When, a small, square loop carries a 29 a current. The on-axis magnetic field strength is 49 cm from the loop is 4.5. Then, the edge length of the square loop is approximately 0.35 meters.
We can use the formula for the magnetic field on the axis of a current-carrying loop;
B = (μ0 / 4π) × (2I / r²) × √(2) × (1 - cos(45°))
where; B is the magnetic field strength on the axis of the loop
μ0 will be the permeability of free space (4π x 10⁻⁷ T·m/A)
I is the current flowing through the loop
r will be the distance from the center of the loop to the point on the axis where we're measuring the field
Since we know B, I, and r, we can solve for the edge length of the square loop.
First, let's convert the distance from cm to meters;
r = 49 cm = 0.49 m
Substituting the known values into the formula, we get;
4.5 x 10⁻⁹ T = (4π x 10⁻⁷ T·m/A / 4π) × (2 x 29 A / 0.49² m²) × √(2) × (1 - cos(45°))
Simplifying this equation, we get;
4.5 x 10⁻⁹ T = (2.9 x 10⁻⁶ T·m/A) × √(2) × (1 - 1/√2)
Solving for the edge length of the square, we get;
Edge length = √(π r² / 4)
= √(π (0.49 m)² / 4)
≈ 0.35 m
Therefore, the edge length of the square loop is approximately 0.35 meters.
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Red laser light passes through a single slit to form a diffraction pattern. If the width of the slit is increased by a factor of two, what happens to the width of the central maximum?
If the width of the slit is increased by a factor of two , then the central maxima will get decreased by half.
since , width of the central maxima is inversely proportional to the width of the slit . Which implies if width of the slit get increased then width of the central maxima will get decreased and vice versa.
central maxima = (2 * wavelength * D) / width of the slit
= (2 * lambda * D) / d
if initially width of the slit = d
then, after increasing it by a factor of two it become = 2d
central maxima = (2 * lambda * D) / 2d
= (lambda * D) / d
If the width of the slit is increased by a factor of two , then the central maxima will get decreased by half.
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. A coil is wrapped with 400 turns of wire on the perimeter of a circular frame of radius 8.5cm. Each turn has the same area, equal to that of the frame. A uniform magnetic field is turned on perpendicular to the plane of the coil. This field changes at a constant rate from 10.0 to 80.0mT in a time of 20.0ms. What is the magnitude of the induced emf in the coil at the instant the magnetic field has a magnitude of 50.0mT
The emf in the coil when the magnetic field is 50.0 mT is 31.78 V.
What is emf?
According to Faraday's law of electromagnetism, the emf of a coil
is the negative of the rate of change of magnetic flux with respect to time.
The emf of a coil is given by the formula,
[tex]E=-\frac{d\phi}{dt}[/tex]
where E is the emf, dΦ is the change in flux and dt is the change in time.
Magnetic flux: The scalar product of the magnetic field B and the total area vector A perpendicular to it is called the magnetic flux. The magnetic flux for a circular coil with n number of turns is given by,
[tex]\phi=n\pi r^2B[/tex]
where r is the radius of the coil.
Substitute [tex]\phi=n\pi r^2B[/tex] in the above equation and solve it.
[tex]E=-\frac{d(n\pi r^2 B)}{dt}\\E=-n\pi r^2 \frac{dB}{dt}[/tex]
Where dB/dt is the rate of change in the magnetic field with respect to time.
Note: 1mT/ms= 1 T/s, 1 cm= 0.01 m and 1mT=0.001 T
Given the magnetic field changes from 10.0mT to 80.0mT, the change in magnetic field dB = 80-10=70mT. The time interval dt= 20.0ms. Therefore,
dB/dt = 70/ 20 =3.5mT/(ms)
dB/dt = 3.5 T/s
Substitute dB/dt= 3.5T/s, n=400, r=8.5 cm or r=0.085 m in the formula of E and solve it. Since the value of magnitude is positive, ignore the negative sign.
