For a telescope of a particular size, the angular resolution is poorer at shorter wavelengths of light. True False

Hello!

Recall that the magnetic field produced by a solenoid with a time-varying current is given by:

[tex]B(t) = \mu_0 ni(t)[/tex]

[tex]B(t)[/tex] = time-varying magnetic field (T)

[tex]\mu_0[/tex] = Permeability of free space (4π × 10⁻⁷ Tm/A)

[tex]n[/tex] = number of turns/meter (20000)

[tex]i(t)[/tex] = time-varying current

**Since we have AC current, we can use a sinusoidal function to represent the current.

Let's now figure out the expression for the current.

The typical format of a sinusoidal function for current is:

[tex]i(t) = Asin(\omega t + \phi)[/tex]

A = amplitude (max current, 10 A)
ω = angular frequency (rad/sec)
φ = phase shift (we will assume there is not one since it is not given.)

We are also assuming we are starting from t = 0 s.

Now we need to solve for the angular frequency to complete our equation.

If the current changes direction every 0.01 seconds, that means that the PERIOD of the current is double this (aka, how long it takes for the current to repeat the same magnitude and direction).

Think about AC current like an oscillating mass on a spring. When the current changes directions, (every 0.01 sec), there is momentarily no current (temporarily no moving charge). The peak current will occur at the halfway point between each change in direction, or every 0.005 sec. Additionally, using this analogy, the mass on a spring changes direction TWICE before it returns to its original position, which is why our period here is double the time it takes for the current to switch directions.

So:
[tex]T = 2(0.01) = 0.02[/tex]

Now, we can convert from period to angular frequency.

[tex]\omega = \frac{2\pi}{T} = \frac{2\pi}{0.02} = 100\pi[/tex]

We have the current equation as:
[tex]i(t) = 10sin(100\pi t)[/tex]

So, our magnetic field produced by the solenoid will be:

[tex]B(t) = (4\pi *10^{-7})(20000)(10sin(100\pi t) )= 0.251sin(100\pi t)[/tex]

Since we have that figured out, we can use Faraday's Law to find the induced emf:
[tex]\epsilon = -N \frac{d\Phi_B}{dt}[/tex]

ε = Induced EMF (V)
N = number of loops in COIL (10 loops)

[tex]\Phi_B[/tex] = Magnetic Flux (Wb)

The area of the coil is constant so we can rewrite the equation as:
[tex]\epsilon = -N * A\frac{dB}{dt}[/tex]

Where 'A' is the cross-sectional area of the COIL.

Let's calculate that:
[tex]A = \pi (0.01^2) = 0.000314 m^2[/tex]

Now, let's calculate the induced emf. Using our equation for 'B' we got earlier:
[tex]B(t) = 0.251sin(100\pi t)\\\\\frac{dB}{dt} = (100\pi)(0.251)cos(100\pi t) = 78.957cos(100\pi t)[/tex]

Combining this into Faraday's equation:
[tex]\epsilon = -N * A\frac{dB}{dt}\\\\\epsilon = -(10)(0.000314)(78.957cos(100\pi t) = -2.48cos(100\pi t)[/tex]

The magnitude is the absolute value, so:
[tex]\epsilon = \boxed{2.48cos(100\pi t) \text{ V}}[/tex]

A hydroelectric power station turns energy from kinetic into electrical.

Thus, we can conclude that hydroelectric power station turns energy from kinetic into electrical.

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Answer:

bussy

Explanation:

shart

The deflection angle would have been 37.29º if the prism had been made of polystyrene plastic.

As we know that the deflection angle is an angle between the moving object from its directed course.

In the following question the deflection angle as laser enters the beam is, B = 22.6º

refractive index of glass, n1= 1.52

refractive index of polystyrene plastic, n2 = 1.59

Now when we see for the second surface then ,

B  = 45º - 22.6º

B  = 22.40º

So from Snell's law:

n1 sinθ1 = n2 sinθ2

→ sin B / sinθ = n1 / n2

sinθ = (sin 22.40º) × ( 1/ 1.59)

θ = 37.29º

Thus, the deflection angle should be 37.29º if the prism is made of polystyrene plastic.

