a grating that has 3700 slits per cmcm produces a third-order fringe at a 26.0 ∘∘ angle.
Part A
What wavelength of light is being used?
Express your answer to two significant figures and include the appropriate units.

The mass of Jupitar is obtained from the calculations as 5.8 * 10^-14 Kg.

There are nine planets in the solar system and the sun lies at the enter of our solar system. This is the heliocentric model of the solar system.

Given that;

T^2 = GMr^3/4π

T = period

G = gravitational constant

r = radius

M = mass of Jupitar

Now;

1 day = 86400 seconds

1.77 days = 1.77 days *  86400 seconds/1 day

= 152928 seconds

Making M the subject of the formula;

M =4πT^2/Gr^3

M = 4 * 3.142 * (152928)^2/6.67 × 10^-11 * (422 × 10^9)^3

M = 2.9 * 10^11/5.0 * 10^24

M = 5.8 * 10^-14 Kg

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The lion has a kinetic energy of 5000 j, the speed of the lion is  v = 100 / [tex]\sqrt{M1}[/tex]  m/s

Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy or Kinetic energy is the energy that an object possesses due to its motion. It is basically the energy of mass in motion. Kinetic energy can never be negative and it is a scalar quantity i.e. it provides only the magnitude and not the direction.

given

kinetic energy = 5000 J

speed = ?

since , mass is not given in the question

Let mass of lion will be = M1

kinetic energy = 1/2 * M1 * [tex]v^{2}[/tex]

             5000 J = 1/2 * M1 *  [tex]v^{2}[/tex]

             [tex]v^{2}[/tex] = [tex]\sqrt{10,000 / M1}[/tex]  m/s

              v = 100 / [tex]\sqrt{M1}[/tex]  m/s

The speed of the lion =  v = 100 / [tex]\sqrt{M1}[/tex]  m/s

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21 cm is  the wavelength of the 21-cm-line if it was coming from a distance of 8,000,000,000 (8*10^9) light-years

Only when relative velocity changes do wavelength alter. Thus, the wavelength will not change. A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in consecutive cycles.

This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm). The relationship between frequency and wavelength is inversely proportional. The wavelength of the wave with the highest frequency is the shortest. Half the wavelength corresponds to twice the frequency. The wavelength in the red spectrum is the longest.



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The temperature rises of in the block if the current flows for 10 minutes is, 34.78K.

To find the answer, we need to know about the power of the electric heater.

                           [tex]P=40 W\\m=1.5kg\\S=460\\t=10minutes=10*60s=600s[/tex]

                             [tex]P*t= mS[/tex]ΔT

                           ΔT [tex]=\frac{P*t}{mS} =\frac{40*600}{1.5*460} =34.78K[/tex]

Thus, we can conclude that, the temperature rises in the block if the current flows for 10 minute is 34.78K.

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If the current flows for 10 minutes, the temperature in the block rises by 34.78 K.

We must understand the electric heater's power in order to determine the solution.

              [tex]P=40Watts\\m=1.5kg\\s=460\\t=10 min=600s[/tex]

                    [tex]Pt=ms[/tex]ΔT

We must determine the increase in temperature, T.

             ΔT[tex]=\frac{Pt}{ms} =34.78 K[/tex]

Thus, we can infer that if the current flows for 10 minutes at 34.78K, the temperature in the block will increase.

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(a) The diameter of the largest orbit just before the protons exit the cyclotron is 39 cm.

(b) The number of orbits completed by the proton during this 1.0 ms is 14000 revolutions.

What is  kinetic energy?

The kinetic energy of an object is the energy that it possesses due to its motion.

It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Formula of KE:

K.E = 1/2mv²

mv² = 2 K.E

v = sqrt( 2*KE / M)

Here,

(a)

The KE of the medical isotopes = 6.5 MeV

substituting the values,

v = sqrt( 2* 6.5* 1.6* 10^-13 / 1.67* 10^-27 )

v = 3.53 × 10⁷ m/s

Now the centripetal force:

mv² / R = qvB

r = q*v / mv²

r = ( 1.67* 10^-27 * 3.53 × 10⁷ ) / ( 1.9* 1.6* 10^-19 )

r = 0.19415 m

diameter d = 2r,

d= 2(0.19415  m)

d= 0.39 m ≅ 39 cm

(b)

The time period to complete a revolution around the spiral trajectory is:

T = 2πr / v

T = 2*3.14* 0.1941 / 3.53*10^7

T = 0.7 × 10⁻⁷ s

Thus, the number of orbits that the proton does to complete the revolution in 1 ms is:

n = t / T

n = 10^-3 / (0.7*10^-7)

n = 14285.71  ≅ 14000 revolutions

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Your question is incomplete, but most probably full question was:

A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 T.

