A car accelerated from rest for 12 s, at which time it
had traveled 480 m. What were its average and final
velocities?

The magnetic field inside the solenoid is

B = μo nI

Here n = N/l

Here I be the current

N be the number of turns

l be the length of solenoid

Because the magnetic field in this instance is independent of radius, "c) it is unaffected."

Electric charges in motion create magnetic fields. Everything is constructed of atoms, and each atom contains a nucleus that is composed of protons and neutrons, with orbiting electrons. Each atom creates a tiny magnetic field because the orbiting electrons are tiny moving charges.

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The sound level from 1 km away is 46.4 dB and the sound energy radiated through the windows and doors in 20 min is 332.6 J

Multiple plate modes participate in the forced vibration of a baffled plate that produces sound. The emitted sound power depends on the activation of each plate mode by the external pressures as well as the radiation characteristics of the individual plate modes and their mutual interaction via their radiated sound, as shown in eq (20) and (24). The net contribution of the mutual interaction between plate modes to the overall sound power may be disregarded if a plate is activated in a manner that results in a plate vibration field that can be defined as reverberant with an equal distribution of energy over all modes.

(Lw) = 10·log (W/Wo) dB

Given:

sound level,  [tex]\beta= 101 dB[/tex]

Area, A = [tex]22\;m^{2}[/tex]

Time, [tex]\triangle t = 20\;min=1200\;s[/tex]

Intensity, [tex]I=1\times 10^{-12}\;W/m^{2}[/tex]

[tex]r=1\;km=1000\;m[/tex]

(a)

We know that, Sound level is,

[tex]\beta=10\times log(\frac{I}{I_{o} } )[/tex]

Solving the above equation for sound intensity,

[tex]I=I_{o} \times 10^{\frac{\beta}{10} }[/tex]

[tex]I=1 \times 10^{-12} \times 10^{\frac{101}{10} }[/tex]

[tex]I=0.0126\;W/m^{2}[/tex]

Therefore, The sound energy is,

[tex]E=P\times \triangle t[/tex]

Substitute [tex]P=I \times A[/tex] in the above equation,

[tex]E=I \times A \times \triangle t[/tex]

[tex]E=0.0126 \times 22 \times 1200[/tex]

[tex]E=332.6\;J[/tex]

(b)

Half of a sphere area with 1 km radius is equal to Area of the sound at 1 km distance,

[tex]A_{hemisphere} = \frac{1}{2} \times 4 r^{2} \pi[/tex]

Substitute the known value in the above equation ,

[tex]A_{hemisphere} = \frac{1}{2} \times 4 (1000)^{2} \pi[/tex]

[tex]A_{hemisphere} = 6283185\;m^{2}[/tex]

Sound Intensity is,

[tex]I = \frac{P}{A_{hemisphere}}[/tex]

Substitute [tex]P=I \times A[/tex] in the above equation,

[tex]I = \frac{I \times A}{A_{hemisphere}}[/tex]

Substitute the known value in the above equation,

[tex]I = \frac{0.0126 \times 22}{6283185}[/tex]

[tex]I = 4.4 \times 10^{-8}\;W/m^{2}[/tex]

Sound level is,

[tex]\beta=10\times log(\frac{I}{I_{o} } )[/tex]

Substitute the known value in the above equation,

[tex]\beta=10\times log(\frac{4.4 \times 10^{-8} }{1 \times 10^{-12} } )[/tex]

[tex]\beta=46.4\;dB[/tex]

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Answer: Conclusion White matter hyperintensities predict an increased risk of stroke, dementia, and death. Therefore white matter hyperintensities indicate an increased risk of cerebrovascular events when identified as part of diagnostic investigations, and support their use as an intermediate marker in a research setting

By unit conversion, the converted unit is

a. 1.8 km = 1.8 x 10⁹ μm

b. 1.8 μm = 1.8 x 10¯⁴ cm

c. 1.8 yard = 1645920 μm

We need to know about unit conversion to solve this problem. The unit conversion can be used to convert a unit to another unit. It can be defined as

a = xb

where a is unit a, b is unit b and x is the constant of conversion.

