In each part below, find the exact value of the probability if it is possible to do so with the information given. If it is not possible, provide the best lower and upper bounds you can. a) the chance that at least one of 10 flights at an airport is late, if each flight at the airport has a 1% chance of being late b) the chance that not all suits appear in a bridge hand of 13 cards dealt at random without replacement from a standard deck [A standard deck consists of 13 cards in each of 4 suits, making 52 cards in all.] c) the chance that all s office hours slots are selected, if each of g GSis selects one of the s slots at random without being influenced by the choices of others d) the chance that it rains every day next week if the daily chances of rain are given by Sun Mon Tue Wed Thu Fri Sat 0.9 0.95 0.95 0.9 0.9 0.85 0.8

Answers

Answer 1

a) The exact value of the probability that at least one of 10 flights at an airport is late, if each flight at the airport has a 1% chance of being late is 0.095.

b) The exact value of the probability that not all suits appear in a bridge hand of 13 cards dealt at random without replacement from a standard deck is 0.334507.

c) The exact value of the probability that all s office hours slots are selected, if each of g GSis selects one of the s slots at random without being influenced by the choices of others is 1/(sg).

d) The exact value of the probability that it rains every day next week, if the daily chances of rain are given by Sun Mon Tue Wed Thu Fri Sat 0.9 0.95 0.95 0.9 0.9 0.85 0.8, is 0.255104.

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Related Questions

Solve problem 1 for the input waveforms in figure 7–71 applied to an active-low s - r latch

Answers

Problem 1:Consider the waveform shown in figure 7-71 to be the input waveform of an active-low s-r latch. The solution to the problem is as follows:A clock pulse is used to trigger the latch. As a result, the input is latched into the output. When the clock pulse goes low, the latch is turned off, and the output is latched.

As a result, the output is determined by the input. As seen from the waveform, the output follows the input in a digital waveform. In this way, a simple waveform is converted to a digital waveform.The active low s-r latch consists of two NAND gates and two NOR gates. As a result, the inputs of the NAND gates should be connected to the NOR gates. The outputs of the NAND gates should be connected to the input of the NOR gates.

To construct an active low s-r latch, this arrangement is necessary. The S-R latch, in general, has four types of outputs, and the output is determined by the input. Thus, the solution to the problem is that the waveform of figure 7-71 is latched into the output of the active low s-r latch.

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A box slides off a perfectly horizontal table with an initial speed of 2 m/s. The table is 1.5m off the ground.
Vx = 2.0 m/s
1.5 m
What is the speed of the box just as it hits the ground?

Answers

Answer:

The speed of the box just as it hits the ground is 5.8 m/s

Explanation:

Given;

initial velocity of the box, u = 2 m/s

height of the table, h = 1.5 m

The speed of the box, just before it hits the ground is given by;

v² = u² + 2gh

v² = (2)² + 2 x 9.8 x 1.5

v² = 4 + 29.4

v² = 33.4

v = √33.4

v = 5.8 m/s

Therefore, the speed of the box just as it hits the ground is 5.8 m/s

7. A 100 kg log is dragged across a horizontal siand of concrete. 7.1 Show by calculation that the weight of the log is 980 N. Use the equation w = mg in which g = 9,8 m.s-2. (Refer back to Unit 6 on page 30.)​

Answers

The weight of the log is 980N

What is the Weight of an object?

The force of gravity acting on an object is its weight, which is equal to its mass times the acceleration of gravity, or w = mg. The newton is the SI unit for weight since it is a force.

The weight of a 100 kg log can be calculated using the equation w = mg,

where m is the mass of the log (100 kg) and g is the acceleration due to gravity (9.8 m/s^2).

So, w = (100 kg)(9.8 m/s^2) = 980 N.

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Explain how radioactive decay works for measuring the absolute age of ancient objects.

Answers

Answer: Radioactive decay is the breakdown of a material into stable isotopes which are used for determining the age of the ancient material.

