two identical spheres with mass are hung from silk threads of length (fig. p21.60). the spheres have the same charge, so the radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. show that if the angle is small, the equilibrium separation between the spheres is (hint: if is small, then )

Answer:

In physics, the amount of work done on an object is the product of the force applied to the object and the distance over which the force is applied, also known as the force's displacement. Mathematically, it is represented as W = F * d.

Explanation:

Answer:

A pH meter that reads 0.5 off or a calculator that rounds incorrectly would be the source of instrumental errors.

The impulse is equal to the average net external force times the length of time it takes for that force to act, as shown by the equation.

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If the total number of joints in a simple truss is three, the total number of members in the truss is three.

In engineering, a truss is a structural member made of straight pieces of metal or wood that are joined together to form a series of triangles that lie in a single plane. Roofs, bridges, and towers are the most common structures that use trusses. Truss structures are classified into three types: simple, planar, and space frame. Various truss varieties have been developed over the years within these three basic types. A framework is made up of straight members joined at their ends to form a truss structure. Trusses can support both moving and stationary loads. Trusses are commonly used in roof supports, bridges, and other similar structures.

Here,

m=2j-3

j=3

m=2*3-3

m=3

The total number of members in the truss is 3 if the total number of joints in a simple truss is three.

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The appropriate values into the equation: E = (500 kg) (9.81 m/s2) (change in height between A and C).

An equation is a mathematical statement that expresses the relationship between two or more variables. It is composed of algebraic expressions, including constants, coefficients, variables, and operators, arranged in a particular order.

The energy loss due to friction from A to C can be calculated using the equation E = mgh, where m is the mass of the car (500 kg), g is the acceleration due to gravity (9.81 m/s2), and h is the change in height between points A and C.
Assuming that the track is level between A and C,
then the change in height is zero and the energy loss due to friction is also zero. If, however,
the track is not level and there is a change in height between A and C,
then the energy loss due to friction can be calculated by plugging in the appropriate values into the equation: E = (500 kg) (9.81 m/s2) (change in height between A and C).

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The type, degree, and duration of force that is employed during the moment was not necessary.

in mechanics, any action that seeks to preserve, modify, or deform a body's motion. Isaac Newton's three laws of motion, which are outlined in his Principia Mathematica, are frequently used to illustrate the concept of force (1687).

Simple people with simple minds teach simple subjects, like physics. The first thing physicists do when they examine an object is to simplify it. A book is a box, not a collection of paper sheets attached with glue and string. A automobile is a box; it doesn't have rotating rubber tires, six-way adjustable seats, lots of cup holders, or a rear window defogger. A human is not formed of bone, muscle, skin, and hair; rather, they are a box with two arms, two legs, and a head. This is the start of a free body diagram, a style of drawing popular among engineers and physicists.

The foundation of physics is the logical process of analysis, which involves dissecting complex circumstances into a collection of smaller ones.

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The four different forms of speed are as follows: uniform speed. variable rate Typical rate.

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Elements are most simply made up of atoms. A pure element will only have one type of atom, for example, a pure chunk of gold will only have gold atoms, making it chemically pure.

Two identical atoms bonded chemically, most frequently by covalent bonds, to form a molecule. Halogens are typically diatomic molecules; for example, chlorine is known as Cl2.

A pure substance is made up of various elements that have been chemically combined. Ionic chemicals that are connected by ionic bonds are the most common way to observe this. Please remember that a compound is not the same as a mixture! Keep in mind that a combination is not linked chemically.

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According to Newton's law of cooling, the rate of cooling is inversely related to the temperature differential between the object and its surroundings. For this, the equation is:

dT/dt = k (T - Ts) (T - Ts)

where T is the object's temperature, Ts is the environment's temperature, and k is the cooling constant. where dT/dt is the rate of change in temperature.

This equation can be used to calculate the cooling constant k for the cup of tea. We know that the temperature started off at 95 degrees Celsius, dropped to 75 degrees Celsius, and took 5 minutes to cool down.

