Therefore, the maximum uncertainty in the horizontal position is 1.75 m / 2 = 0.875 m.

(b) According to the Heisenberg uncertainty principle, the product of the uncertainties in position and momentum is greater than or equal to a certain minimum value. Mathematically, it is expressed as Δx * Δp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the reduced Planck's constant (approximately 6.626 x 10^-34 J·s). In this case, we're interested in the uncertainty in the horizontal velocity, which is related to momentum.

The mass of the marble is given as 10.0 g, which is equivalent to 0.01 kg. Since the marble is gently placed on the tabletop, we can assume a negligible initial momentum. Therefore, we can estimate the minimum uncertainty in horizontal velocity (Δv) as follows:

Δx * Δp ≥ h/4π

Δx * m * Δv ≥ h/4π

Δv ≥ h/4π(m * Δx)

Substituting the values, Δx = 0.875 m and m = 0.01 kg, we can calculate the minimum uncertainty in horizontal velocity:

Δv ≥ (6.626 x 10^-34 J.s) / (4π * (0.01 kg) * (0.875 m))

Δv ≥ 2.38 x 10^-33 m/s

Therefore, the minimum uncertainty in the horizontal velocity of the marble is approximately 2.38 x 10^-33 m/s.

(c) The uncertainty principle tells us that the product of the uncertainties in position and momentum (or velocity) has a lower limit. Since the minimum uncertainty in the horizontal velocity is non-zero, it implies that the marble cannot have an exactly zero horizontal velocity. However, it does not provide information about the actual velocity of the marble.

(d)To estimate the longest time the marble could remain on the table, we can calculate the time it would take for the marble to traverse the entire width of the tabletop with its minimum uncertainty velocity. Assuming a constant velocity, we can use the equation:

Time = Distance / Velocity

Time = 1.75 m / (2.38 x 10^-33 m/s)

Time ≈ 7.35 x 10^32 seconds

Comparing this time to the age of the universe (approximately 14 billion years), we find that the time it would take for the marble to traverse the tabletop is incredibly long. In fact, it is many orders of magnitude larger than the age of the universe, indicating that the marble could essentially remain on the table indefinitely from a practical perspective.

However, it's important to note that this analysis is based on the fundamental principles of quantum mechanics and the uncertainty principle. In classical physics, the marble would come to rest due to friction and other factors. The uncertainty principle is primarily applicable to microscopic particles and not macroscopic objects like marbles in everyday scenarios.

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In Translational motion, the body moves in a straight line whereas in Rotational motion, the body moves in a circular path.

In Translational motion, the body moves in a straight line and the body same displacement in equal interval of time while on the other hand, in Rotational motion, the body moves in a circular path and the body travels same angular displacement in equal interval of time..

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