Which of the following is NOT correct for a simple magnifying glass?
a) The image is virtual.
b) The object is closer to the lens than the focal point.
c) The image is erect.
d) The lens is diverging.
e) The image is larger than the object.

When comparing the camera and the human eye, the film of the camera functions as the retina. The correct option is A.

A camera is a device that records and captures images. A camera, whether digital or film, relies on the same basic technology to work: light enters a camera and is focused onto a photosensitive surface that converts the light into an electrical signal.

The human eye is a sensory organ that helps people to see. The eye is comprised of several components that work together to allow light to enter the eye, focus it, and create an image that is sent to the brain. The retina, the part of the eye that corresponds to the film of the camera, is responsible for capturing the image that is formed by the eye’s lens. In comparison, the film of the camera functions as the retina.

The retina is located at the back of the eye and contains photoreceptor cells that detect light and convert it into neural signals that are sent to the brain. Similarly, the film in a camera captures the image created by the camera’s lens and converts it into an image that can be viewed or printed.Both the human eye and a camera are complex systems that work together to create images.

However, the processes that occur within the eye and the camera are quite different. The human eye relies on biological processes to create images, while a camera uses electronic and mechanical processes to capture and record images. The correct option is A.

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-- impurities in the water

-- air pressure is higher than standard

The magnetic field lines pοint tοwards the East (A).

Magnetic field lines are a visual representatiοn used tο depict the directiοn and strength οf the magnetic field arοund a magnet οr a current-carrying cοnductοr. They indicate the path that a hypοthetical magnetic nοrth pοle wοuld take if placed in the vicinity οf the magnetic field.

The prοtοn is a pοsitively charged particle and is traveling due nοrth. Since the electric field lines pοint due west, the electric fοrce οn the prοtοn is directed tοwards the west. In οrder fοr the prοtοn tο cοntinue traveling in a straight line due nοrth, the magnetic fοrce οn the prοtοn must be directed tοwards the east. This can be achieved if the magnetic field lines pοint tοwards the east.

Therefοre, the magnetic field lines pοint tοwards the East directiοn which is οptiοn A.

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Answer:

its true

Explanation:

ape x

The height (in feet) of the weight above the ground as a function of time will be given by the equation h = -16t² + 20t + 186. The weight will reach its zenith at t = 0.625 seconds at a height of 197.125 feet above the ground.

The given problem is a classic example of projectile motion where an object is thrown from a height and lands on the ground. The height (in feet) of the weight above the ground as a function of time will be given by the equation h = -16t² + 20t + 186, where h represents the height of the weight above the ground and t represents the time in seconds.The zenith is the highest point of the weight, i.e., the point where the weight stops moving upward and starts moving downward. To find the zenith, we need to find the time when the vertical component of the weight's velocity becomes zero, i.e., when it stops moving upwards. This can be found by differentiating the equation for height with respect to time and setting it equal to zero, which gives us the time when the vertical velocity is zero. This time is t = 0.625 seconds.

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The minimum angular separation resolvable for a 200-m radio telescope investigating sources emitting a 21-cm wavelength is 0.073°.

The angular resolution of a telescope is determined by the ratio of the wavelength of the radiation being observed to the diameter of the telescope. In this case, the telescope has a diameter of 200 meters, and the wavelength being observed is 21 cm (or 0.21 m).

The formula for calculating the angular resolution is given by θ = λ/D, where θ is the angular resolution, λ is the wavelength, and D is the diameter of the telescope. Substituting the given values into the formula, we get θ = 0.21 m / 200 m = 0.00105 radians.

To convert this to degrees, we multiply by (180/π), which gives us approximately 0.073°. Therefore, the minimum angular separation resolvable for this system is 0.073°.