95 - 75 = 20, dT/dt = k (20), dT/dt = k (20) *(1/5), and dT/dt = 4k.

Then, we can determine how long it will take for the temperature to cool to the desired level by using this cooling constant and the target temperature (35°C).

35 - 75 = -40\s-40 = 4k(t) (t)

t = -40 / 4k

We are unable to solve for t since we lack the value for k. But if we assume that the cooling rate is comparable to the rate we currently know, we can come up with an estimate. If we assume that the rate of cooling is constant, we can calculate how long it will take for the tea to cool from 75 to 35 degrees by using the rate of cooling from 95 to 75 degrees.

t = -40/20 equals 2 minutes.

It would take around 2 minutes to cool the tea from 75c to 35c under the assumption of similar cooling rate.

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The answer is that A device compresses the audio file before transmitting it to a second device. The second device restores the compressed file to its original version.

To compresses an  audio file is a term that connote the act of making an audio file to be smaller in size so as to fit into a given device or app. Note that the option that best demonstrates the use of lossless compression of the original file is that A device compresses the audio file before transmitting it to a second device. The second device restores the compressed file to its original version before playing it and as such, option A is correct.

Here,

The solution is that before sending the audio file to a second device, A compresses it. The second device converts the compressed file back to its original state.

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when 270 million people jump at the same time the Earth will move at 1.3 m/s.

The vector quantity of a force. It is a quantity with both magnitude and direction, hence.

We must specify both the size and the direction of the force operating on an object in order to adequately understand it. The average force is the force applied by an item traveling over a specific period of time at a defined rate of speed, or velocity.

This velocity is not instantaneous or precisely calculated, as the word "average" indicates. As a result, the average force is determined by multiplying the body's mass by the object's average velocity during the specified period of time.

Therefore,  when 270 million people jump at the same time the Earth will move at 1.3 m/s.

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It will take 91.125 sec (approximately 1 min and 30 sec) to complete the process using a hot pot with a power rating of 600 watts.

The process of converting 150 pieces of ice at -15 degrees Celsius into liquid water at 50 degrees Celsius is an endothermic process, meaning that heat is absorbed by the system. To represent this process in an energy-interaction diagram, we would start with the initial state of the ice at -15 degrees Celsius, with the horizontal axis representing the amount of energy absorbed by the system (in joules) and the vertical axis representing the temperature. As heat is added to the system, the temperature of the ice will increase, and the energy absorbed by the system will also increase. The process will continue until the ice has completely melted and reached a temperature of 50 degrees Celsius, at which point the energy absorbed by the system will reach its maximum value.

The amount of heat added to the system to complete this process can be calculated using the formula:

Q = mcΔT

where Q is the heat added (in joules), m is the mass of the ice (in kilograms), c is the specific heat capacity of ice (about 2.1 J/gC), and ΔT is the change in temperature (50 - (-15) = 65 degrees Celsius). The heat absorbed by the system is therefore calculated as follows:

Q = 150 pieces × 0.02 (kg/piece) × 2.1 (J/g*C) × 65(C) = 54675 J

It will take 91.125 sec (approximately 1 min and 30 sec) to complete the process using a hot pot with a power rating of 600 watts.

The process of converting 150 pieces of ice at -15 degrees Celsius into liquid water at 50 degrees Celsius is an endothermic process, meaning that heat is absorbed by the system. To represent this process in an energy-interaction diagram, we would start with the initial state of the ice at -15 degrees Celsius, with the horizontal axis representing the amount of energy absorbed by the system (in joules) and the vertical axis representing the temperature. As heat is added to the system, the temperature of the ice will increase, and the energy absorbed by the system will also increase. The process will continue until the ice has completely melted and reached a temperature of 50 degrees Celsius, at which point the energy absorbed by the system will reach its maximum value.