From the question above, we know that

a. 1.8 km = .... μm

b. 1.8 μm = .... cm

c. 1.8 yard = .... μm

Find the microns (1 km = 10⁹ μm)

1.8 km = 1.8 x 10⁹ μm

Find the centimeter (1 cm = 10⁴ μm)

1cm = 10⁴ μm

1/10⁴ cm = 1 μm

Hence,

1.8 μm = 1.8/10⁴ cm

1.8 μm = 1.8 x 10¯⁴ cm

Find the microns (1 yd = 914400 μm)

1.8 yard = 1.8 x 914400 μm

1.8 yard = 1645920 μm

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When the electrons accelerated through a potential difference of 84 kV, the electrons have half the speed that she wishes.

When the potential is quadrupled to 336 kV, the electrons acquire the desired speed.

Let u be the speed of the electrons after accelerating through a potential difference ΔV.

Now,

K = eΔV = (γ - 1)mc² where K is the kinetic energy.

K = (γ - 1)mc² =[ 1/ ( √1 - (u/c)² ) - 1]mc²

Therefore,

[ 1/ ( √1 - (u/c)² ) - 1] = (eΔv / mc² ) + 1 = (eΔV + mc² ) / (mc²)

1 - (u/c)² = [ (mc²) / (eΔV + mc² ) ]²

u/c = √[ 1 - ( m / {(eΔV/c²) + m})² ]

u / c = √[ 1 - ( 9.11 × 10⁻¹³ / {(1.6 × 10⁻¹⁹ × 8.4 × 10⁴ /(3 × 10⁸)² +  9.11 × 10⁻¹³ })² ]

u = 0.512c

Despite the increased accelerating voltage, this speed cannot be doubled because it is greater than half that of light. The electrons move at u = 0.798c faster if the accelerating voltage is quadrupled to 336 kV.

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The electric charge on the rod is no longer separated.

If the magnetic field is parallel to the position of the exposed surface the magnetic flux produced will be zero if the magnetic field is non-zero. If a charged particle moving parallel to the magnetic field has a velocity parallel to the magnetic field, then the force is zero In the above case the velocity is parallel to the magnetic field lines, so the magnetic force is zero.

Induced currents can be created by changing the strength of the magnetic field changing the size of the wire loop, or changing the direction of the wire loop. The main difference between magnetic flux and flux density is that magnetic flux is a scalar quantity whereas flux density is a vector quantity. Flux is the scalar product of flux density and area vector.

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Answer:

40s to run the second 200 m

Explanation:

the average speed is 4.0 m/s

if he is moving at a constant speed he should be able to run the first and second have at the same time

The total capacitance of the capacitor circuit is 40 μF.

We need to know about capacitor circuits to solve this problem. The capacitance will be summed up when the capacitor is combined in parallel. The total capacitance can be determined as

Ct = C1 + C2 + C3

From the question above, we know that:

C1 = 25 μF

C2 = 3 μF

C3 = 12 μF

By substituting the parameters, we can get

Ct = C1 + C2 + C3

Ct = 25 μF + 3 μF + 12 μF

Ct = 40 μF

Hence, the total capacitance of the circuit is 40 μF.

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The position of the wire is at a distance of 12 cm, in the direction left of the wire.

It is given that I₁ = 1.50 A and I₂ = 4.00 A and the distance between wire 1 and wire 2 = 20cm = 0.2m

Let the distance of wire 3 from wire 2 be " d " .

We have to place the 3 wire such that each wire experiences no net force which means force on wire 2 due to wire 3 = force on wire 1 due to wire 3

   [tex]F_2=F_1[/tex]

Using equation (1) , we get

[tex]\frac{u_0I_2I_3}{0.2+d}=\frac{u_0I_1I_3}{d} \\\\\frac{I_2}{0.2+d} =\frac{I_1}{d} \\\\\frac{4.00}{0.2+d} =\frac{1.50}{d} \\\\4.00d=1.50(0.2+d)\\\\4.00d=0.3+1.50d\\\\\2.5d=0.3\\\\d=0.12m[/tex]

d= 12 cm in the direction left of the wire.