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Answer:

[tex]Pressure = 29723.1\ N/m^2[/tex]

Explanation:

Given

[tex]Force = 8694N[/tex]

[tex]Length = 0.45m[/tex]

[tex]Width = 0.65m[/tex]

Required

The force exerted on the floor by the box

First, calculate the area covered by the box (i.e. the base area)

[tex]Base\ Area = Length * Width[/tex]

[tex]Base\ Area = 0.45m * 0.65m[/tex]

[tex]Base\ Area = 0.2925m^2[/tex]

Pressure is calculated as:

[tex]Pressure = \frac{Force}{Area}[/tex]

[tex]Pressure = \frac{8694N}{0.2925m^2}[/tex]

[tex]Pressure = 29723.0769231\ N/m^2[/tex]

[tex]Pressure = 29723.1\ N/m^2[/tex] --- approximated

Answer:

As we navigate down a group the atoms get bigger and bigger with more and more electrons. This means the outermost electrons get further and further away from the positively charged nucleus.

Answer:

As we navigate down a group the atoms get bigger and bigger with more and more electrons. This means the outermost electrons get further and further away from the positively charged nucleus

Hope this helps!!!!

The weight of the original mass on the spring was approximately 6.75 Newtons (N). The period of oscillation of a spring/mass system is determined by the mass and the spring constant.

Let's assume the original mass on the spring is represented by M and the corresponding weight is W.

Given that the original period is 5 seconds and the modified period is 3 seconds, we can set up the following equation using the formula for the period of an oscillating spring/mass system:

T = [tex]2\pi \sqrt{M/k}[/tex], Where T is the period, M is the mass, and k is the spring constant.

For the original system with a period of 5 seconds, we have:

5 = [tex]2\pi \sqrt{M/k}[/tex] ...(1)

When 12 N are removed from the spring, the modified system has a period of 3 seconds. This implies that the spring constant has changed, but the mass remains the same. Let's assume the new spring constant is k'.

3 = [tex]2\pi \sqrt{M/k'}[/tex] ...(2)

Dividing equation (1) by equation (2), we can eliminate the mass M:

5/3 = [tex]\sqrt{k'/k}[/tex]

Squaring both sides of the equation gives:

25/9 = k'/k.

Rearranging the equation gives:

k' = (25/9)k.

Since the spring constant is directly proportional to the weight of the mass, we can conclude that the weight of the original mass W is also reduced by a factor of (25/9).

Let's assume the weight of the original mass on the spring is W0. Thus, the weight of the modified mass is (W0 - 12 N).

Using the proportionality, we have: (W0 - 12 N) = (25/9)W0.

Simplifying the equation, we find: (9/9)W0 - (12 N) = (25/9)W0, (-16/9)W0 = 12 N.

Multiplying both sides by (-9/16) gives: W0 = (-9/16)(12 N), W0 = -6.75 N

Therefore, the weight of the original mass on the spring was approximately 6.75 Newtons (N).

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Answer:

D. Newton's first law

Explanation:

Newton's first law of inertia says that an object will remain how it is, unless affected by an outside force. In this case, the plates want to remain stationary(not moving). Therefore, if you pull the table cloth fast enough, the force of friction produced will be small enough so that the Inertia of the plates will overcome the force of friction.

The economic impact resulting from the collapse of two large power grids and 130 million people being without power for two months due to a 4800 nT/min geomagnetic storm disturbance in the United States would be substantial, likely amounting to billions of dollars.

1. Loss of productivity: The major factor contributing to the economic impact would be the loss of productivity during the two-month period. Without power, businesses, industries, and essential services would be severely disrupted, leading to a decline in output and economic activity.

To estimate the economic impact, we need to consider the following factors:

a. GDP per capita: According to the World Bank, the United States' GDP per capita was approximately $63,416 in 2020.

b. Average number of working days in two months: Assuming an average of 22 working days per month, we have a total of 44 working days affected by the power outage.

c. Workforce participation rate: As of September 2021, the U.S. labor force participation rate was around 61.6%.

d. Affected population: Given that 130 million people are without power, we need to calculate the percentage of the workforce among them. Assuming the workforce participation rate remains constant, the affected workforce can be estimated as follows:

