55. Cars A car moves 65 km due east then 45 km due
west. What is its total
displacement?

The amount of charge that will flow from the battery is 77000pC

A capacitor is a device that stores electrical charge. The amount of charge stored in a capacitor is proportional to the voltage applied across it, according to the equation Q = C*V.

where Q is the charge in coulombs, C is the capacitance in farads, and V is the voltage in volts.

In this case, the capacitance of the air-gap capacitor is 3500pF (pico-farads) and the voltage is 22V, so the charge stored in the capacitor is:

Q = 3500pF * 22V = 77000pC (pico-coulombs)

When a piece of mica is placed between the plates, it reduces the space between the plates, which will increase the capacitance of the capacitor. The increase in capacitance will result in an increase in the amount of charge stored in the capacitor.

It's worth noting that the charge that flows from the battery is equal to the initial charge stored in the capacitor. Since the initial charge stored in the capacitor is 77000pC, this is the amount of charge that will flow from the battery.

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Because the acceleration caused by gravity affects escape velocity. Therefore, the moon's escape velocity must be lower than that of the earth. Moreover, due to a lower escape velocity.

Ve therefore equals 11.2 km/s x 103 m/s. On Mars, the escape speed is approximately 40,270 kmph, or 11,186 m/s. For instance, when a rocket is used to propel a spacecraft into orbit, the velocity obtained must be higher than the orbital speed to prevent the rocket from returning to Earth.

Escape velocity is indeed the bare minimum speed at which a body must be propelled in order to escape the earth's gravitational pull. The smallest speed at which an object must move in order to escape the gravity field is.

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To maintain an exposure level equivalent to f/16 at 1/30 of a second, the new stop should be f/5.6. Due to their inverse relationship, the aperture and shutter speed must be adjusted to account for changes in either one by photographer.

When the shutter speed is increased from 1/30 of a second to 1/500 of a second, the aperture must likewise be changed in order to keep the same exposure level. The amount of light entering the camera, which is managed by the aperture and shutter speed, determines the exposure level. The "exposure triangle" describes the connection between aperture, shutter speed, and exposure. The "reciprocal rule," which dictates that if the shutter speed is increased by a factor of 16, the aperture should be reduced by a factor of 4, should be followed by the photographer in order to maintain the same exposure level. In this instance, the new stop should be f/4 since the photographer wishes to raise the shutter speed from 1/30 to 1/500 while maintaining the same exposure level.

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Due to the satellite's overshooting circular course and movement away from Earth against the pull of gravity, the speed of satellite in such a closed circular orbit would be greater than 8 km/s.

The direction of gravity always seems to be toward the core of the Earth when a satellite travels around it in a circular orbit.

Thus, due to the satellite's overshooting circular course and movement away from Earth against the pull of gravity, the speed of satellite in such a closed circular orbit would be greater than 8 km/s.

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Simple harmonic oscillation occurs when an object regularly returns to an equilibrium position and experiences a position-dependent force of the form , where is some positive constant.

Harmonic oscillation is a type of periodic motion where an object oscillates back and forth along a path in a predictable and regular pattern. Examples of harmonic oscillation include the motion of a simple pendulum, the oscillation of a spring, and the vibration of a guitar string. The motion of an object undergoing harmonic oscillation can be described mathematically using a sinusoidal function such as sine, cosine, or a combination of the two.

This force is often associated with a mass-on-a-spring system, and the motion of the object can be defined by a sine or cosine curve.

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(i) The magnitudes of the electric fields they separately create at a radial distance of 6 cm is [tex]E_{a}[/tex]=[tex]E_b}[/tex]. and (ii) The magnitudes of the electric fields they separately create at radius 4 cm is [tex]E_{a} =E_{b}[/tex], so the correct option is option b.

A conductor refers to a material that allows an electric current to flow through it with ease. In other words, it has a low electrical resistance. Conductors are materials that have a high number of free electrons that are able to move freely through the material. Examples of conductors include copper, aluminum, gold, and silver. These materials are commonly used in the electrical industry to make wires and other electrical components that need to conduct electricity. In addition to materials, a conductor can also refer to a person or an organization that is responsible for directing or leading an orchestra or a choir. In this context, a conductor is in charge of maintaining the ensemble's rhythm and intonation, and interpreting the score in a way that brings out the music's emotional content and intended meaning.