Explanation:

The radioactive decay is a natural process in which an ancient or old material whether in the form of rock, object or fossil break down into elements. Carbon 14 is an unstable isotope which decays to produce stable elements, the dating procedure uses these stable elements and the rate of decay of the isotopes to determine the age of absolute ancient of the objects but exact age cannot be determined just an approximation can be accepted.

A light beam with a 70° angle of incidence travels through a medium with an index of refraction of 1.8. The light enters a second medium and has an angle of refraction of 37°. What is the index of refraction of the second medium?

Answers

Answer:

Explanation:

For refraction , the formula is

sin i / sin r = μ₂ / μ₁

where light is travelling from medium 1 to 2 having refractive index of μ₁ and μ₂ . Angle of incidence in medium 1 is i and angle of refraction in medium 2 is r .

Here i = 70°, r = 37°

μ₁ = 1.8 ,μ₂ = ?

sin70 / sin 37 = μ₂ / 1.8

.939 / .602 = μ₂ / 1.8

1.56 =  μ₂ / 1.8

μ₂ = 2.81 .

The value of refraction index for the second medium will be  \(\mu_2=2.16\)

What will be the refractive index?

Every material has a different refractive index. The refracted index of any material shows that the light is refracted by how much angle.

So like for water its value will be different also for glass its value will be different.

Now it is given in the question that

Angle of incidence \(i=70^o\)

Refractive index of the first medium \(\mu_1=1.8\)

Angle of refraction \(r=37^o\)

Now from snells law

\(\dfrac{Sin \ i}{Sin \ r} = \dfrac{\mu_2}{\mu_1}\)

\(\dfrac{Sin70}{Sin37} = \dfrac{\mu_2}{1.8}\)

\(\mu_2= \dfrac{Sin70\times1.8}{Sin37}\)

\(\mu_2=2.16\)

Thus the value of the refraction index for the second medium will be  \(\mu_2=2.16\)

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How much would an 80.0kg person weigh on Mars, where the acceleration of gravity is 3.93m/s and in Earths moon, where the acceleration of gravity is 1.63m/s

Answers

Answer:

this is the answer

Explanation:

This is the solution, hope it helps

How much would an 80.0kg person weigh on Mars, where the acceleration of gravity is 3.93m/s and in Earths
How much would an 80.0kg person weigh on Mars, where the acceleration of gravity is 3.93m/s and in Earths

what are the two types of covalent bonds ? provide a description of each

Answers

Answer: Polar and Nonpolar

Polar molecules occur when there is an electronegativity difference between the bonded atoms.

Nonpolar molecules occur when electrons are shared equal between atoms of a diatomic molecule or when polar bonds in a larger molecule cancel each other out

Consider three widely separated galaxies in an expanding universe. Imagine that you are located in galaxy 1 and observe that both galaxies 2 and 3 are moving away from you. If you asked an observer in galaxy 3 to describe how galaxy 2 appears to move, what would he or she say?

Answers

Answer:

The observer will say that galaxy 2 is moving away from galaxy 3 where he stands.

Explanation:

Since the galaxies are expanding, each one would move away from the others. Observers on all three galaxies have their frame of reference fixed on their own galaxies. Judging from their own galaxies, each observer will perceive the other galaxies moving away from his/or galaxy.

The observer at galaxy 3 will talk about galaxy 2 by doing is; he will say that galaxy 2 is moving far from him.

We are told that the universe is expanding and as such, the galaxies would be expanding and moving away from each other.

Since the galaxies are expanding, it means that they will be moving away from each other.

From time dilation principle, an observer at galaxy 3 will say that galaxy 2 is moving far from him.

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which block does uranium belong to? select the correct answer below: s block p block d block f block

Answers

Uranium belongs to the f-block of the periodic table. The correct option is fourth.

The f-block is located at the bottom of the periodic table, and it consists of the lanthanide and actinide series. Uranium is an actinide element, which means it is part of the second row of the f-block. It is widely used in nuclear power plants, as well as in nuclear weapons.

The f-block elements are known for their unique electron configurations, which include partially filled f-orbitals. These elements are also called "inner transition metals" because they fill their d-orbitals before filling their f-orbitals. Uranium is a radioactive metal that has 92 protons in its nucleus.