Affected workforce = Workforce participation rate * Affected population

Affected workforce = 0.616 * 130,000,000

Affected workforce  ≈ 79,976,000

e. Loss of productivity per day: To estimate the loss of productivity per day per worker, we can divide the GDP per capita by the average number of working days in a year:

Loss of productivity per day per worker = GDP per capita / 365

Loss of productivity per day per worker  ≈ $63,416 / 365

Loss of productivity per day per worker   ≈ $173.63

f. Total loss of productivity: The total loss of productivity during the two-month period can be calculated by multiplying the loss of productivity per day per worker by the number of affected working days and the affected workforce:

Total loss of productivity = Loss of productivity per day per worker * Number of affected working days * Affected workforce

                        ≈ $173.63 * 44 * 79,976,000

                        ≈ $610,964,195,520

Additional costs: The economic impact would also include additional costs incurred due to the power outage, such as emergency response efforts, infrastructure repairs, and the financial burden on individuals and businesses.

Based on the calculations, the economic impact resulting from the collapse of two large power grids and 130 million people being without power for two months due to a 4800 nT/min geomagnetic storm disturbance would be estimated at approximately $610.96 billion in terms of loss of productivity alone.

This estimate does not include the additional costs associated with the power outage, which would likely further increase the economic impact.

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True. The Sun radiates at an effective temperature of 5780 K and has a radius of about 696,000 km.

The Sun's effective temperature refers to the temperature at which a black body (an idealized object that absorbs all incident radiation) would emit the same amount of radiation as the Sun. This value is approximately 5780 K, representing the temperature of the Sun's photosphere, the visible surface. Regarding the Sun's radius, it has an estimated average radius of about 696,000 km. This measurement defines the distance from the center of the Sun to its outer edge. The Sun is classified as a G-type main-sequence star, and its size is relatively large compared to other stars, making it an important reference point for understanding stellar characteristics.

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Answer:

Explanation:

The autonomic nervous system has two components, the sympathetic nervous system and the parasympathetic nervous system. The sympathetic nervous system functions like a gas pedal in a car. It triggers the fight-or-flight response, providing the body with a burst of energy so that it can respond to perceived dangers.

To determine the mass of air in the tank, we need to convert the given parameters and apply the ideal gas law. The mass of air in the tank is approximately 5.04 kg.

To determine the mass of air in the tank, we need to consider the ideal gas law and convert the given parameters to appropriate units.

Given:

Volume of air (V) = 2 m³

Temperature (T) = -93°C

Gauge pressure (P) = 1.4 MPa

Local atmospheric pressure (P_atm) = 1 atm

First, let's convert the temperature from Celsius to Kelvin:

T = -93°C + 273.15 = 180.15 K

Next, we need to convert the gauge pressure to absolute pressure by adding the atmospheric pressure:

P_abs = P + P_atm = 1.4 MPa + 1 atm = 2.4 MPa

Now, we can use the ideal gas law equation to calculate the mass of air (m):

PV = nRT

Where:

P = absolute pressure

V = volume

n = number of moles of air

R = ideal gas constant

T = temperature

Rearranging the equation to solve for mass (m):

m = (n * M) / N_A

Where:

M = molar mass of air

N_A = Avogadro's number

To find the number of moles (n), we can use the equation:

n = PV / RT

Given that the molar mass of air is approximately 28.97 g/mol, and the ideal gas constant R is 8.314 J/(mol·K), we can calculate the mass of air.

Calculations:

n = (P_abs * V) / (R * T)

m = (n * M) / N_A

Substituting the values:

n = (2.4 MPa * 2 m³) / (8.314 J/(mol·K) * 180.15 K)

m = (n * 28.97 g/mol) / 6.022 x 10^23 mol⁻¹

Calculating the mass of air (m):

m ≈ 5.04 kg

Therefore, the mass of air in the tank is approximately 5.04 kg.

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If a node is observed at a point 0.340 m from one end, in what mode and with what frequency is it vibrating . The correct answer is B. The frequency is the third state at 18.2 Hz.