The amount of heat added to the system to complete this process can be calculated using the formula:

Q = mcΔT

where Q is the heat added (in joules), m is the mass of the ice (in kilograms), c is the specific heat capacity of ice (about 2.1 J/gC), and ΔT is the change in temperature (50 - (-15) = 65 degrees Celsius). The heat absorbed by the system is therefore calculated as follows:

Q = 150 pieces × 0.02 (kg/piece) × 2.1 (J/g*C) × 65(C) = 54675 J

To find out how long it will take to complete the process using a hot pot with a power rating of 600 watts, you can use the formula:

time (in seconds) = energy (in joules) / power (in watts)

time = 54675 J / 600 W = 91.125 sec (approximately 1 min and 30 sec)

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Halving the area of the pipe will double the speed of the water in the pipe. Therefore, option(c) is the correct answer.

Given,

initial flow speed, V₁ = v

let's area, A₁ = A

Now, to double the speed of the water flow

V₂ = 2v

we know that,

using continuity equation of flow:

A₁V₁ = A₂V₂

or A x v = A₂ x 2v

A₂ = A/2 or A₁/2

Therefore, By Halving the area of the pipe will double the speed of the water in the pipe.

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The complete question is:

water flows with speed v through a horizontal, cylindrical pipe. which of the following changes in the geometry of the pipe will double the speed of the water in the pipe?

(a) Doubling the area of the pipe

(b) Doubling the radius of the pipe

(c) Halving the area of the pipe

(d) Halving the radius of the pipe

Journalists frequently misinterpret research studies in their media articles in a number of ways. Such practices can lead to inaccurate and potentially harmful messages about scientific research.

Misinterpretation of research studies occurs in several ways:

First, journalists may inaccurately represent the findings of a study, either by overstating its conclusion or by misinterpreting its results. For example, they may suggest that a study shows a causative relationship between two variables when the actual findings only show a correlation.

Second, journalists may fail to provide enough context for readers to understand the research. This includes not providing enough information about the study sample and design, as well as failing to explain the statistical methods used in the analysis.

Third, journalists may selectively report on research studies, emphasizing those that are most sensational or that support a particular narrative. By omitting certain study results, they may give an incomplete picture of the research at hand.

Finally, journalists may report on studies that contain weak or unreliable evidence. This is particularly problematic when the research is based on a small sample size or uses methods that are not well-validated.

In summary, journalists are prone to misrepresenting research studies by giving an incomplete account of the findings, failing to provide adequate context, selectively reporting on studies, and relying on unreliable evidence. Such practices can lead to inaccurate and potentially harmful messages about scientific research.

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The fraction of its initial kinetic energy lost can be estimated to be 0.10 to 0.20.

Initial kinetic energy is the energy possessed by an object due to its motion. It is the energy of an object before any other external forces, such as gravity, friction, or air resistance, act upon it. Kinetic energy is a scalar quantity, meaning it has magnitude but not direction.

The fraction of kinetic energy lost will depend on the nature of the collision and the amount of energy dissipated. Generally, it is estimated that about 10% to 20% of the initial kinetic energy is lost in a collision. Therefore, the fraction of its initial kinetic energy lost can be estimated to be 0.10 to 0.20.

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The direction of the acceleration of the pendulum at moment 5 is towards A (center), which is perpendicular to the direction of motion of the bob.  

There is no any component of force acting along the tangent direction, when the bob is at the equilibrium mid-position as the string is completely vertical. Restoring force is momentarily absent in the bob when it is moving through the equilibrium position. The restoring force is only required when the pendulum bob has been slightly displaced away from the equilibrium position.

In the equilibrium position, the tension force is greater than the perpendicular component of gravity when the bob moves through this equilibrium position. As the bob continues its motion along a circular arc, so there must be a net centripetal force towards the center. So the direction will be towards A.

--The given question is incomplete, the complete question is:

"what is the direction of the acceleration of the object at moment 5? enter the letter of the arrow with this direction from the compass rose in the figure. type z if the acceleration vector has zero length."

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The speed of the waves at the beach in Florida is 2.167 m.s.

The wavelength of a wave is the distance between successive points in a wave.