In summary, uranium belongs to the f-block of the periodic table, specifically the actinide series.

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rank in order, from fastest to slowest, the speeds of the points labeled 1 through 5. rank items from fastest to slowest. to rank items as equivalent, overlap them.

Answers

Order from fastest to slowest

\(1\geq 2\geq 3\geq 4\geq 5\)

Sort the items in order of speed. Overlap items to rank them equally.

The wheel in the is rolling to the right without slipping.

Rank in order, from fastest to slowest, the speeds of the points labaled 1 through 5.

Rank items from fastest to slowest. To rank items as equivalent, overlap them.

an sphere is pure rolling speed of context point 5 meet be zero w.r.t ground.

Hence, v-ωR=0

v=ωR

\(v_5_/_g\geq v_5_/_c+v_c_/_g...............(1)\)

part.5

speed= 0 \(v_5=0\)

part.2

\(v_2=\sqrt{v^2+v^2}\)

\(= \sqrt{2} v\)

=(1.414)v

part.3

\(v_3= \sqrt{v^2\)ω\(^{2}\)\(R^2/4\) = 1.118v

part. 1

\(v_1\)=v+ωR

=2v

part. 4

\(v_4\)=v

order from fastest to slowest

\(1\geq 2\geq 3\geq 4\geq 5\)

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when talking about Acceleration ,what is significant about the about the sign(+ or -)?​

Answers

Answer:

Acceleration at its most basic is the act of increasing your running speed. From a standing start (or blocks), you explode into action. If you’re already running, you pick up the pace. Acceleration continues until you can no longer increase your speed, at which point you achieve maximum velocity (top-end speed). Acceleration seems simple enough. The plus means your increasing speed, the k=minus means your decreasing in speed.

Explanation:

gas particles can change to solid particles if the temperature

Answers

Gas particles can change to solid particles if the temperature decreases.

The state of matter of a substance is determined by its temperature and pressure. When the temperature of a gas decreases, its particles lose kinetic energy and slow down. This decrease in kinetic energy leads to a decrease in the average speed of gas particles.

As the temperature continues to decrease, the particles lose energy and move closer together. At a certain temperature known as the condensation point or the freezing point, the gas particles no longer have enough energy to overcome the intermolecular forces holding them together.

At this point, the gas undergoes a phase transition and changes into a solid. The process of gas turning into a solid is called condensation or freezing, depending on the specific substance.

During condensation, the gas particles arrange themselves in a more orderly and structured manner, forming a solid. The transition from gas to solid involves the release of energy, known as heat of fusion.

In summary, when the temperature of a gas decreases below its condensation or freezing point, the gas particles lose energy, slow down, and eventually come together to form a solid.

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A fire is burning in a fireplace. Where is the radiation?

A. You touch warm bricks next to the fireplace
B. You can feel the heat from across the room
C. Heat is rising up from the chimney

Answers

I think it’s A.
........

PLEASE HELP ME!
A student notices that when calcium chloride is placed in water, the test tube feels warm. What kind of reaction has taken place?


A. Combustion Reaction


B. Endothermic Reaction


C. Exothermic Reaction


D. Endergonic Reaction

Answers

Answer:

C. Exothermic Reaction

Explanation:

Let's go through the choices

A. Combustion - Combustion is a highly exothermic / redox reaction which produces light and heat (i.e basically it bursts into flames). In the description, the only reaction is that it feels warm, hence this is not the answer.

B. Endothermic - Recall that endothermic reactions absorbs heat and thus cools the surroundings thereby making test tube feel cooler. this is obviously not the case so this is not the answer.

C. Exothermic - Recall that exothermic reactions releases heat and thus causes the surroundings thereby making the test tube feel warmer (or hotter in some cases). This describes our situation so THIS IS THE ANSWER.

D. Endergonic reactions require an input of energy from an external source that is adsorbed by the reaction (for example if heat was applied by an external source). In this case, there is no mention of additional energy sources. Hence this is probably not the answer.