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During photosynthetic electron transport, protons accumulate at high concentration inside the thylakoid space.

Photosynthesis:

Plants and other living things employ a process called photosynthesis to transform light energy into chemical energy that can then be released through cellular respiration to power the organism's activities.

The word "photosynthesis" comes from the Greek words "light" and "putting together," and refers to the process of creating molecules of carbohydrates from carbon dioxide and water. These molecules, such as sugars and starches, are then stored with some of this chemical energy.  Photoautotrophs are creatures that perform photosynthesis, including most plants, algae, and cyanobacteria. The majority of the energy required for life on Earth is produced and maintained by photosynthesis, which is also substantially responsible for producing and maintaining the oxygen content of the atmosphere.

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C) A current is induced in the coiled wire, which lights the light bulb

The moving magnetic field creates electricity which lights the light bulb

Hope it helps!

Answer:

C) A current is induced in the coiled wire, which lights the light bulb

Explanation:

Answer:

1/4

Explanation:

Fgravity is proprtional to  1 / r^2

   now double r   to 2r

        1 / (2r)^2   = 1/4 * 1/r^2   <======this shows the  force to be reduced to 1/4  of original  when the distance is doubled

You should slow your pwc to "slow, no wake speed" when within 100 feet of anchored vessels or non-motorized craft.

This is the process of operating a personal watercraft at the slowest possible speed.

This helps to maintain steerage which prevents different forms of accident or risks when in motion in the water.

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Color of third band of a coded resistor is Brown.

What is Resistance:

The color code specify the resistance value, the tolerance, and sometimes the reliability or failure rate.

How to identify resistor's color codes:

Here,

the value of resistance is 2.3x10^2 Ω

R = 23x10^1 Ω

here power of 10 is 1

so, the color of third band of a color coded resistor will be related to number 1

Hence,

color of third band of a coded resistor is Brown.

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The speed or the linear velocity of the stone is 9.93 m/s; option C

The linear velocity of the stone is given by the formula below:

where w is angular velocity and r is radius.

w = θ/t

1 complete revolution = 2π radians

5 revolutions = 10π radians

w =  10π/4.4 rad/s

v = 10π/4.4 rad/s * 1.4

v = 9.93 m/s

In conclusion, the linear velocity is obtained from the angular velocity and radius of the string.

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The magnetic flux through one turn of the wire making the solenoid is 7.88*10^-7 T m^2.

B = unI

= 4pi*10^-7*(100/0.1)*2

= 0.00251 T

Therefore, Flux = B*Area

= 0.00251*pi*(0.01^2)

= 7.88*10^-7 T m^2

Magnetic flux is a measurement of the entire magnetic discipline which passes thru a given vicinity. It's far a useful device for helping describe the outcomes of the magnetic pressure on something occupying a given vicinity. The size of the magnetic flux is tied to the specific location chosen.

The SI unit of magnetic flux is the Weber (Wb). A flux density of 1 Wb/m2 (one Weber in keeping with rectangular meter) is one Tesla (T).

A magnetic subject describes a location in which a magnetic pressure may be felt. Magnetic flux describes how a good deal of magnetic discipline passes through a place.

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The electrical energy used = 3.11 x 107 J; option A

The energy used is calculated using the formula below:

The total power = 3450 Watts

Total time in seconds = 2.5 × 3600 = 9000 s

Energy used = 3450 × 9000 = 3.11 x 107 J

In conclusion, electrical energy is the product of power and time.

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The coefficient of kinetic friction between the box and the floor will be 3.83.

It is a type of opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N).

it is defined as the product of the coefficient of friction and normal reaction.

Given data;

m is the mass of a boy = 60 kg

Horizontal force,f = 115 N

The coefficient of kinetic friction between the box and the floor,μ

Acceleration,a = 0.5 m/s²

The friction force is found as;

f = μN

The normal force is found as;

N =ma

f=μma

115 N = μ × 60 kg × 0.5 m/s²

μ = 3.83

Hence, the coefficient of kinetic friction between the box and the floor will be 3.83.