E=400*π*(0.085)^2*(3.5)
E=31.78 V
Since the rate of change of magnetic field is constant, so the magnitude of the emf of the coil will remain the same at all instants. Hence E=31.75 V when the magnitude of the magnetic field is 50.0 T
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There may be installations where grounded conductors of different systems are installed within the same raceway, cable, or box. In these cases, it's imperative that the system-grounded conductors remain
A. separated.
B. disconnected.
C. spliced.
D. buried.
It is imperative that the system-grounded conductors remain buried and is denoted as option D.
What is a Conductor?This is referred as a substance which allows electricity and heat to flow through it and examples include metals.
These conductors have to be buried so as to prevent the risk of contact and electrocution of individuals thereby making it a safe method.
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Supposing the half-life of element x to be 1 year, if you have a 100 gram sample of x, how much of element x would be left after 4 years? (do not use significant digits in answering this question.)
75 g
50 g
25 g
6.25 g
6.25 gram of element x would be left after 4 years.
What's half life of an element?Half - life is the time period of decay of an element to half of its initial number of nuclei.After n no. of half lives, no. of nuclei left in the sample is initial number of nuclei / 2^nWhat's the amount of 100 gm of element x left after 4 half lives ?Leftover amount of the element x = 100/2^4
= 100/16 = 6.25 gram
Thus, we can conclude that 6.25 gram of element x would be left after 4 years.
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compare and contrast the medical understanding of death (that you have read about and learned about in this chapter) and the popular, typical understanding of death. this is chapter 11 for forensics
The medical understanding of death is related to the scientific approach, and the popular understanding is related to the inclusive spiritual and cultural approaches.
What is death for science?Death occurs when an individual's cardiorespiratory and brain functions cease due to some factor, thus ending his life.
Popular understanding, on the other hand, is aligned with scientific knowledge, but it is also encompassing cultural and religious teachings, which define topics not proven by science, such as life after death for example.
Therefore, death is a delicate topic for society, and spirituality is the basis found for greater emotional comfort in individuals who suffer significant losses of loved ones.
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Draw a vector representing the direction of the electric field. The orientation of the vector will be graded. The location and length of the vector will not be graded.
1. E is a vector pointing to the right.
2. E is a vector pointing to the left.
3. E is a vector pointing to the right.
4. E is a vector pointing to the left
What is a Vector ?A vector is an object that has both a magnitude and a direction
Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head.Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.Learn more about Vectors here:
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A 540 gram object is attached to a vertical spring, causing the spring’s length to change from 70 cm to 110 cm.
What is the change in the object’s gravitational potential energy?
Group of answer choices
-2.1 J
-0.84 J
2.1 J
0.84 J
The change in the object’s gravitational potential energy is 2.11 J.
Change in the object's gravitational potential
ΔP.E = mg(hf - hi)
where;
m is mass of the objecthf is final height hi is initial heightΔP.E = 0.54 x 9.8(1.1 - 0.7)
ΔP.E = 2.11 J
Thus, the change in the object’s gravitational potential energy is 2.11 J.
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At a point in space an electric force acts vertically upward on an electrion, the directon of the electric field at that point is:____
Answer:
F = Q E force acting on charge Q due to field E
A positive electric field is directed from positive to negative.
An electron will be attracted to the positive terminal.
Thus if the electric force is upwards the direction of the field must be directed downwards, or
if F is positive and Q is negative E must also be negative or downwards.
(taking upwards as positive)
A 1500 pound car is stopped in traffic on a hill that is at an incline of 10. Determine the force that is required to keep the car from rolling down the hill.
A 1500 pound car is stopped in traffic on a hill that is at an incline of 10. The force that is required to keep the car from rolling down the hill will be 1133.53 N.
When all the forces that act upon an object are balanced, then the object is said to be in equilibrium motion. The forces are considered to be balanced if the rightward forces are balanced by the leftward forces and the upward forces are balanced by the downward forces.