To obtain the number of meters from a distance measured In centimeters, you must ____ by the number _____​

Answers

Answer:

Divide by the number 100

Explanation:

Since there are 100 centimeters in 1 meter, we can see that if you are given a number in centimeters, the number of meters is that number divided by 100. Hope this helps!

Answer:

Divide by 100

Explanation:

Which statement best describes balancing equations and the law of conservation of mass?

There are more atoms in the reactants than in the products, and the total mass is the same in the reactants and in the products.
The number of atoms is the same in the reactants and in the products, and the total mass is the same in the reactants and in the products.
There are fewer atoms in the reactants than in the products, and the total mass is less in the reactants than in the products.
There are more atoms in the reactants than in the products, and the total mass is higher in the reactants than in the products.

Answers

Answer:

it would be c, there are fewer atoms in the reactants than in the products, and the total mass is less in the reactants than in the products.

Explanation:

Answer:

ccccccccccccccccc

Explanation:

:DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

··

ω

Δ

ω

what volume of aluminum has the same number of atoms as 9.0 cm3cm3 of mercury? express your answer with the appropriate units. vv

Answers

The volume of aluminum that contains the same number of atoms as 9.0 cm³ of mercury is approximately 0.622 cm³.

To find the volume of aluminum that contains the same number of atoms as 9.0 cm³ of mercury, we need to consider the densities and molar masses of the two elements.

First, let's find the number of atoms in 9.0 cm³ of mercury. To do this, we need to know the density of mercury, which is approximately 13.6 g/cm³.

Using the density formula: density = mass/volume, we can find the mass of 9.0 cm³ of mercury. mass = density × volume mass = 13.6 g/cm³ × 9.0 cm³ mass ≈ 122.4 g

Next, we need to convert the mass of mercury to the number of atoms. To do this, we use Avogadro's number, which tells us the number of atoms in one mole of a substance.

Avogadro's number is approximately 6.022 × 10²³ atoms/mol.

Number of atoms = (mass in grams / molar mass) × Avogadro's number

The molar mass of mercury is 200.59 g/mol. Number of atoms = (122.4 g / 200.59 g/mol) × (6.022 × 10²³ atoms/mol) Number of atoms ≈ 3.68 × 10²² atoms

Now, let's find the volume of aluminum that contains the same number of atoms. We'll use the molar mass and density of aluminum. The molar mass of aluminum is 26.98 g/mol, and the density is 2.70 g/cm³.

First, we calculate the mass of aluminum:

mass = (number of atoms / Avogadro's number) × molar mass mass

= (3.68 × 10²² atoms / 6.022 × 10²³ atoms/mol) × 26.98 g/mol mass

≈ 1.68 g

Next, we find the volume of aluminum using its density:

volume = mass / density volume = 1.68 g / 2.70 g/cm³

volume ≈ 0.622 cm³

Therefore, the volume of aluminum that contains the same number of atoms as 9.0 cm³ of mercury is approximately 0.622 cm³.

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A car and a truck move on the road in the same direction at the same
speed. Both vehicles slow down with the same stopping force.
Which statement best explains why the truck needs to more time to stop?

Answers

Answer:

The statements are not given, so I will answer in a general way.

We know that when one object is moving with a velocity V, and it wants to come to stop, it needs to accelerate in the opposite direction to the initial velocity (Or decelerate).

As larger this acceleration is, the faster the object will come to a full stop.

Now we have a car (with a mass m) and a truck (with a mass M) are moving with a velocity V.

We can assume that the mass of the truck is larger than the mass of the car, then:

M > m.

Now also remember Newton's second law:

F = m*a

Force equals mass times acceleration.

And we know that both vehicles stop with the same stopping force.

Then the acceleration (deceleration actually) that experiences the car is:

a = F/m

While the acceleration that experiences the truck is:

a' = F/M

Because M is larger than m, we will have:

a' < a

Then the deceleration of the truck is smaller than the one of the car, which means that the car will come to a full stop faster than the truck (or the truck needs more time to stop)

At night the sand cools off...
Conduction
Convection
Or radiation

Answers

Answer:

I feel like it's Convection because if its dry , then the water comes over it and it warms it also the sun gives it light it's gonna be more warmer. So I think your answer will be Convection.