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The complete question is given below .

A schematic of the information provided in the question can be seen in the image attached below.Two long wires hang vertically. Wire 1 carries an upward current of 1.50 A . Wire 2,20.0cm to the right of wire 1, carries a downward current of 4.00 A . A third wire, wire 3 , is to be hung vertically and located such that when it carries a certain current, each wire experiences no net force. (b) the position of wire 3 and

Answer:

Car velocity when crossing checkpoint = 60 m/s

Explanation:

For an object traveling at an acceleration of a m/s², with an initial velocity of u m/s the displacement at time = t secs is given in meters by the equation
[tex]\displaystyle d=ut+\frac{1}{2}at^{2}[/tex]

Here we are given displacement, and time but not acceleration and initial velocity : d = 225 meters, t = 5 seconds

Let's find an equation relating u and a in terms of d and using data given

Switching sides we get
[tex]ut+\frac{1}{2}at^{2}=d[/tex]

Substituting values for t = 5, d = 225 we get
[tex]5u+\frac{1}{2}a.25=225[/tex]

Multiplying both sides by 2 yields
[tex]10u+25a=450\;\;\; ...... (1)[/tex]

We also have the formula:
[tex]\displaystyle a=\frac{{v-u}}{t}[/tex]
where v is the current velocity and u the initial velocity

So
[tex]\displaystyle a=\frac{30-u}{5}[/tex]
[tex]u+5a=30\;\;...... (2)[/tex]

Multiply equation (2) by 5 and subtract from (1) to eliminate the a terms and solve for u
[tex]\displaystyle 10u+25a-5u-25a=450-150\\\\5u=300\\\\u=60m/s\\\\\textsf{which is the speed at which the car passes the checkpoint}\\[/tex]

The density of crushed iron ore is equivalent to 2 500 kg/m3, or 2.5 grams per cubic centimeter, which is the weight of the material. The density is equal to 156.07 pounds per cubic foot in either the Imperial or US customary measuring systems.

When weights are expressed in kilograms of air, the air gives buoyancy, and because a kilogram of copper has a larger volume than a kilogram of lead, it displaces more air and hence receives more support. As a result, on a scale in the air, a kilogram of lead will weigh more than a kilogram of copper. Copper has a density of 8.94 grams per cubic centimeter, or 8 940 kilograms per cubic meter, or 20°C (68°F or 293.15K), at ordinary atmospheric pressure.

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The distance the proton traveled in the field is 2.09m.

A stable subatomic particle known as a proton with the symbols p, H+, or 1H+ and an elementary electric charge of +1e. It has a mass that is somewhat lower than that of a neutron, and because of the proton to electron mass ratio, it has an 1836-fold greater mass than an electron. The term "nucleons" refers to protons and neutrons, both of which have masses of roughly one atomic mass unit (particles present in atomic nuclei).

In the nucleus of every atom, there are one or more protons. They offer the central force of electrostatic attraction that holds the atomic electrons together.

Explanation:

Now as the initial and final velocity makes 180degree angle, So, the proton must have travelled only half a revolution. So, the distance ,d will be :

d=2πr/2=πR

d=2.09m

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Yes, this situation is possible. No, It is not possible in more than one way.

A schematic of the information provided in the question can be seen in the image attached below.

 From the picture: Assuming that the forces exerted on the wire by the other two  wires are equal and opposite,  the third wire exerts no net force. So you can say: Yes the situation is possible.

The forces acting on the other two wires will be in opposite directions, so they cannot have multiple passes, but they will not be of the same  magnitude.

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The radius of the copper cable, carrying 300A current with 2 W/ m power loss, is 0.0156 m or 15.6 mm.

First, let us list the given:

The formula that will be used to solve for the radius of the cable is shown below.

Wherein: R = resistance, L= length of cable, and A = cross-section area of cable.

In solving for R, the length of the cable is assumed to be 1 m since the unit of power should be in W.

(2 W / m)(1 m) = [tex](300 A)^{2}*R[/tex]

R= 2.22 x 10 -5 Ω

Solve for the cross-section area of the cable.