The wavelength of the given wave is obtained as follows:

Wavelenegh of the wave = 13 meters

The frequency of the wave is 1/6 per second

The wavelength, speed, and frequency of the wave is related as follows;

The velocity of  a wave = wavelength * frequency

The speed or velocity of the wave = 13 * 1/6

The speed or velocity of the wave = 2.176 m/s

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Magnitude of the charge on each bead is calculated as 14.7 nC

In physics, charge is a characteristic of unit of matter that expresses the extent to which it has more or fewer electrons than protons.

As, F = kΔL, where F is the force, k is the spring constant, and ΔL is the change in length of the spring.

Given mass is 2.6 gm and unstretched length is 4.0 cm .

So, F = mg = 2.6g * 9.8 m/s^2

ΔL = 5.1 cm - 4 cm = 1.1 cm

Hence, k = F/ΔL = (2.6*9.8)/(0.011) = 469.09 N/m

ΔL = 4.4 cm - 4 cm = 0.4 cm

F = kΔL = 469.09 N/m * 0.4 cm = 187.63 N

As we know, q = F/E

q = 187.63 N / (1/(4π8.85410^-12)) = 1.4710^-8 C

So, the magnitude of the charge on each bead is 1.4710^-8 Coulombs, or 1.4710^-8 * 10^9 = 14.7 nC

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The ball takes 1.62 seconds to return to the ground after reaching its  maximum height  As a result, the ball is in the ground for

1.5 seconds + 1.62 seconds, which is 3.12 seconds.

The student  throws the ball with the initial velocity vi=15m/s

The final velocity of the ball is [tex]v_{f} =0 \\[/tex] The gravitational acceleration is g=10m/[tex]s^{2}[/tex]

Let the maximum height the ball reached is  s

Using the equation of motion,

[tex]v_{f} ^{2} -v_{i} ^{2} =2gs-(15)^2[/tex]=11.25m

Consequently, the ball traveled 11.25 meters from student height till it began to fall to the ground. Identify the time t right now.Taken by ball to reach the height 11.25 musing the equation of motion

[tex]v_{f} =v_{i}+gt_{o}=15+(-10) t_{t} =1.5sec[/tex]

As a result, the ball reaches its highest point in 1.5 seconds.

Given that the girl's hand was 2 meters above the ground. Consequently, the ball travels the distance before touching the ground.

11.25m + 2m = 13.25m

Using the equation of motion

[tex]S=v_{i} t+\frac{1}{2} gt^{2}[/tex]

S=13.25m, [tex]v_{i} =0[/tex], g=10m/[tex]s^{2}[/tex]

Substitute the values,

[tex]13.25=0 +\frac{1}{2} (10)t^{2}[/tex]

t=[tex]\sqrt\frac{13.25}{5}[/tex]

t=1.62sec

The time taken by ball to return to ground from maximum height is 1.62 sec.

Hence, The ball remains in ground before it hits the ground is 1.5 sec + 1.62 sec = 3.12 sec

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The free-fall and oscillation sections, which is [tex]$3.02 \ s + 2.01 \ s = 5.03 \ s$[/tex].

Oscillation sections are sections of a waveform that repeat themselves over a certain period of time. This period of time is known as the oscillation period and is typically measured in seconds or milliseconds.

The time interval between the bungee jumper leaving the bridge and reaching the bottom of her motion can be found by summing the time intervals associated with the free-fall and oscillation sections of the motion.
The time interval associated with the 15.0 m free-fall can be found using the equation for the time it takes an object to fall a given distance, which is:
[tex]$t_{fall} = \sqrt{\frac{2d}{g}}$[/tex]
where d is the distance fallen and g is the acceleration due to gravity, which is [tex]9.81 m/s$^2$.[/tex]
Therefore, the time interval associated with the free-fall can be calculated as follows:
[tex]$t_{fall} = \sqrt{\frac{2 \cdot 15.0 \ m}{9.81 \ m/s^2}} = 3.02 \ s$[/tex]
The time interval associated with the 26.0 m of oscillation can be found using the equation for the period of a simple harmonic oscillator, which is:
[tex]$T = 2 \pi \sqrt{\frac{m}{k}}$[/tex]
where $m$ is the mass of the object and k is the spring constant.
In this case, the mass of the object is 64.0 kg, and the spring constant is the force of gravity acting on the jumper, which is [tex]$mg = 64.0 \ kg \cdot 9.81 \ m/s^2 = 628.64 \ N/m$[/tex]
Therefore, the time interval associated with the oscillation can be calculated as follows:
[tex]$T = 2 \pi \sqrt{\frac{64.0 \ kg}{628.64 \ N/m}} = 2.01 \ s$[/tex]
The total time interval between the bungee jumper leaving the bridge and reaching the bottom of her motion is the sum of the time intervals for the free-fall and oscillation sections, which is [tex]$3.02 \ s + 2.01 \ s = 5.03 \ s$[/tex].