Explanation:

Because conduction is Anything being warmed by objects touching.

And radiation is Anything being warmed by heat transferring through space.

And the meaning of Convection is Anything being warmed in WATER.

I hope this is right and I hope this will help you in any way!! <3

What is the shortest distance in which you can stop, after the brakes are applied, without the groceries sliding off the seat? the static and kinetic coefficients of friction are, respectively, 0. 65 and 0. 45. Assume that the surface of the seat is horizontal.

Answers

when the brakes are applied, the groceries will start sliding off the seat immediately. There is no stopping distance without the groceries sliding off the seat.

The shortest distance in which you can stop without the groceries sliding off the seat depends on the friction between the groceries and the seat. In this case, the static and kinetic coefficients of friction are given as 0.65 and 0.45, respectively.

To determine the stopping distance, we need to consider the forces acting on the groceries. When the brakes are applied, a force is exerted on the groceries in the forward direction. This force can be calculated using the equation:

Force = mass x acceleration

Since the groceries are at rest initially, the acceleration can be assumed to be zero. Therefore, the force exerted on the groceries is also zero.

When the brakes are applied, the force of static friction acts in the opposite direction of the applied force. The maximum force of static friction can be calculated using the equation:

Force of static friction = static coefficient of friction x normal force

In this case, the normal force is equal to the weight of the groceries. However, since the surface of the seat is horizontal, the weight of the groceries is balanced by the normal force, resulting in a net normal force of zero. Therefore, the force of static friction is also zero.

Since the force of static friction is zero, the groceries will not experience any frictional force that prevents them from sliding off the seat. Therefore, they will start sliding as soon as the brakes are applied, and there is no stopping distance without the groceries sliding off the seat.

In conclusion, when the brakes are applied, the groceries will start sliding off the seat immediately. There is no stopping distance without the groceries sliding off the seat.

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At what displacement from equilibrium is the speed of SHO half the maximum value?

Answers

Answer:

X = A sin ω t      is the simplest equation for SH

V = ω A cos ω t   describes the velocity where    ω A is the maximum speed

cos ω t = 1/2       describes 1/2 the maximum speed

then ω t = 60 deg      (cos 60 = 1/2)

X = A sin 60   will then be the displacement at 1/2 the maximum speed

or X = .866 A = 3^1/2 / 2 A

At 0.866 displacement from the point of equilibrium, the speed of the SHO is half the maximum value.

What is Equilibrium?

Equilibrium is the state of such a system in which neither its internal heat state nor its state or motion tend to change over time. If a simple mechanical body experiences neither accelerometers nor angular acceleration, it is considered to be in equilibrium.

That state will last as long as it is not disturbed by an external factor. Equilibrium for a single particle occurs when the vector sum of the forces acting on the particle is zero.

X = A sin ω t    

V = ω A cos ω t, it describes the velocity.

Here,

ω A = maximum speed

cos ω t = 1/2      

then ω t = 60 deg      

∵ cos 60 = 1/2

X = A sin 60, then the displacement will be at half the maximum speed.

X = 0.866 A

= \(3^{1/2}\) / 2 A

= 0.866

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A car accelerates uniformly in a straight line from rest at the rate of 3.7 m/s2
What is the speed of the car after it has traveled 63 m? Answer in units of m/s.
How long does it take the car to travel 63 m? Answer in units of s

Answers

Explanation:

Using equations of motion :

(A) we know that,

u = 0

a = 3.7 m/s^2

S = 63

\( {v}^{2} = {u}^{2} + 2as\)

\(v = \sqrt{0 + 2 \times 3.7 \times 63} = 21.6 \: m{s}^{ - 1} \)

(B)

v = u + at

21.6 = 0 + 3.7 * t

t (time to reach 63 m) = 5.83 seconds

A star is observed to have an apparent brightness which is 10⁻⁴ times its absolute brightness. How far away is it?

Answers

The star is located at a distance of 31.62 parsecs from us.