(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d = 57 cm Previous

(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?

The particle that was given off in the reaction beta rays is β–. Option C

A nuclear reaction will involve the change in the nucleus of an atom. It often leads to the production of new nucleus. As we can see the equation, there was a transformation from nitrogen nucleus to oxygen atom.

Thus, the particle that was given off in the reaction beta rays is β–. The fact that the mass number remained the same but the atomic number increased by one unit from left to right implies that a beta decay has occurred.

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Answer:

1.66m/s

Explanation:

here

initial velocity(u): 0m/s

final velocity (v):60km= 60×1000/60×60

:16.6m/s

time taken(t): 10s

now

acceleration:v-u/t

or a: 16.6-0/10

:16.6/10

acceleration: 1.66 m/s

In physics, acceleration is the rate at which the velocity of an object changes in relation to time. The sum of all forces exerted on an object results in its acceleration. The acceleration is  1.66 m/s².

The rate at which velocity, either in terms of speed or direction or both, varies over time is known as acceleration. A circle's motion accelerates despite its constant speed because its direction is continually shifting.

Here

initial velocity(u) = 0m/s

final velocity (v) = 60km

v = 60 × 1000 / 60 × 60

v = 16.6 m/s

Time taken(t) =  10s

Now.

acceleration =  v-u / t

a = 16.6-0/10

a = 16.6/10

a = 1.66 m/s²

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The clothing seems white because the entire light is reflected.

Absorption:

This occurs when light is transformed into another type of energy. This happens when light vanishes while travelling through another medium.

reflection:

It is referred to as light reflection when a light ray hits a polished, smooth surface and bounces back. The incident light rays hit the surface and are reflected off of it. The beam that returns is referred to as the reflected ray.

according to the question we know that a shirt appears a color because it reflects that color of light. A shirt appears black when it absorbs all wavelengths of light. In case  of white shirt no wavelength is absorbed by the shirt due to which the shirt appears white and in simple words the entire light is reflected back.

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The amount of excess load that can be imposed on the wing of an airplane depends upon the speed of the airplane.

What is meant by wing loading?

Wing loading in aerodynamics is the ratio of the loaded weight of the aircraft and the area of each wing. It is given as:

W_L = W (weight of the aircraft) / S (gross wing area of the airplane)

The more speed an aircraft gains, the more lift is produced by each unit of wing area.

Thus, with a high value of wing loading the aircraft lands and takes-off at higher speeds with low maneuvering control. Generally, Airliners have high wing loading while smaller airplanes have lower wing loading.

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Answer:

R = ρ L / A     where R is the resistance and ρ the resistivity:

R2 / R1 = (L2 / A2) / (L1 / A1) = L2 * A1 / (L1 * A2)

R2 / R1 =  (2 L * A) / (L * 2 A) = 1

Their resistances should be the same.

They are useful in providing larger frictional force.

The force produced by two surfaces coming into contact and sliding against one another is referred to as frictional force.

The following variables impact the frictional force: Surface roughness and the amount of force pressing them together have the biggest impact on these forces.

Football shoes have spikes or studs because they offer more frictional force when running on grass than regular shoes do.

The studs make it easier for players to move faster and change directions rapidly without slipping while also preventing them from slipping on the grass.

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Since , e"(h) = M >0

hence ,  At p3 3ε/M  function e(h) has a minimum of function.

In mathematics, point at which the value of a function is less than or equal to the value at any nearby point (local minimum) or at any point (absolute minimum) or the minimum value of a function is the lowest point of a vertex

e(h) = ∈ /h +( [tex]h^{2}[/tex]/6) M

e'(h) = - ∈ /[tex]h^{2}[/tex] + (2h/6) M

putting , e'(h)  = 0

- ∈ /[tex]h^{2}[/tex] + (2h/6) M  = 0

h = [tex](3 /M)^{1/3}[/tex] *  (∈^(1/3))

e"(h) = 2∈ / [tex]h^{3}[/tex] + (2M)/6                          equation 1

substituting value of h in equation 1, we get

e"(h) = 2∈M / 3∈ + M/3

e"(h) = M >0

hence ,  At p3 3ε/M  function e(h) has a minimum

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The frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.