To determine the mode and frequency of vibration for a node observed at a point 0.340 m from one end, we need to consider the fundamental frequency and the harmonics of the vibrating system. The fundamental frequency is the lowest natural frequency at which the system can vibrate. It corresponds to the first harmonic mode of vibration. The harmonics are integer multiples of the fundamental frequency.

To find the fundamental frequency, we can use the formula:

F₁ = v / (2L)

Where f₁ is the fundamental frequency, v is the velocity of the wave, and L is the length of the vibrating medium.

Since the node is observed at a point 0.340 m from one end, the length of the vibrating medium is twice that distance, which is 0.680 m.

Now, we need to examine the options and determine if any of them match the calculated fundamental frequency or any of its harmonics.

A. The frequency is the fifth state at 30.3 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.

B. The frequency is the third state at 18.2 Hz: This option matches the calculated fundamental frequency, as it is the first harmonic or third state.

C. The frequency is the fifteenth state at 18.2 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.

D. The frequency is the fifth state at 15.2 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.

Therefore, the correct option is B. The frequency is the third state at 18.2 Hz, corresponding to the fundamental frequency or first harmonic of the vibrating system

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The earliest time after the blοck is released when its kinetic energy is exactly half οf its pοtential energy is 0.35 secοnds.

Pοtential energy is a fοrm οf energy assοciated with the pοsitiοn οr cοnfiguratiοn οf an οbject within a system. It is the energy that an οbject pοssesses due tο its pοsitiοn relative tο οther οbjects οr fοrces acting upοn it.

In simple harmοnic mοtiοn, the kinetic energy (K) and pοtential energy (U) οf a blοck attached tο a hοrizοntal spring are related by the equatiοn:

K = (1/2) U

Given the frequency (f) οf the blοck is 0.72 Hz, we can determine the angular frequency (ω) using the fοrmula:

ω = 2πf

ω = 2π * 0.72

≈ 4.52 rad/s

The periοd (T) οf the blοck's mοtiοn can be calculated as:

T = 1/f

T = 1/0.72

≈ 1.39 s

Since the blοck is released frοm rest, at t = 0 s, the pοtential energy (U) is at its maximum while the kinetic energy (K) is zerο.

Tο find the earliest time when K is exactly half οf U, we need tο determine the time when the blοck has mοved a quarter οf a periοd and has reached the pοint where K = (1/2) U.

A quarter οf a periοd is given by T/4:

t = T/4

t = (1.39 s) / 4

t ≈ 0.35 s

Therefοre, the earliest time after the blοck is released when its kinetic energy is exactly half οf its pοtential energy is 0.35 secοnds.

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Answer:

The coin is denser than any of the liquids, and will sink through everything. The oil is the least dense liquid, so it will float on the water, and the syrup is the densest liquid, so it will sink below the water.

Explanation:

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° :. ° . ☆ . . • . ● .° °★ Not sure how to copy and paste? Just right click your mouse and choose copy in options, to release repeat the process and just paste it. No mouse? Select the text with your computer pad and use ctrl c to release, ctrl v. On mobile? Press on your screen and select the text, use the option copy and paste wherever you would like!

You can use the information below to calculate it :)

Density of water: 1000 kg/m3.

Density of the coin: copper 8.96   g/cm^3

nickel   8.90   g/cm^3

1 kg = 1000 g

All you have to do now is convert it and thats it

The increase in the time period of the pendulum with the increased length is 0.1 times or 10% of the initial time period.

What is a time period?

The time period of a periodic motion refers to the time it takes for one complete cycle or oscillation to occur. It is the time interval between two successive identical points in the motion.

The time period (T) of a simple pendulum is given by the equation:

T = 2π√(L/g)

where L is the length of the pendulum and g is the acceleration due to gravity.

Let's assume the initial length of the pendulum is L and the increased length is L + 0.21L = 1.21L (as it is increased by 21%).