To determine the distance of the star, we need to use the inverse square law, which states that the apparent brightness of a star decreases as the square of its distance increases. Mathematically, it can be represented as:
Apparent brightness ∝ 1/Distance²
Given that the star's apparent brightness is 10⁻⁴ times its absolute brightness, we can write:
Apparent brightness = Absolute brightness/ (Distance)²
10⁻⁴ = Absolute brightness/ (Distance)²
Solving for distance, we get:
Distance = √(Absolute brightness/10⁻⁴)
However, we don't have the value of absolute brightness. But we can use the information that the star is observed to have an apparent magnitude of 10. Since apparent magnitude is a logarithmic scale, we know that a difference of 5 magnitudes corresponds to a difference of 100 times in brightness. Therefore, the star's absolute magnitude can be calculated as:
Absolute magnitude = Apparent magnitude - 5 log(distance/10)
Substituting the values, we get:
10 = Absolute magnitude - 5 log(distance/10)
Absolute magnitude = 10 + 5 log(10⁻⁴) = 14
Therefore, the distance can be calculated as:
Distance = 10^(1+((Apparent magnitude - Absolute magnitude)/5))
= 10^(1+((10 - 14)/5))
= 31.62 parsecs
Thus, the star is located at a distance of 31.62 parsecs from us.

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Question 11 (3 points)
1. How many amperes does a 125 watt bulb require when operating on 12 volts?

a. 0.096 watts
b. 10.41 Watts
С. 10.41 Ampere
D. 1500 ampere

Answers

Answer:

С. 10.41 Ampere

Explanation:

Given that,

Power, P = 125 watts

Voltage, V = 12 volts

We need to find current. Power in terms of current and voltage is given by :

P = VI, I = current

\(I=\dfrac{P}{V}\\\\I=\dfrac{125\ W}{12\ V}\\\\I=10.41\ A\)

So, the current is 10.41 A.

A bullet of mass, 50g, travelling at 500m/s strikes a stationery block of mass 2kg resting on a smooth surface. The bullet goes through and comes out on the other side at 200m/s. Calculate the speed of the block after th3 bullte has come out.​

Answers

bullet points are for week people got to have more heart

Gravitation always does negative work. question 48 options: true false

Answers

The statement indicating that 'Gravitation always does negative work' is FALSE.

What is Gravitation?

Gravitation is a fundamental physical force that makes objects attract each other in the Universe.

This force (Gravitation) is required to maintain both constant positions and movement of objects.

In conclusion, the statement indicating that 'Gravitation always does negative work' is FALSE.

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Answer:false

Explanation:

a 1.00-m3 object floats in water with 20.0% of its volume above the waterline. what does the object weigh out of the water? the density of water is 1000 kg/m3.

Answers

The weight of the object out of water is 800 kg.

To solve this problem, we need to use the principle of buoyancy. When an object is placed in water, it experiences an upward force called buoyant force, which is equal to the weight of the water displaced by the object.

In this case, the object has a volume of 1.00 m³, and 20.0% of its volume is above the waterline. Therefore, the volume of the object submerged in water is:

Vsubmerged = 1.00 m3 - 0.20 x 1.00 m³ = 0.80 m³

We also know the density of water is 1000 kg/m³. Therefore, the weight of the water displaced by the object is:

Wwater = density of water x volume of water displaced
Wwater = 1000 kg/m³ x 0.80 m³
Wwater = 800 kg

This means the buoyant force acting on the object is 800 kg. In order for the object to float, the buoyant force must be equal to the weight of the object. Therefore, we can find the weight of the object as:

Weight of object = Buoyant force = 800 kg

So the object weighs 800 kg out of the water.

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An internal resistance of 5 ohm and a battery of 15 ohm is connected to a resistance of 20 ohm calculate the electric current

Answers

Answer:

.6 A

Explanation:

Battery 15 VOLTS

V = IR

V / R = I

15 / ( 5+20) = .6 amps

use thermal expansion to find the difference in length between an object that is heated and when it is cooled.