The frequency heard by the observer is calculated by applying the principle of Doppler effect.

f₀ = f'[(v/v - vs)]

where;

f₀ = 500[(343 / 343 - 36)]

f₀ = 500(343/307)

f₀ = 558.6 Hz

Thus, the frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.

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The force require to keep grouper submerged is 8.207N.

According to Archimedes principle  buoyant force of any object must equal to weight of fluid it displaced.

The expression for the force exerted to stay submerged in salt water is

           F = F(b) - w(fish)

 where F(b) = buoyant force

              w(fish) = weight

      now substitute w(b) for F(b)

   →  F = Vρg - w(fish)

where  V = volume of sea water

             ρ = density of sea water

Now by Archimedes principle   V = m(fish)  / ρ(fish)

    →    F = (m(fish) / ρ (fish) ) ρg - m(fish)g

           F =   (85 kg/1015 kg-m^-3) (1.025× 10³ kg-m^-3) (9.8 m/s^2)

                                  -   (85kg)  × 9.8 m/s^2

           F = 841.207N - 833N

           F = 8.207 N

  Hence, the force require to keep grouper submerged is 8.207N.

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A rubber ball and a stone of the same size are examples which will have more inertia and is therefore denoted as option A.

This is referred to as the property exhibited by a body in which it has the tendency to remain at rest or in uniform motion.This property is dependent on the mass of the substance as we can deduce that the greater the mass, the greater the inertia and vice versa.

The size of a rubber ball and stone will have different masses in which that of the stone will be greater. This is as a result of the difference in the nature of the substances which are used to make both items mentioned above.

This is therefore the reason why  a rubber ball and a stone of the same size as having more inertia(mass) where chosen as the most appropriate choice in this scenario.

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X and Y are two things that travel in the same direction. The mass of the things is the same. 5.0 m/s is the velocity of object x as it moves to the right. The velocity of object y to the left is 3.0 m/s. Objects x and y collide and adhere to one another. Following their collision, they both move at a speed of 1.0 m/s to the right.

Their velocity after colliding is 1.0 m / s to the right.

What is the velocity during the collision?

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The magnitude of the electric potential difference between the plates is 37.63 V.

Given:

Distance between the plates, d = 9 cm

Surface charge density, ρ = 3.7 nC/m² = 3.7 × 10⁻⁹ C/m²

Calculation:

For two parallel plate conductors, the electric field is given as:

E = ρ/ε₀

where ρ is the charge density

           ε₀ is the permeability of free space

Applying values in the above equation we get:

E = ( 3.7 × 10⁻⁹ C/m²)/(8.85 × 10⁻¹² C²/m)

  = 418.08 V/m

Now, the potential difference between the plates separated by a distance 'd' is given as:

ΔV = Ed

where E is the electric field

           d is the distance of separation between the plates

Applying values in the above equation we get:

ΔV = (418.08 V/m) × (0.09 m)

     = 37.63 V

Therefore, the magnitude of the electric potential difference between the plates is 37.63 V.

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Increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.

Work is a measure of energy expended in moving an object. It is calculated by multiplying the force by the distance.

According to this question, work is required to move a car from one position to another.

The distance moved from 0 - 30mph is more than that moved from 50 - 60mph, therefore, increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.

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Answer:

1. 571.43m/s

2. 142.9m and 342.9m

Explanation:

1.Take the difference in time.

1.2-0.7=0.7 seconds

Take the distance between them and divide with differnce in time.

400÷0.7=571.43 seconds.

2.Take the time of the two men and divide by two.

0.5÷2= 0.25 secs

1.2÷2= 0.6 secs

multiply each with the velocity.

0.25×571.43=142.9m

0.6×571.43=342.9m

SOLUTION:

Acceleration = Force/mass

= 100N / 2 kgs

= 50 m/s

.

.

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Answer: 37 Celsius and 310.15 K

Explanation:

C/5 = (F-32)/9 = (98.6-32)/9 = 66.6/9 = 7.4

C = 7.4 * 5 = 37 so the temperature is 37 Celsius

K = C + 273.15 = 37 + 273.15 = 310.15 K

In the pinball game, momentum is transferred from the plunger to the ball.

What is momentum?

Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity.

The formula of the momentum is: p = m*v

Here a pinball game machine is given.

We know that,

Hence,

In the pinball game, momentum is transferred from the plunger to the ball.