The new time period (T') of the pendulum with the increased length can be calculated using the same equation:

T' = 2π√((1.21L)/g)

To find the increase in the time period, we subtract the initial time period (T) from the new time period (T'):

ΔT = T' - T

= 2π√((1.21L)/g) - 2π√(L/g)

= 2π(√(1.21L/g) - √(L/g))

= 2π(√(1.21)√(L/g) - √(L/g))

= 2π(1.1√(L/g) - √(L/g))

= 2π(0.1√(L/g))

Therefore, the increase in the time period of the pendulum with the increased length is 0.1 times the initial time period:

ΔT = 0.1T

Hence, the increase in the time period is 10% of the initial time period.

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The maximum electrical force that these protons will exert on each other is 2.48 x 10^-13 N.

The electrical force between two charged particles can be calculated using Coulomb's Law:

F = (k * q1 * q2) / r^2

Where:

F is the electrical force,

k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2/C^2),

q1 and q2 are the charges of the particles (in this case, both are protons, so each charge is q = 1.6 x 10^-19 C),

and r is the distance between the particles (assuming they are in contact, r ≈ 2 x 10^-15 m).

To find the maximum electrical force, we need to calculate the force when the protons are closest to each other. This occurs when they are just about to collide, so their separation distance is equal to the sum of their radii (r ≈ 2 x 10^-15 m).

Plugging the values into the formula, we have:

F = (8.99 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (2 x 10^-15 m)^2

F ≈ 2.48 x 10^-13 N

The maximum electrical force that these protons will exert on each other is approximately 2.48 x 10^-13 N. This force arises due to the interaction between their positive charges and is inversely proportional to the square of the distance between them.

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Answer:

Velocity can be directly added or subtracted.

For example, if a boat has a velocity V in still water.

And now you put the boat in a river with a current that has a velocity V'

The total velocity of the boat in that river is just the addition of these two velocities.

Velocity in the river  = V + V'

Where the only tricky part is that the velocity is a vector, so you need to take in account the directions of each vector.

In this case, we have a plane with a maximum velocity of 160km, let's assume a direction for this velocity, let's say that is in the positive x-direction.

Then we can write the velocity in the vector form:

velocity  = (vel in x-axis, vel in y-axis)

The velocity of the plane can be written as:

v = (160km/h, 0)

Now we add a crosswind of 30km/h

crosswind means that it is perpendicular, then it acts on the y-axis.

Then the total velocity of the plane will be:

velocity = (160km/h, 0) + (0, 30km/h)

velocity = (160km/h, 30km/h)

Now you can compute the total velocity of the airplane as the module of that vector.

Remember that for a vector (x, y) the module is:

mod = √(x^2 + y^2)

Then the module of the velocity is:

v = √( (160km/h)^2 + (30km/h)^2) = 162.8 km/h

I agree with Student 2: The frequency of the wave will remain the same as it is only dependent on the source, while the wavelength will increase as the wave moves into medium 2.

The equation that relates the velocity (v), frequency (f), and wavelength (λ) of a wave is:

v = f * λ

According to this equation, if the velocity increases in medium 2 compared to medium 1, and the frequency remains constant (as stated by Student 2), then the only way to maintain the equation is for the wavelength to increase in medium 2.

This behavior can be explained by the fact that different media have different properties, such as density and elasticity, which affect the propagation of the wave. When a wave travels from one medium to another, the speed of the wave can change. However, the frequency of the wave is determined by the source and remains constant. Therefore, in order to maintain the equation v = f * λ, the wavelength must adjust to compensate for the change in velocity.

In summary, Student 2 is correct in stating that the frequency of the wave will remain the same, while the wavelength will increase as the wave moves into medium 2 to keep the equation of the wave velocity valid.

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Answer:

fiber

Explanation:

To determine the child's near point, we need to use the formula: Near Point = 100 cm / (Lens Power in Diopters) Given that the child's contact lens prescription is 0.750 D, we can substitute it into the formula

To determine the child's near point, we need to use the formula:

Near Point = 100 cm / (Lens Power in Diopters)

Given that the child's contact lens prescription is 0.750 D, we can substitute it into the formula:

Near Point = 100 cm / 0.750 D

Near Point ≈ 133.33 cm

Therefore, the child's near point is approximately 133.33 cm.