R = 2.22 x 10 -5 Ω = [(1.7 X 10 -8 Ω m)*(1 m)] / A

A = 7.65 x 10 -4 square meters

Solve for the radius of the cable.

A = 7.65 x 10 -4 square meters = *[tex]radius^{2}[/tex]

radius = [tex]\sqrt{\frac{7.65x10^{-4} }{pi} }[/tex] = 0.0156 m or 15.6 mm

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1000kg  is the mass of the roller coaster in kg

The speed of the roller coaster is, v=20ms−1

Ek=1/2⋅1000⋅20∧2=2⋅10∧5J

The mass and speed of an item affect its kinetic energy, which is the energy of motion. As the coaster cars lose height, the train accelerates. As a result, their initial potential energy, which was caused by their height, is converted into kinetic energy (revealed by their high speeds).

Kinetic energy has the following formula where m is the object's mass and v is its square velocity. The kinetic energy is measured in kilograms-meters squared per second squared if the mass is measured in kilogrammes and the velocity is measured in metres per second.

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[tex]4.78\times 10^8\ \mathrm{Pa}$[/tex]  is the stress in the rod.

Given:

Young's modulus, Y = [tex]20 \times 10^{10}\;N/m^{2}[/tex]

Steel density, [tex]\rho = 7.86 \times 10^{3}\;kg/m^{3}[/tex]

Length of the rod, L = 80 cm = 0.800m

The speed of the wave in the rod is,

[tex]$t=\frac{L}{v} = \frac{0.800\ \mathrm{m}}{5044\ \mathrm{m/s}} = 1.58\times 10^{-4}\ \mathrm{s}$[/tex]

Hence the time taken by the wave to travel the end of the rod is,

[tex]$t=\frac{L}{v} = \frac{0.800\ \mathrm{m}}{5044\ \mathrm{m/s}} = 1.58\times 10^{-4}\ \mathrm{s}$[/tex]

The velocity of the rod is, [tex]$v_r = 12.0\ \mathrm{m/s}$[/tex]

The other end will keep moving after the front end hits the wall until the wave reaches the other end, given the period determined by the above problem.

As a result, before the wave reaches the end of the rod, it has traveled a distance of

[tex]$\Delta L = v_r t = (12.0\ \mathrm{m/s}) (1.58\times\ \mathrm{s}) = 1.90\times 10^{-3}\ \mathrm{m} = 1.90\ \mathrm{mm}$[/tex]

The strain in the rod is given by,

[tex]$\frac{\Delta L}{L} = \frac{1.90\times 10^{-3}\ \mathrm{m}}{0.800\ \mathrm{m}} = 2.37\times 10^{-3}$[/tex]

The Young's modulus is given by,

[tex]$Y = \frac{F/A}{\Delta L/L}$[/tex]

Now, we may write that the stress is given by using the equation above,

[tex]$\frac{F}{A} = Y\frac{\Delta L}{L} = \left( 20\times 10^{10}\ \mathrm{N/m^2} \right) \left ( 2.73\times 10^{-3} \right ) = 4.78\times 10^8\ \mathrm{Pa}$[/tex]

Hence, [tex]4.78\times 10^8\ \mathrm{Pa}$[/tex] is the stress in the rod.

Stress is a tangible property in continuum mechanics. It happens as a result of a body being subjected to tension or compression forces. Stress is defined as a force per unit area within a material that results from externally applied forces, unequal heating, or persistent deformation and that enables an accurate description and prediction of elastic, plastic, and fluid behavior in physical sciences and engineering. By dividing a force by an area, a stress is expressed.

Various forms of stress exist. Shear stress results from forces that are parallel to and reside in the plane of the material's cross-section, whereas normal stress results from forces that are perpendicular to the area.

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The speed of rocket is ,V₀ = 268.42ft/sec

A projectile is an object upon which the only force is gravity.

a rocket launched in vertical direction by a group of students.