(i) The magnitude of the electric field created by a charged conductor is given by the formula E = [tex]\frac{kq}{r}[/tex], where k is the Coulomb constant, q is the charge, and r is the distance from the center of the sphere.

For a good conductor, like sphere A, the charge will be distributed evenly on the surface of the sphere. So, the electric field at a radial distance of 6cm will be Eₐ = [tex]\frac{kq}{r^{2} }[/tex] = [tex]k\frac{210^{-6} }{(619^{-2} )}^{2} =\frac{k}{72}[/tex]

For an insulator, like sphere B, the charge is distributed uniformly throughout its volume. The electric field at a radial distance of 6cm will be [tex]E_{b}[/tex]=  [tex]\frac{kq}{r^{2} }=k\frac{210^{-6} }{(619^{-2} )}^{2} =\frac{k}{72}[/tex]

As we can see, the magnitudes of the electric fields created by both spheres are equal, so the answer is (b) [tex]E_{a} =E_{b}[/tex]

(ii) For the radius of 4cm, the electric field created by sphere A and sphere B will

[tex]E_{a} =\frac{kq}{r^{2} }=k\frac{210^{-6} }{(410^{-2} )^{2} } =\frac{k}{16}\\E_{b} =\frac{kq}{r^{2} }=k\frac{210^{-6} }{(410^{-2} )^{2} } =\frac{k}{16}\\[/tex]

As we can see, the magnitudes of the electric fields created by both spheres are equal at a radius of 4cm, so the answer is (b) [tex]E_{a} =E_{b}[/tex]

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The maximum amount of static friction that the tyres can generate on the road can be used to calculate the maximum speed at which the car can go without slamming off the interstate.

The only force acting on the car when friction is eliminated is gravity, which pulls the vehicle towards the curve's centre.

The formula for calculating the maximum static friction force is

f_max = μ_s * m * g, where

μ_s = coefficient of static friction

m = mass of the car

g = acceleration due to gravity (9.8 m/s^2)

The maximum static friction force can be computed as follows using an assumed static friction coefficient of 0.7:

f_max = 0.7 * m * 9.8 = 6.86 * m N

The formula for the gravitational force is:

f_gravity = m * g * sin(θ), where

θ = bank angle (10°)

The difference between the gravitational force and the maximal static friction force is the net force operating on the automobile. The car won't skid off the road if the net force is zero.

The formula for calculating the maximum velocity is:

v = sqrt(R * g / sin(θ))

where

R = radius of the curve (20 m)

By substituting the values, we get:

v = sqrt(20 * 9.8 / sin(10)) = 26.51 m/s = 94.91 km/h

As a result, the maximum speed at which the car may move without swerving off the highway is roughly 94.91 km/h.

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A skier with mass of 62 kg is sliding down a snowy slope. The coefficient of kinetic friction is 0.0738 N

The coefficient of kinetic friction can be found using the formula:

Friction = coefficient of kinetic friction × Normal force

We know that the friction force is 45 N and the normal force is equal to the skier's weight, which can be found using the formula

Weight = mass × gravity

Where the mass is 62 kg and the acceleration due to gravity is approximately :9.8 m/s²

So the normal force is: 62 kg × 9.8 = 607.6 N

Therefore, the coefficient of kinetic friction is: Friction / Normal force  or approximately

= [tex]\frac{45}{607.6}[/tex] = 0.0738

The force that opposes the motion of two surfaces in contact as they slide against one another is known as kinetic friction, but other names for it include sliding friction and dynamic friction. The properties of the two surfaces in contact, such as the roughness of their surfaces and the materials they are made of, determine its strength. It acts in the opposite direction of the force applied to an object.

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The angular velocity of the rider is 2.9 rad/s. The result is obtained by using the formulas in circular motion.