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Answer:

17640

Explanation:

Power = workdone/time

Power = (force x displacement)/time

Power = (mg x 60)/60

Power = (1800 x 9.8 x 60)/60

=> power = 17640 watt

(a) The inductance of the solenoid is 0.0775 mH when solenoid is of radius 4.5 cm, has 660 turns and a length of 25 cm.

The inductance of a solenoid can be calculated using the formula:

L = μ₀N²A / l,

where L is the inductance, μ₀ is the permeability of free space (4π × 10^(-7) T·m/A), N is the number of turns, A is the cross-sectional area, and l is the length of the solenoid.

We are given that the radius of the solenoid is 4.5 cm (0.045 m), the number of turns is 660, and the length is 25 cm (0.25 m).

First, we need to calculate the cross-sectional area:

A = πr² = π(0.045 m)² ≈ 0.006366 m².

Now, we can substitute the values into the formula to calculate the inductance:

L = (4π × 10^(-7) T·m/A) × (660 turns)² × (0.006366 m²) / (0.25 m).

L ≈ 0.0775 mH.

(b) The rate at which current must change through the solenoid to produce an emf of 50 mV is 645.16 A/s (amperes per second).

According to Faraday's law of electromagnetic induction, the induced electromotive force (emf) in a coil is given by:

ε = -L(dI/dt),

where ε is the emf, L is the inductance, and (dI/dt) is the rate of change of current with respect to time.

We are given that the emf is 50 mV (0.05 V) and we need to find the rate of change of current.

Rearranging the formula:

(dI/dt) = -ε / L.

Substituting the given values:

(dI/dt) = -(0.05 V) / (0.0775 mH).

Converting mH to H (Henries):

(dI/dt) = -(0.05 V) / (0.0775 × 10^(-3) H).

(dI/dt) ≈ -645.16 A/s.

Since we are asked for the magnitude, we take the absolute value:

Rate of change of current ≈ 645.16 A/s.

(a) The inductance of the solenoid is approximately 0.0775 mH.

(b) The rate at which the current must change through the solenoid to produce an emf of 50 mV is approximately 645.16 A/s.

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The following statements are true:

- In region I, the magnetic field is into the page and is never zero.

- In region II, the field is into the page and can be zero.

- In region III, it is possible for the field to be zero.

The magnetic field produced by a current-carrying wire follows the right-hand rule. When two parallel wires carrying currents in opposite directions are considered, the magnetic field in the regions around the wires can be determined.

In region I, the magnetic field is between the two wires. According to the right-hand rule, the magnetic field produced by the current in wire I1 is into the page, while the field produced by the current in wire I2 is out of the page. These fields add up to create a net magnetic field into the page. Since the currents are non-zero, the magnetic field in region I is never zero.

In region II, the magnetic field is outside the wires. The fields produced by the currents in wires I1 and I2 are still into the page and out of the page, respectively. However, at certain points between the wires, the magnitudes of these fields can cancel each other out, resulting in a net magnetic field of zero. Therefore, in region II, the field can be zero.

In region III, which is outside both wires, the magnetic field produced by each wire individually decreases with distance. At a certain distance from the wires, the magnetic fields can cancel each other out, resulting in a net magnetic field of zero. Therefore, in region III, it is possible for the magnetic field to be zero.

In summary, in the given scenario of two long, parallel wires carrying currents in opposite directions, the magnetic field is into the page in region I and can be zero in regions II and III. This understanding is based on the right-hand rule and the superposition principle for magnetic fields.

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The overall angular magnification of the object, considering two significant figures, is approximately -0.4.

To find the overall angular magnification of the object using the given parameters, we can use the formula for angular magnification:

Magnification (M) = -(focal length of the objective lens) / (focal length of the eyepiece)

Given data:

Focal length of the objective lens (f_objective) = 10.0 mm = 1.0 cm

Focal length of the eyepiece (f_eyepiece) = 2.5 cm

Substituting these values into the formula, we have:

M = -(1.0 cm) / (2.5 cm)

M = -0.4

The negative sign indicates that the image formed is inverted.