Answers

Thermal expansion is the phenomenon in which the length of a material changes as a result of temperature changes. When heated, most materials expand, whereas when cooled, they shrink. As a result, we can determine the difference in length between a heated and a cooled object using thermal expansion.

Thermal expansion is a phenomenon in which the length of a material changes as a result of temperature changes. When a substance is heated, its constituent atoms vibrate more quickly and energetically, causing them to spread out and take up more space. The difference in length between an object that is heated and when it is cooled can be calculated using the following formula:ΔL = αL₀ΔTWhere:ΔL is the change in length of the object, α is the coefficient of linear expansion, L₀ is the original length of the object, and ΔT is the temperature difference experienced by the object. The coefficient of linear expansion is a measure of how much a material's length changes in response to temperature changes. It is represented by the symbol α and has units of per degree Celsius (°C⁻¹) or per kelvin (K⁻¹).

Thermal expansion is a phenomenon in which the length of a material changes as a result of temperature changes. When a substance is heated, its constituent atoms vibrate more quickly and energetically, causing them to spread out and take up more space. As a result, the substance's volume expands as well as its length. Similarly, when a substance is cooled, its atoms vibrate less quickly and energetically, causing them to pack together more tightly and take up less space. The temperature difference is the difference between the object's temperature when it is heated and when it is cooled.To illustrate this, consider an iron rod that is 1.0 meter long at a temperature of 20°C. The coefficient of linear expansion for iron is 1.2 x 10⁻⁵ K⁻¹. Suppose the rod is heated to a temperature of 200°C and then cooled back to its original temperature. The temperature difference experienced by the rod is therefore ΔT = 200 - 20 = 180°C. Using the formula above, we can calculate the difference in length of the rod as follows:ΔL = αL₀ΔT = (1.2 x 10⁻⁵ K⁻¹) (1.0 m) (180°C) = 0.00216 m = 2.16 mmTherefore, the difference in length between the rod when it is heated and when it is cooled is 2.16 mm.

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(E) V = kQ/r so the smaller sphere is at the lower potential (more negative = lower) Negative charge
flows from low to high potential so the charge will flow from the smaller sphere to the larger.
The flow of charge ceases when there is no difference in potential.

Two conducting spheres of different radii, as shown above, each have charge -Q. Which of the following
occurs when the two spheres are connected with a conducting wire?

(A) No charge flows.
(B) Negative charge flows from the larger sphere to the smaller sphere until the electric field at the surface of
each sphere is the same.
(C) Negative charge flows from the larger sphere to the smaller sphere until the electric potential of each
sphere is the same.
(D) Negative charge flows from the smaller sphere to the larger sphere until the electric field at the surface of
each sphere is the same.
(E) Negative charge flows from the smaller sphere to the larger sphere until the electric potential of each
sphere is the same.

Answers

The correct statement is " Negative charge flows from the smaller sphere to the larger sphere until the electric potential of each sphere is the same." The correct Option (E).

When the two spheres are connected with a conducting wire, the negative charge will flow from the smaller sphere to the larger sphere until the electric potential of each sphere is the same. This is because the electric potential at a point in space is proportional to the amount of charge present at that point and inversely proportional to the distance from the point to the center of the charged sphere.

Option (A) is not true because charge will flow due to the difference in potential between the two spheres.

Option (B) is not true because the electric field at the surface of each sphere will not necessarily be the same after charge flows.

Option (C) is not true because the electric potential at a point in space is the same for all charged conductors connected by a wire.

Option (D) is not true because the negative charge will flow from the smaller sphere to the larger sphere, not the other way around.

Therefore, The correct answer is option E.

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Two conducting spheres of different radii with each negative charge connected with a conducting wire, Negative charges flow from the smaller sphere to the larger sphere until the potential becomes the same. Thus, option E is correct.

The potential V = kQ / r,  Potential and charge are directly proportional to each other, more potential gives more negative charge. More negative charge gives lower potential. The potential always flows from a lower to a higher potential. Thus the negative charge flows from the smaller sphere to the larger sphere to equal the potential.

Thus, the correct option is E.

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