The path of projectile will be parabola.

to find the speed of the rocket is  we use the equation of a projectile motion the data determined by them is

Initial height is.[tex]y_{0 } =[/tex] 89.6 ft

 final height is  [tex]y_{f} =[/tex] 0ft

 time taken, t = 17sec

as we know , g = 32.2 ft/s²

g is acceleration due to gravity.

 [tex]y_{f} - y_{o} = V_{o}t - \frac{1}{2} g t^{2}[/tex]

0 = 89.6 + 17V₀ - 16.1 × (17)²

V₀ = 268.42ft/sec

The speed of rocket is ,V₀ = 268.42ft/sec

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The work it takes to slide a crate 20 m along a loading dock by pulling on it with a 200-n force at an angle of 30° from the horizontal is 346.4J.

The energy that is transmitted to or from an object when a force is applied along a displacement is referred to as work in physics. In its simplest form, it is typically explained as the outcome of force and displacement. Positive work is the term for the component of a force that moves the point of application when it is applied. A force is said to do negative work if, at the point of application, one of its components points in the opposite direction of the displacement.

Calculations:

Work done= component of force  along displacement x displacement

                  =  F cosΘ x d

                  = 200cos 30 x2

                  = 346.4 J

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The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.

The average rate of change for the function f(x) from [tex]x_{1} =a[/tex] and [tex]x_{2}=b[/tex] is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

It is the average amount by which the function changed per unit throughout that time period.

Actually, this is the angle of the line on the function's graph that passes through two points.

The value of the comic book fell by an average of $0.04 per month (a unit in this case is a month) between m = 36 and m = 60 if the average rate of change of the function f(x) between m = 36 and m = 60 is -0,04.

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The repulsive force between the two pith balls is 9.6 × 10⁻⁴ N.

A pith ball, which is a tiny pith ball suspended on a thread, may detect the presence and intensity of an electric charge in an object that is near or touching it.

Two pith balls are 11 cm apart from each other and both have equal charges of -36 nC.

r = 11 cm = = 11 × 10⁻² m = 0.11 m

q = q₁ = q₂ = -36 nC = -36 × 10⁻⁹ C

According to Coulomb's law, the force between two charges is given as:

F = k [ q₁ q₂ / r² ]

The constant k = 8.99 × 10⁹ N.m² / C²

Therefore,

F = (8.99 × 10⁹ ) [ (-36 × 10⁻⁹) (-36 × 10⁻⁹) / (0.11)² ]

F = (8.99 × 10⁹ ) [ 1296 × 10⁻¹⁸ / 0.0121 ]

F = (8.99 × 10⁹ ) [ 10.7 × 10⁻¹⁴ ]

F = 9.6 × 10⁻⁴ N

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Frequency 1200 Hz  is monitored by the leading ship.

Here, the leading ship serves as the observer while the trailing ship serves as the source.

Therefore, the source's velocity is v' = 64 km/h = 17.777 m/s.

Observer's speed v "= 45 km / h = 12.5 m / s

The leading ship measures frequency using the formula f'= [(v -v ') / (v - v "()] f where v = source speed = 1520 m/s

Values obtained by substitution are f' = 1502.23/1507.5*1200 = 1195.8

The study of illness frequency and distribution in a specific community is known as epidemiology.

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The ball that is thrown straight up into the air with a velocity of 63. 7 m/s after 3s will have a velocity of: 34.3 m/s

The formula for the vertical launch upward and the procedure we will use is:

vf = v₀ - g * t

Where:

Information about the problem:

Applying the final velocity formula we get:

vf = v₀ - g * t

vf = 63. 7 m/s - 9.8 m/s² * 3 s

vf = 63. 7 m/s - 29.4 m/s

vf = 34.3 m/s

In physics vertical launch upwards is the motion described by an object that has been launched vertically upwards in which the height and the effect of the earth's gravitational force on the launched object are taken into account.

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It is not possible to accelerate an object to the speed of light.

The speed of light is generally regarded as the fastest speed on earth. We can tell from the Newton's law that the force that acts on a body is the product of the mass and the acceleration of the body.

It then follows that the force that is required to accelerate an object to the speed of light is a very high force that s somewhat unattainable and as the object approaches the speed of light, the mass of the object has to become infinitely small.