Circular motion is a motion of an object along a circular path. When an object moves with an acceleration, it has a centripetal acceleration calculated by

ac = v²/r

Where

In circular motion, an object moves with linear and angular velocity. The relationship between both velocities is

v = ωr

Where

A rider moves in a circular motion with

Find the angular velocity! (ω = ?)

We find the centripetal acceleration in m/s².

ac = 10.5g

ac = 10.5 × 9.8 m/s²

ac = 102.9 m/s²

The linear velocity is

ac = v²/r

102.9 = v²/12.5

v² = 102.9 × 12.5

v² = 1,286.25

v ≈ 35.9 m/s

Use the equation of relationship between linear and angular velocity!

v = ωr

35.9 = ω (12.5)

ω ≈ 2.9 rad/s

Hence, the rider has the angular velocity of 2.9 rad/s.

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The average speed of a helium atom at a certain temperature is 1100 m/s expressed in miles per hour is: 2460.63 mi/h

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

Information about the problem:

By converting the speed units from (m/s) to (mi/h) we have:

v= 1100 m/s * 1 mi/1609.34 m * 3600 s/1 h

v= 2460.63 mi/h

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The value shown by the letter E is 24V.

Define resistance

A material's ability to obstruct the flow of electrical current is referred to as resistance. The capital letter R serves as a symbol for it. A conductor's ability to obstruct the flow of charges through it is referred to as resistance.

A closed loop is referred to as a circuit where electrons can move. The circuit receives power from an electricity source, like a battery. There won't be any electron movement until the circuit is finished, or until it has made a full circuit loop back to the electrical source.

V = IR

For circuit 5, V = E

I = 8A

R = 3

E = 8*3 = 24V

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Answer:

8

Explanation:

The kinetic energy of the block of wood would be 1148 m/s. The result is obtained by using the law of conservation of momentum.

The law of conservation of momentum states that the momentum of a closed system before and after the collision is constant. A closed system means there is no external force acting on the system. The formula would be:

∑p initial = ∑p final

p₁ + p₂ = p₁' + p₂'

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

Where

A bullet moving through a block of wood that is at rest. It has

Find the kinetic energy of the block that results from collision!

If a bullet moving through a block of wood, it means that the bullet will be united with the block of wood. Then, the speed of both bullet and wood after collision is the same, v'.

The speed of the bullet is

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

m₁v₁ + m₂v₂ = (m₁ + m₂)v'

v' = (m₁v₁ + m₂v₂)/(m₁ + m₂)

v' = (24(1200) + 1(-100))/(24 + 1)

v' = (28800 - 100)/25

v' = (28700)/25

v' = 1148 m/s

The kinetic energy of the block of wood would be

KE₂ = ½m₂v₂'

KE₂ = ½(1)(1148)²

KE₂ = 13,171,904 Joule

Hence, after the collision, the kinetic energy of the block of wood is 13,171,904 Joule.

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The wavelength of light that is inclined at a specified angle when falling on double slits is calculated to be 428.57 nm.

Angle = 30°

Order of interference m = 3

Distance between the slits d = 3 μ m = 3 × 10⁻⁶ m

We know the relation between wavelength, order of interference and distance as,

λ = d sinθ/(m+1/2)

By putting in the values, we have,

⇒ (3 × 10⁻⁶× sin30°)/(3+1/2) = 4.2857 × 10⁻⁷ m

By converting it to nm, we have,

⇒ 4.2857 × 10⁻⁷ × 10⁹ = 428.57 nm

Thus, the required wavelength of light is calculated to be 428.57 nm.

The question is incomplete. The complete question is 'Calculate the wavelength of light that has its third minimum at an angle of 30.0∘ when falling on double slits separated by 3.00 μm. Explicitly, show how you follow the steps in Problem-Solving Strategies for Wave Optics.'

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Net work the engine perform during the cycle is b) 330 J.

The net work done by a heat engine is the difference between the heat absorbed by the engine and the heat exhausted. Therefore, the net work done by the engine during a cycle is

1240 J - 910 J = 330 J.

How does the temperature of the hot reservoir affect the efficiency of a heat engine?