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Head restraints are energy-absorbing device that protects against such injuries.

Head restraints are a car protection characteristic, connected or included into the pinnacle of each seat to restrict the rearward motion of the grownup occupant's head, relative to the torso, in a collision to save you or mitigate whiplash or damage to the cervical vertebrae.

Powerful head restraints are designed to reduce the rearward motion of the head in a rear-end crash and reduce the probability of occupants maintaining whiplash neck injuries. Head restraints are generally known as head rests.

Make certain the top of the top restraint is at least a degree from the pinnacle of your head. The role is the pinnacle restraint so it's as near the again of your head as possible. You may need to alter the again of seat.

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The centripetal acceleration of the satellite will be less than acceleration due to gravity on earth (g).

Calculation of centripetal acceleration of satellite:

Let the radius of earth be, R

Let the radius of satellite be, R'

Let the gravitational constant be, G

Let the acceleration due to gravity (earth) be, g

Let the mass of earth be M

Step 1:

We know that the orbital velocity of satellite can be given as:

v =√GM/R'     - ( 1 )

Thus, the centripetal acceleration of the satellite will be:

a_c = v²/R' = GM/R'²            - ( 2 )

The acceleration due to gravity is given as:

g = GM/R²                             - ( 3 )

Step 2:

From equation 2 and 3 we get:

a_c/g = GM/R'² ÷ GM/R²

a_c/g = R²/R'²  < 1  

Step 3:

Thus we get:    

a_c/g < 1

a_c < g

Therefore, the centripetal acceleration of the satellite is smaller than acceleration due to gravity on earth.

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Answer:

12.6 s

Explanation:

y =  1/2 at^2

780.1 =  1/2 ( 9.81) t^2           answer can only have 3 s.d. due to the 9.81

t = 12.6 s

The star is moving toward the earth.

It is due to the phenomenon of the Doppler shift.

The Doppler effect, commonly referred to as "Doppler shift," is the change in the wavelength or frequency of waves as a result of an observer's motion in relation to the wave source.

It is possible to see this apparent wavelength change in the visible light emitted by stars and galaxies.

As a result, a star moving toward Earth appears to emit light with a shorter wavelength than a light source that is stationary. It is known as blueshift because shorter wavelengths cause the spectrum to shift toward the blue end.

While a star traveling away from us appears to shift its light towards longer wavelengths. Astronomers refer to this as redshift since it is closer to the red end of the spectrum.

As the spectrum of a particular star shows the hydrogen line appearing at a shorter wavelength of 480 nm in comparison to the laboratory measurements, that show the same hydrogen lines at a greater wavelength of 500 nanometers, that’s why we conclude that the star is moving toward earth.

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The average speed can be calculated by dividing the total distance traveled by the total time taken.

The average speed of a vehicle can be calculated by finding the ratio of the total distance traveled and the total time taken on the journey.

Average speed = total distance covered/total time taken

Since there are markers that indicate every 100-meter journey. The total number of such marker posts encountered multiplied by 100 will give an estimate of the total distance traveled in meters.

A record of the time taken on the journey will give the total time taken.

Hence, average speed = total number of marker posts x 100/total time.

The unit will be in m/s.

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Potential and kinetic energy both decrease with the acorn's falling potential and kinetic energy.

The acorn's potential energy is at its peak when it reaches the top of the tree, yet its kinetic energy is zero (i.e., it is not accelerating).

The height of the ball reduces along with the potential energy as the acorn tumbles down the tree, but the kinetic energy rises (energy due to motion)

The height will be 0 and the kinetic and potential energy will be zero at the ground. This demonstrates that as an item falls, both potential and kinetic energy are lost.

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Answer:

v = 10m/s.