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The current in each of the single wires being the same in an electric circuit with a single wire connected to three branches that contain resistors and then connecting back to a single wire is explained by the conservation of charge.

Conservation of charge states that total charge in an isolated system remains constant. In electric circuit, charge flows through circuit in the form of electric current. Therefore, amount of charge flowing into any point in the circuit must be equal to the amount of charge flowing out of that point.

This means that current flowing into a branch in the circuit must be equal to the current flowing out of that branch. As the current in the single wire connected to the three branches is the same, current flowing into and out of each branch must also be the same, as per the conservation of charge principle.

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The angle its final velocity makes with the horizontal is 60⁰.

The time taken for the particle to travel through the 0.9 m radius is calculated by applying the following equation.

t = ( 2v sin (θ) ) / g

where;

t = ( 2 x 0.55 x sin 30 ) / ( 9.8 )

t = 0.056 s

The final vertical velocity is calculated as follows;

Vy = Vi + gt

Vy = ( 0.55 x sin 30 ) + (9.8 x 0.056 )

Vy = 0.82 m/s

The final horizontal velocity is calculated as follows;

Vx = V cos (30)

Vx = 0.55 m/s  x  cos ( 30 )

Vx = 0.48 m/s

The angle made with the horizontal is calculated as;

θ = arc tan ( Vy / Vx )

θ = arc tan  ( 0.82 / 0.48 )

θ = 59.7⁰ ≈ 60⁰

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Respect to the ultimate strength, determine the total load p=294k that can be supported by the pad.

What is meant by strength?

σ U =50ksi

n=3.5

σ allow = nσ /U = 50ksi/3.5 =14.29ksi

d=4.5in.

t=0.4in.

[tex]d_{0}[/tex] =d−2t=3.7in.

A= π/4 [tex](d^{2} -d^{2} _{0})[/tex] = π/4[[tex](4.5in.)^{2} (3.7in.) ^{2}[/tex] ]=5.152[tex]in.^{2}[/tex]

P 1 = allowable load on one pier

P 1 =σ allowA =(14.29ksi)(5.152[tex]in.^{2}[/tex])=73.62k

Total load P = [tex]4P_{1}[/tex]=294k

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Answer:

  about 792 J

Explanation:

You want the mechanical energy lost by a 65.2 kg base runner who slides into second base from a speed of 4.93 m/s, reaching the base with a speed of 0.

The runner's kinetic energy is ...

  KE = 1/2mv²

  KE = 1/2(65.2 kg)(4.93 m/s)² = 792.33974 J

As the runner slides into second base, his speed decreases to zero, so all of his kinetic energy is lost to friction.

The energy lost to friction is about 792 J.

The average velocity of the marble based on the image is 2.75 m/s.

The ratio of the change in position or displacement (x) and the time periods (t) during which the displacement happens is known as average velocity.

Mathematically;

where;

The change in the displacement of the marble, ∆x = 7 m - (-4) m

The change in the displacement of the marble, ∆x = 11 m

The change in time, ∆x = 8/2 seconds

The change in time, ∆x = 4 seconds

The average velocity of the marble = 11 m / 4 seconds

The average velocity of the marble = 2.75 m/s

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In order to determine the average normal stress at points D and E, we need to know the applied loading and the cross-sectional areas of the pipe and rod at these points.