Hence, it is not possible to accelerate an object to the speed of light.

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Middle part of the ear have a solid medium. The ossicles, which are bones that amplify sound waves, are located in the middle ear, therefore the medium is solid.

The outer ear is the first place that sound waves pass through, followed by the middle ear and lastly the inner ear. The first medium is gas because the external auditory canal, which is part of the outer ear, is filled with ambient air.  The ossicles, which are bones that amplify sound waves, are located in the middle ear; therefore the second medium is solid. The last medium is liquid because the inner ear is loaded with fluids like endolymph and perilymph that vibrate when sound waves pass through them.

The middle ear amplifies sound after being directed toward it by the outer ear, which is in charge of catching it.  Amplified sound waves are sent from the middle ear to the inner ear, where hair cells detect the sound waves and transmit the data to the brain.

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Answer:

± .55 kg

Explanation:

55  * 1% = .55 kg

± .55 kg

The time when the object is not moving on the velocity time graph is  at the point in which the line crosses the x - axis.

The velocity time graph can be used to observe the movement of a particle. The graph consist of three main parts;

We can say that the time when the object is not moving on the velocity time graph is  at the point in which the line crosses the x - axis.

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If the nails dimensions were expressed in meters, we would have to divide it by 100.

In earlier times there were 3 main types of measurement systems:

1.The CGS system(centimetre, gram and second)

2.• The FPS system( foot, pound and second)

3.• The MKS system(metre, kilogram and second)

But in the present day, we use Système Internationale d’ Unites (French for International System of Units), abbreviated as SI.

The SI Unit of length is meter, but in many cases the length is given in centimeters.

So, we have to convert the value given in centimeter to meter by using the conversion factor which is,

1 meter = 100 centimeters

1 cm = 1/100 meter

Therefore, if the nails dimensions were expressed in meters, we would have to divide it by 100.

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Speed and velocity are similar in term of their unit. the speed of the jet is 42 m/s

What is Speed ?

Speed can simply be defined as how fast an object moves. It is the distance covered per time taken.

Given that acceleration = 2.8 m/s² and If after take-off, the jet continues to accelerate at the same rate for another 15 s, to know how fast it will be going at that time, we will use acceleration formula.

Acceleration = Velocity / time

speed = acceleration × time

speed = 2.8 × 15

Speed = 42 m/s

Therefore, the speed or the velocity of the jet is 42 m/s

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the charge of each cylinder given the following additional information about each one is 10434.445 coulomb, 14906.35 Coulomb, 178876.2 coulomb, 223,595.25 coulomb.

To solve this question we are to use the equation 1 below :

Charge Q = uniform charge density p × Total area of the cylinder A

From the question, we are given radius, R to be 2.33 cm and length, L to be 5.82 cm.

Calculate for the total area of the cylinder, A. equation 2

Total area of the cylinder, A = area of the top surface + area of the bottom + area of the curved surface of the cylinder.

Hence, total area of the cylinder A is;

πR^2 + πR^2 + 2πRL.

Then, total area of the cylinder A is;

(L + R)2πR.

find the charge of each cylinder equation 3

For the first cylinder; we have the uniform charge density to be 35 nC/m^2.

Therefore, the combination of equation (1) and (3) gives equation 4

Charge Q= p × (L + R)2πR

Hence,

Charge Q = 35 × [(5.82 + 2.33) 2× 3.143 × 5.82]

Charge Q = 10434.445 coulomb.

For the cylinder B, we have a uniform charge density of 50 nC/m^2.

Using equation (4),

charge Q =  p × (L + R)2πR

= 50 × [(5.82 + 2.33) 2× 3.143 × 5.82]

= 14906.35 Coulomb

For The cylinder C, the uniform charge density is 600, we use of equation (4);

Charge Q = 600 × 298.127

Charge Q = 178876.2 coulomb.

For cylinder D, the uniform charge density is 750 nC/m^2. use of equation (4)

Charge Q = 298.127 x 750

charge Q = 223,595.25 coulomb.

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