Explanation:

100 = 1/2×2×v^2

100 = 1×v^2

v^2 = √100

v=10 m/s

Imagine that a star-forming cloud collapses but retains all of its mass in a single blob. In order to conserve angular momentum, the cloud must spin faster.

Conservation of angular momentum is a physical characteristic of a rotational system that keeps its rotation constant unless it is affected by an external torque. In other words, the speed is constant as long as the net torque is zero.

In angular kinematics, conservation of angular momentum refers to the tendency of the system to preserve angular momentum in the absence of external torque. If the objects collide without net external torque, the angular momentum is constant. The two objects exert equal but opposite angular momentums to maintain the full angular momentum of the colliding system.

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Answer:

See below

Explanation:

You have to heat the calorimeter to 100 C  from 20 C

  this will take   .20 kg *    390 j /kg-C   *  80 C = 6240 j

You have to heat the mass of water to boiling point (100 C ) from 20C

this will take    

    .50 kg * 4182 j/kg-C  * 80 = 167,280 j

AND you have to add enough heat to boil off  .03 kg of water:

   .03 kg * (2260000 j/kg-C )  = 67,800 j

Power = joules / sec =  (6240 + 167280 + 67800) / 274.8 = 878 watts

Your answer may differ just a bit for slightly different or rounded values of specific heat or heat of fusion for water .....

The final velocity for object a is 5.6 m/s in the opposite direction.

From the conservation of momentum, we know that the collision between two objects will result in the conservation of initial momentum and the final momentum i.e.,

                                    Pi  =  Pf

It is given that,

                      m₁ = 1.5 kg

                       u₁ = 11.2 m/s

                       m₂= 4.5 kg

                        u₂= 0

                         v₂= 5.6 m/s

We need to find v₁.

              Using momentum conservation

               m₁ u₁ + m₂ u₂ =  m₁ v₁ + m₂ v₂

               1.5 × 11.2 + 4.5 × 0 =  1.5 × v₁ + 4.5 × 5.6

                                   16.8 + 0 =  1.5 × v₁ +  25.2

                                  -8.4/ 1.5  =  v₁

                                    v₁ = - 5.6 m/s

Here, the negative sign shows that body is moving in the opposite direction.

Hence, option (d) is correct.

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(a) mass = 80kg

height h= 2km

the potential energy at the peak of the mountain= mgh=80*9.8*2000=1568000J

therefore the potential energy at the peak of the mountain is 1568000J

(b) Work done in reaching the peak will be equal to the change in potential energy = 1568000)

therefore the work done is 1568000J

(c) Power is given by

P=W/t=1568000/(30*60)=871.11W

therefore the Power is 871.11W

The work done by force can be defined as the product of the displacement of an object and the component of the applied force acting in the direction of the displacement of the object.

Potential energy is stored energy that depends on the relative position of different parts of the system. Springs have more potential energy when compressed or stretched. Steel balls have more potential energy to be lifted across the ground than after they have fallen to Earth.

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Answer:

An electrically polarized object can have zero net charge, while a charged object cannot have zero net charge.

I hope this helps :D

Answer:

The current in a circuit can be determined as total amount of charge passes through a wire's full cross section area.

Explanation:

The current is a flow of electrical charge carriers electrons.

The current is denoted with symbol uppercase letter I.

The standard unit for current is the ampere, symbolized by A.

Current is the change in charge with change in time.

Hence we can say that,

The current in a circuit can be determined as total amount of charge passes through a wire's full cross section area.

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A train travels at a speed of 24 m/s. Then it slows down uniformly at 0.065 m/s² until it stops the distance does the train travel while slowing down are 4430.75 m.

Distance measures length. For example, the gap of a street is how lengthy the street is. In the metric gadget of size, the maximum not unusualplace devices of distance are millimeters, centimeters, meters, and kilometers.

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Answer:

ocean-continent convergent boundaries

Examples of ocean-continent convergent boundaries are subduction of the Nazca Plate under South America (which has created the Andes Range) and subduction of the Juan de Fuca Plate under North America (creating the mountains Garibaldi, Baker, St.