The efficiency of a heat engine is directly related to the temperature of the hot reservoir. The higher the temperature of the hot reservoir, the more thermal energy is available for conversion into work. This means that the efficiency of the heat engine increases as the temperature of the hot reservoir increases. The maximum efficiency of a heat engine is given by the Carnot efficiency, which is only achievable when the temperature of the cold reservoir is 0 K (absolute zero) and the temperature of the hot reservoir is infinite.

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The reasons why conifer sap is important include:

Conifer sap is rich in sugars and other nutrients that the tree needs to grow and survive. It is transported from the roots to the branches and leaves where it is used to fuel the tree's growth and metabolism.

Conifer sap is also known to contain compounds that protect the tree from pathogens and pests. These compounds act as a natural defense mechanism, helping the tree to resist infections and infestations.

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The celestial model doesn't shows the Sun and the stars moving around the earth.

Celestial globes depict the apparent positions of the stars in the sky. They exclude the Sun, Moon, and planets since their positions differ from those of the stars, but the ecliptic, along which the Sun moves, is depicted.

A fictitious sphere surrounding the Earth in which the stars, Sun, Moon, and planets appear to reside.

The celestial sphere is a hypothetical sphere centered on the Earth onto which all celestial bodies can be projected. An observer on the Earth's surface can only view half of the celestial sphere at any given moment because the other half is hidden beneath the horizon.

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The level of the sound can be decreased by gradually draining the air from a plastic bottle. The sound about an alarm clock cannot be heard at all since sound cannot travel through a vacuum.

A ringing alarm clock will gradually grow quieter when air is gently drawn out of the area around it and placed beneath a glass jar. Because sound is indeed a mechanical wave that moves across a medium, this is the case.

We can hear the sound because the air molecules in the jar shake as sound waves pass through them. The amount of air particles available to vibrate and convey sound waves declines when air is eliminated, which lessens the sound's strength.  There will be so little remaining air to vibrate due to the almost full removal of the air that the sound will be almost undetectable.

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Answer : Original Speed is 6m/s while acceleration is 0.3m/s^2.

What is speed?

--In everyday use and in kinematics, the speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time;

-- it is thus a scalar quantity.

Here in this question we have given final speed , we have to find the intial speed as well as the acceleration of the body.

d = V1 + V2 /2 × t

45 = V1 + 3/2 × 10

V1 = 6 m/s.

Hence initial speed of body is 6m/s .

By using first equation of motion we find the acceleration

we get acceleration is 0.3 .

What is velocity?

-- Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time .

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The maximum amount of trans fat as a percentage that could be in this cereal should be 0.5%.

This cereal is formulated to be as healthy as possible, which is why we limit the amount of trans fat to 0.5% or less. Trans fat is an unhealthy form of fat that has been linked to several health conditions, so we strive to keep our trans fat content as low as possible. By limiting trans fats to 0.5% or less, we are confident that this cereal is a healthy choice.

This cereal contains no more than 0.5% trans fat, as mandated by the FDA. Trans fat is an unhealthy type of fat that can increase bad cholesterol levels and the risk of heart disease and stroke. To ensure optimal health and safety, this cereal only contains the amount of trans fat that is legally allowed.

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After 150 seconds, the rocket is moving at a velocity of 32700 m/s and has traveled 1,623,500 meters.

A constant acceleration is a change in velocity that does not change over time. If a car accelerates by 20 mph one minute and then another 20 mph the next, its average acceleration remains constant at 20 mph per minute.

We can use the equations of motion to calculate the speed and distance traveled of the rocket. The equation for velocity as a function of time is:

v = at

where v is the velocity, a is the acceleration, and t is the time. Substituting in the given values, we get:

v = 218 m/s * 150 s = 32700 m/s

To find the distance traveled, we can use the equation:

d = 1/2 * at^2

Substituting in the given values, we get:

d = 1/2 * 218 m/s^2 * 150 s^2 = 1,623,500 m

So after 150 seconds, the rocket is moving at a velocity of 32700 m/s and has traveled 1,623,500 meters.