Now, to calculate the overall angular magnification, we need to consider the object distance (d_object) and the image distance (d_image) in relation to the objective lens.

Object distance from the objective lens (d_object) = 0.90 mm = 0.09 cm

Since the final image is formed at infinity, we can consider the image distance (d_image) to be at infinity.

Using the formula for angular magnification with distances:

Overall Magnification (M_overall) = M * (1 + d_image / d_object)

As d_image is infinity, we can approximate the overall magnification as:

M_overall ≈ M

Substituting the value of M, we have:

M_overall ≈ -0.4

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Answer:

Shear stress  is 50.63 Pascal

Explanation:

As we know shear stress = [tex]\frac{\rho V^2 f}{8} \\[/tex]

Rho is the density

V is the velocity

f is the value from Moody's chart

We will know determine Reynolds number  to determine the flow type and then the f value

[tex]R_e = \frac{ \rho*V*D}{u}[/tex]

[tex]R_e = \frac{1000*3*0.0254}{0.001} = 76200[/tex]

This is a turbulent flow and hence the roughness index is [tex]\frac{E}{D} = 0.0157[/tex], From this we get f = 0.045

Now shear stress = [tex]\frac{1000 * 3^2 * 0.045}{8} = 50.63[/tex] Pa

(a) The radial velocity and tangential velocity exiting from the impeller tip are 3.768 m/s and 10.472 m/s respectively.

(b) The stagnation temperature out of the diffuser (To₃) is 400 × [tex](P_3 / 400)^{0.4[/tex].

(c) The overall pressure ratio (Po₃/Po₁) is (P₃ / P₁) × [tex](To_3 / To_1)^{(y/(y-1))[/tex].

(d) The axial Mach number entering the eye region is √((2 / (1.4 - 1)) × [tex]((Po_1 / 100)^{((1.4-1)/1.4) - 1))[/tex]

Given:

Inner diameter (root) of the eye region: 0.15 m

Outer diameter (tip) of the eye region: 0.3 m

y = 1.4

Cp = 1 kJ/(kg K)

Impeller tip diameter: 0.5 m

Impeller height: 0.05 m

Impeller speed: N = 200 rev/s

Number of impeller blades: 12

Slip factor: σ = 1 - (0.63π / n)

Power input factor: n = 1.04

Isentropic efficiency: nc = 0.95

The static temperature at the impeller tip (station 2): T2 = 400 K

Static pressure at impeller tip (station 2): P2 = 400 kPa

Pressure at station 1 (eye region): P₁ = 100 kPa

The temperature at station 1 (eye region): To₁ = 300 K

(a) Radial velocity (Vr₂):

Vr₂ = (π × D₂ × N) / (60 × σ × n)

Vr₂ = (π × 0.5 × 200) / (60 × (1 - (0.63π / 1.04)))

Vr₂ ≈ 3.768 m/s

Tangential velocity (Vt₂):

Vt₂ = (π × D₂ × N) / 60

Vt₂ = (π × 0.5 × 200) / 60

Vt₂ ≈ 10.472 m/s

(b) Stagnation temperature out of the diffuser (To₃):

To₃ / To₂ = [tex](P_3 / P_2)^{((y-1)/y)[/tex]

To₃ / 400 = [tex](P_3 / 400)^{(0.4)[/tex]

To₃ = 400 × [tex](P_3 / 400)^{0.4[/tex]

(c) Overall pressure ratio (Po₃ / Po₁):

Po₃ / Po₁ = (P₃ / P₁) × [tex](To_3 / To_1)^{(y/(y-1))[/tex]

(d) Axial Mach number entering the eye region (M₁):

M₁ = √((2 / (y - 1)) × [tex]((Po_1 / P_1)^{((y-1)/y) - 1))[/tex]

M₁ = √((2 / (1.4 - 1)) × [tex]((Po_1 / 100)^{((1.4-1)/1.4) - 1))[/tex]

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