It can be observed from the diagram that in order resist the car to rolling down the hill we need to apply an equal and opposite force against the inclined force( that is mgsin(x)) to form an equilibrium position because rolling is associated with horizontal forces hence we need to apply force against the force which can drive down the car .
mass = 1500 pound = 680.39 kg
sin(10) = 0.17
F (counter force ) = m*g*sin(x)
= 680.39 * 9.8 * 0.17
= 1133.53 N
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The galaxy M33 is the third largest galaxy in the Local Group after M31 and the Milky Way. The galaxy M33 has a moderate-sized central bulge and two spiral arms that emerge directly out of the bulge and wrap around in rather poorly defined arcs with many cross-connections between the arms. Thus, M33 is classified as a _____ normal spiral.
Galaxy M33 is classified as a Triangulum normal spiral.
The galaxy M33 is the third largest galaxy in the Local Group after M31 and the Milky Way. The galaxy M33 has a moderate-sized central bulge and two spiral arms that emerge directly out of the bulge and wrap around in rather poorly defined arcs with many cross-connections between the arms.
This spiral galaxy is located in the triangle shaped constellation earning a pet name as triangular galaxy. This galaxy star formation rate is ten times higher than average found in Andromeda galaxy. It has relatively bright apparent. This galaxy was given by Charles Messier and he classified it as Triangulum normal spiral.
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Find the minor measurement of the vernier scale by taking 49, 1mm divisions of the main scale and dividing it into 50 vernier divisions.
length of V-50 = 49mm
length of V-1 = 49/50mm
= 0.98mm
so,
minor measurement = (M-1) - (V-1)
= 1mm -0.98mm
= 0.02mm
☆ Therefore,
The minor measurement of the vernier scale is 0.02mm.
☆...hope this helps...☆
_♡_mashi_♡_
A 60 g golf ball is dropped from a level of 2 m high. It rebounds to 1.5 m. How much energy is lost? Group of answer choices 0.5 J 0.88 J 0.29 J 1 J
Answer: A 60 g golf ball is dropped from a level of 2 m high. It rebounds to 1.5 m. Energy loss will be 0.29J
Explanation: To find the correct answer, we have to know more about the Gravitational potential energy.
What is gravitational potential energy?The energy possessed by a body by virtue of its position in gravitational field of earth is called gravitational potential energy.The gravitational potential energy of a body at a height h with respect to the height h will be,[tex]U=mgh[/tex]
Expression for gravitational potential energy loss will be,[tex]E=U_i-U_f[/tex]
How to solve the problem?The total energy before the ball dropped will be,[tex]U_i=mgh_i=60*10^-3kg*9.8m/s^2*2m=1.176 J[/tex]
The total energy after when the ball rebounds to 1.5m will be,[tex]U_f=mgh_f=60*10^-3kg*9.8m/s^2*1.5m=0.882J[/tex]
The total energy loss will be,[tex]E=1.176-0.882=0.294J[/tex]
Thus, we can conclude that, the energy loss will be,0.294J.
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Generating electricity has its risks, no matter what type of fuel is used. Identify which consequences are associated with generating electricity in a coal-fired power plant and which accompany nuclear power. Some risks may belong in both categories.
Power generation has to do with the process by which electricity is generated from various sources.
What are the risks of power generation?Power generation has to do with the process by which electricity is generated from various sources. Now we know that electricity is almost the driving force of several economies globally.
A coal fired power plant will lead to the burning of fossil fuels and the consequent release of CO2 into the atmosphere which leads to global warming. Also, the possibility of the release of SOx from the burring of coal could lead to acid rain.
In the case of nuclear sources, the disposal of the spent nuclear fuel presents a huge risk as well as the possibility of radioactive fallout and possible accident that could release tremendous amount of radiation.
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A standard rum and cola will be absorbed faster than a 5-ounce glass of wine because.
Absorption of Rum and cola:
A standard rum and cola absorb faster than a 5-ounce glass of wine because carbonation causes the pyloric valve to relax.