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The amount of the mass of the radioactive isotope remaining after 1 hour is 1.25 g.

The mass of the sample remaining after an hour is calculated from the half life of the isotope as shown below.

The half life of the radioactive isotope = 10 minutes

The amount of the mass of the radioactive isotope remaining after 1 hour is calculated as follows;

1 hour = 60 minutes

0 half life ---------------------------> 10 g

20 minutes ------------------------> 5 g

40 minutes -----------------------> 2.5 g

60 minutes -----------------------> 1.25 g

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The tension in the rope at the 57. 6° angle is 48.58 N, and the tension in the rope at the 33. 8° angle is 36.28 N.

What is meant by angle?

The tension force exerted by the first rope, T1

The tension force exerted by the second rope, T2

and the force of gravity, mg

T1x = −T1 cos 57.6°

T2x = T2 cos 33.8°

mgx = 0

T1y = T1 sin 57.6°

T2y = T2 sin 33.8°

mgy = −mg

Thus, the x and y components of the resultant force will be:

x:

Rx = T1x + T2x + mgx

Rx = −T1 cos 57.6° + T2 cos 33.8° + 0

Rx = T2 cos 33.8° − T1 cos 57.6° (1)

y:

Ry = T1y + T2y + mgy

Ry = T1 sin57.6°+ T2 sin 33.8° + (−mg)

Ry = T1 sin 57.6° + T2 sin33.8° − mg (2)

The next step is to substitute Rx and Ry in Eq. (1) and Eq. (2) with 0:

Rx = T2 cos 33.8° − T1 cos 57.6°

Ry = T1 sin57.6° + T2 sin 33.8° − mg

↓

0 = T2 cos33.8°− T1 cos 57.6° (3)

0 = T1 sin57.6°+ T2 sin 33.8°− mg (4)

Using these two equations we can easily find T1 and T2.

There are multiple ways in which we can do this. One way would be to first solve Eq. (3) for T2:

0 = T2 cos33.8°− T1 cos 57.6°

T2 cos 33.8° − T1 cos 57.6° = 0

T2 cos 33.8° = T1 cos 57.6°

T2 = T1  cos57.6°/ cos 33.8°

T2 = 0.747T1 (5)

hen, we substitute T2 with 0.735T1 in Eq. (4):

0 = T1 sin 57.6°+ T2 sin 33.8° − mg

0 = T1 sin 57.6° + 0.735T1 sin 33.8°− mg

And we solve it for T1:

0 = T1 (sin 57.6° + 0.747 sin 33.8°) − mg

0 = T1 (0.848) − mg

mg = 0.848T1

0.848T1 = mg

T1 =  mg /0.848

T1 =  (4.2kg) (9.81 N/kg) / 0.848T

T1 = 48.58 N

Finally, we substitute the value of T1 in Eq. (5) to find T2:

T2 = 0.747T1

T2 = (0.747) (48.58 N)

T2 = 36.28 N

Therefore, the tension in the rope at the 57. 6°angle is 48.58 N, and the tension in the rope at the 33. 8°angle is 36.28 N.

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The best way to increase the mechanical advantage of the class 2 lever is to move the load closer to the fulcrum.

option B.

The mechanical advantage of a simple machine is the ratio of output force to input force. It is also the ratio of load overcame by a simple machine to the effort applied by the simple machine.

Mathematically, the formula for mechanical advantage of a simple machine is given as;

M.A = output force / input force

M.A = Load / effort

Efficiency of machine = M.A/V.R x 100% = ( distance travelled by load x load ) / ( distance travelled by effort x effort )

Thus, to increase the mechanical advantage requires decrease in the distance travelled by the effort.