It is assumed that pipe AB and solid rod BC form a built-up shaft that is subjected to an axial load, represented by P. The average normal stress at point D, which is located on the pipe, can be calculated by:

σD = P/A

Where A is the cross-sectional area of the pipe at point D. The cross-sectional area of the pipe can be calculated by:

A = π/4 * (D_o^2 - D_i^2)

Where D_o is the outer diameter of the pipe and D_i is the inner diameter of the pipe

The average normal stress at point E, which is located on the rod, can be calculated by:

σE = P/A

Where A is the cross-sectional area of the rod at point E. The cross-sectional area of the rod can be calculated by:

A = π/4 * D_r^2

Where D_r is the diameter of the rod

Therefore, by substituting the given values into the above equations we can calculate the average normal stress at points D and E.

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It is considerably easier for us to move objects thanks to simple machinery called pulleys that can shift the direction of force. The amount of force necessary to lift something up is reduced by this procedure. Option d

A clear meaning is attached to the word "force." The terms "push" and "pull" are perfectly acceptable at this level to describe forces. An object does not have a force inside of it or within it.

A massed item changes its velocity in response to a push or pull. A body can change its state of rest or motion when an external force acts on it. It is directed and has a magnitude.

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Normal stress in CG is 13.58 Ksi

When the deforming force is applied to an item, it deforms. The object will generate an opposing force from within to revert to its previous dimensions and shape. This restoring force will be applied in the opposite direction and have the same magnitude as the deforming force.Stress is a term used to describe how much of this restorative force is produced per unit area of the material. When the path of the deforming force is perpendicular to the body's cross-sectional area, stress is said to be normal stress. If the wire's length or the body's volume changes, the stress level will remain normal.

Using the portion EFCGB as a free body ,

∑[tex]F_{y} =0 :[/tex]

[tex]\frac{3}{5}F_{AE}[/tex]-3600=0

[tex]F_{AE}[/tex]=6000 lb

Using beam EFG as a free body ,

+[tex]M_{F} =[/tex]0 ,

-(4) [tex]\frac{3}{5}F_{AE}[/tex] + (4)[tex]\frac{3}{5}F_{cc}[/tex] = 0

[tex]F_{cc} =F_{AE} =[/tex]6000lb

cross section area of member CG :

[tex]A_{CG}=\frac{\pi}{4} d^{2}[/tex]= [tex]\frac{\pi}{4} (0.75)^{2}[/tex]

[tex]A_{CG}=0.44179 \:in^{2}[/tex]

Let the normal stress is 'B'

Normal stress in CG

[tex]B_{CG} =\frac{ F_{CG} }{ A_{CG} }[/tex] = [tex]\frac{6000 }{0.44179 }[/tex] = 13,580 psi

[tex]B_{CG} =[/tex]  13.58 Ksi

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Symmetry: According to the problem the charge on the larger ring is 4q.

Symmetry is a type of balanced arrangement of parts or elements of a whole. It is a fundamental concept in mathematics, art, and nature. Symmetry can be seen in everyday objects, such as a human face, a butterfly, a snowflake, and a fingerprint.

This is because of the symmetry of the system. The electric field due to the smaller ring at point P is the same as the electric field due to the larger ring at point P, since the distance from point P to the center of both rings is the same. Since the charge on the smaller ring is q, the charge on the larger ring must also be q in order to produce the same electric field. Since the larger ring has four times the area of the smaller ring, the charge on the larger ring must also be four times that of the smaller ring, which is 4q.

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999mm is added to 100m, we get​ 100999m.

A unit conversion is defined as the same property as a different unit of measurement such that time can be expressed in minutes instead of hours, while distance can be expressed in miles to kilometers or feet or lengths which can be converted to any other measurement.

In the above given information,

We have two numbers which are 999mm and 100m

So, we have to convert 100m into mm.

we know, 1cm=10mm

                     1m=100cm=100×10=1000mm

100m will be=100×1000=100000mm

Now, after adding 999m with 100000mm,

999mm+100000mm =100999mm

Hence, when 999mm is added to 100m we get 100999m.

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