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The weight required to stretch the spring 12.5 cm is 7.5 N (Option A)

The new weight required to stretch the spring can be obtained as follow:

W₁ / L₁ = W₂ / L₂

3 / 5 = W₂ / 12.5

Cross multiply

W₂ × 5 = 3 × 12.5

Divide both sides by 5

W₂ = (3 × 12.5) / 5

W₂ = 7.5 N

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Answer:

See below

Explanation:

The force applied and the length of the arm

The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.

What is torque?

The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction. A vector quantity is a torque.

Torque is defined as Γ=r×F=rFsin(θ). In other words, torque is the cross product of the force vector, where 'θ' is the angle between r and F, and the distance vector (the distance between the pivot point and the place where force is applied).

The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.

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The pattern of organization Alicia chose for her speech outline is referred to as topical.

This type of organization involves the arrangement of subtopics within a large or broad topic.

Alicia talked about speech pathology and the different subtopics include challenges, therapy etc which depicts topical pattern.

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Answer: An object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.

Explanation: To find the answer, we need to know more about the kinetic and potential energies.

                           [tex]KE=\frac{1}{2}mv^2[/tex]

Thus, we can conclude that, an object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.

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The applied voltage is 1.41* 10⁴ kV.

Calculation of applied voltage-

The capacitance of parallel plates in the absence of a dielectric is:

C = ∈₀A/d

where, "d" = the spacing between the plates = 0.01 * 10⁻³ m

"A" = the area of the plates = 4 m²

"∈₀" = the constant = 8.85419*10⁻¹² C²/Nm²

So, C₀ = [tex]\frac{8.85419*10^{-12}*4 }{0.0100*10^{-3} }[/tex]

          = 3541.67 *10⁻⁹ F

The dielectric constant, κ= 3.4, is defined as:

κ = C/C₀

The effective capacitance (with the dielectric) is denoted by "C", whereas the original capacitance is denoted by "C₀". (without the dielectric).

As a result, the new capacitance is:

C = κC₀

However, capacitance is connected to a voltage by:

C = Q/V

utilizing the increased capacitance and accounting for "V":

κC₀ = Q/V

V = Q/κC₀ = [tex]\frac{0.170}{3.4 * 3541.67 *10^{-9} }[/tex] = 1.41* 10⁴ kV

Therefore the applied voltage is 1.41* 10⁴ kV.

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The speed of the ambulance is 4.61 m/s.

Doppler's effect formula is used, which is

[tex]f' = f (\frac{v + vo}{v + vs})[/tex]

Where,

f' = observer frequency of sound

f = actual frequency of sound waves

v = speed of sound waves

vo = velocity of observer

vs = velocity of source

Here, observer is the cyclist and source is the ambulance.

Given,

f' = 1590 Hz

f = 1600 Hz

v = 343 m/s

vo = 2.44 m/s

Now put the given values in the above formula,

[tex]f' = f (\frac{v + vo}{v + vs})[/tex]

[tex]1590 = 1600 (\frac{343 + 2.44}{343 + vs})[/tex]

[tex]1590 = 1600( \frac{345.44}{343 + vs})[/tex]

[tex]1590 = \frac{552,704}{343+vs}[/tex]

[tex]343+vs = \frac{552,704}{1590\\}[/tex]

[tex]343 + vs = 347.61\\[/tex]

[tex]vs = 347.61 - 343[/tex]

[tex]vs = 4.61 m/s[/tex]

Hence, the speed of the ambulance is 4.61 m/s.

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If a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver is making a mistake or he is not conscious of his driving

Traffic light can simply be defined as a set of automatically operated coloured lights such as red, amber, and green, for controlling traffic at road junctions, pedestrian crossings and roundabouts.

Below are the meaning of some traffic light colours:

So therefore, if a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver is making a mistake

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In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of 2,500 rpm for shifting is recommended for gas engines.

The maximum thermal efficiency of modern gasoline engines is over 50%, but legal cars on the road are only about 20% to 35% when used to power cars.

Unfortunately, even with regular car maintenance such as tuning and oil changes, the efficiency of today's gasoline engines is about 30-35%. In other words, about 65 cents per dollar spent on gasoline is wasted.

EPA's 2020 Automotive Trend Report preliminary data shows that the average fuel economy of 2020 model light trucks has increased to 25.7 miles per gallon (MPG). If this preliminary data holds, it will mark the highest average fuel economy ever for a new light commercial vehicle.

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