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The refractive index of the glass is 1.16, if the thickness of the glass slab is 2.25 cm, and the diameter of the circle is 7.60 cm.

incident angle of the light,θ = 90°

Let the angle of internal refraction is θ₁

Let the refractive index of the glass slab, = μ₁

Refractive index of vacuum, μ₂ = 1

By Snell's law, μ₁sinθ₁ = μ₂sin90

Radius of the circle, R = 7.6/2 = 3.8 cm

Thickness of the slab, and radius of the circle, R, makes the right angle triangle with hypotenuse(AC). So applying the pythagorus theorem,

AC² = 2.25² + 3.8²

AC = √(2.25² + 3.8²)

AC = 4.42

So sinθ₁ = 3.8/4.42

sinθ₁ = 0.86

μ₁ × 0.86 = μ₂×sin90

μ₁ × 0.86 = 1 × 1

μ₁ = 1/0.86

μ₁ = 1.16

So the refractive index of the glass slab, μ₁ = 1.16

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when 300 waves pass a point in one minute, the frequency is 5 Hz.

Frequency can be defined as, the no.of waves that pass in a unit of time through a fixed point. frequency is measured hertz (Hz)

Wave: The propagation of disturbances that have place in a medium  is referred to as a wave.

There are two types of waves.

1.Longitudinal waves

2.Transverse waves

Wavelength(λ): The distance between two peaks or two troughs can be used to define a wavelength. It is measured in meters (m), centimeters (cm) or millimeters (mm).

Wavelength Formula: λ=ν/f,

where ν is velocity, f is frequency .

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A frequency of 5 Hz is achieved when 300 waves pass a place in one minute.

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The direction of the field would be towards the positive end of the charge.

We know that the electric field has to do with the region in space where the influence of a charge can be felt. We can see from the question that there is a region around the −10 nC charge where its influence is felt.

Thus, we can see that that the direction of the charge would be in the positive direction to the charge that has been given which is around the charge that has a magnitude of −10 nC.

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The spacing between successive maxima near the center fringe for light of wavelength 500. nm, when l is 1.00 m and d is 1.00 cm is 510^-7 m, Yes, observe the interference of light, distance between the slits be placed for the maxima to be separated by 1.00 mm is 0.5 mm.

Wavelength is a measure of the distance between consecutive peaks (or troughs) of a wave, such as a sound wave or an electromagnetic wave (like light). It is typically measured in meters (m) or nanometers (nm). The wavelength of a wave determines its color, with shorter wavelengths appearing as blue or violet and longer wavelengths appearing as red. In the case of electromagnetic waves, the wavelength also determines the type of radiation, such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

(a) The spacing between successive maxima near the center fringe for light of wavelength 500 nm is given by the formula dsin(θ) = (λ)/d.

Plugging in the given values, we get: dsin(θ) = [tex]\frac{50010^{-91} }{0.01} =510^{-7} m[/tex]

(b) Yes, it would be possible to observe the interference pattern on the screen for this situation.

(c) To find the distance between the slits, we use the same formula and solve for d: d = (λ)/(dsin(θ)) = [tex]\frac{50010^{-91} }{1*10^{-3} } =0.5mm[/tex]

The slits should be placed 0.5 mm apart to have the maxima separated by 1.00 mm for this wavelength and screen distance.

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The electric potential difference through which the proton is moved is [tex]2.49 * 10^-18[/tex]V.

The electric potential difference through which the proton is moved can be calculated using the formula:

V = ΔU/q

Where V is the electric potential difference, ΔU is the change in electric potential energy, and q is the charge of the proton.

Given that the electric potential energy increases from [tex]2.0 * 10^-18[/tex] J to [tex]6.0 * 10^-18[/tex] J and the charge of the proton is 1.602 x 10^-19 C, we can substitute these values into the formula to find the electric potential difference:

V = (6.0 x 10^-18 J - 2.0 x 10^-18 J) / 1.602 x 10^-19 C

V = 4.0 x 10^-18 J / 1.602 x 10^-19 C

V = 2.49 x 10^-18 V

Therefore, the electric potential difference through which the proton is moved is [tex]2.49 x 10^-18[/tex] V.

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Answer:

Explanation:

I think it is the top one as the formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is commonly expressed in units of grams per cubic centimetre.

But I'm not 100% sure

In contrast to the human hearing range of 20 Hz to 20 kHz, mouse hearing extends into the ultrasonic region and ranges from 1 to approximately 100 kHz7,9.

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