What are Rum and Cola:
The second-most common alcoholic beverage in the world is rum and coke, which is very well-liked. Its widespread availability, low cost, and ease of preparation are what contribute to its appeal. It is easy to prepare and challenging to destroy because it can be produced with any quantity or type of rum. Due to the pyloric valve's relaxation caused by carbonation, alcohol like rum and coke is often absorbed more quickly than 5 ounces of wine.Absorption is accelerated by carbonation. Alcohol will enter the bloodstream more quickly when combined with carbonated drinks like Coca-Cola or tonic water.Learn more about the alcoholic beverages here,
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The diagram shows a device that uses radio waves. Two radio towers. The towers are equal distance apart with an arrow between them. The left tower is labeled X. The right tower is labeled Y. The arrow is pointing from Tower X to Tower Y. What is the role of the part in the diagram labeled Y
capture, amplify, and demodulate waves
Question is incomplete and image is not attached in the question. The required image is attached below, so the complete question is:
What is the role of the part in the diagram labeled Y?
modulate, amplify, and send out waves
capture, amplify, and demodulate waves
change the amplitude and frequency of waves
change the pulse and phase of waves.
What are Radio wave?An example of electromagnetic radiation is radio waves. The wavelength of a radio wave is substantially greater than that of visible light. Radio waves are widely used by people for communication. Both rectangular and circular antennas are used by this radio tower to send and receive radio frequency energy.
The radio receiver, also known as component Y in the figure, is what captures, amplifies, and demodulates radio waves.
The radio receiver uses an antenna to separate the necessary radio frequency signals and consists of an amplifier to boost the strength of the receiving signal. The information from the modulated wave is ultimately recovered by demodulators found in receivers.
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Astronomers and physicists now believe they know what is happening to the missing neutrinos from the Sun (the neutrinos that our theories say should be emerging from the Sun, but our experiments in that underground mine could not find). These neutrinos are:
The missing neutrinos from the sun had merely tranformed into muon and tau neutrinos escaped detection.Hardly interacting with other matter,neutrinos comes in three different types electron,muon,and tau.
Hence option (b) turning into different type of neutrino in a neutrino oscillation is correct
Disclaimer:The question given on the portal is incomplete .Here is the complete question .
Question :Astronomers and physicists now believe they know what is happening to the missing neutrinos from the Sun (the neutrinos that our theories say should be emerging from the Sun, but our experiments in that underground mine could not find). These neutrinos are:
a)not being produced by the Sun because our star's nuclear fusion period has ended
b)turning into a different type of neutrino in a neutrino oscillation
c)being converted to antimatter in the core of the Sun and being destroyed as they hit matter
d)changing course before they reach the Earth as they hit other neutrinos in space
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The holding coil on a hydromatic propeller feathering button switch holds a solenoid relay closed that applies power to the propeller?
An electric propeller is powered by a solenoid relay that is kept closed by the holding coil on a hydromatic propeller feathering button switch. It is a kind of feathering pump motor.
What does it mean to feather an engine?
If an engine needs to be turned off, the feather is used. The blades are rotated during feathering such that the extent to which a leader is virtually pointing in the flying direction. The propeller's aerodynamic forces cause a low drag state in this position. It is composed of a solenoid relay.What is meant by solenoid relay?
A form of relay designed to wirelessly change a stronger current is called a solenoid. A coil is utilized to create an electromagnetic environment when power is transferred through it, similarly to the tiny motorized cube relays, that efficiently open or shut the circuit.
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____________ is the unit that measures the pressure or force that pushes the flow of electrons forward through a conductor.
Volt is the unit that measures the pressure or force that pushes the flow of electrons forward through a conductor.
When there is a circuit having a cell / battery , that cell/battery forms an electric field due to difference in voltages , and set a voltage of value equals to the difference in the voltage of two end of that cell/ battery . Because of which a electric field got set up in the conductor , which pushes electron to move inside the conductor . Unit of voltage is volt .
VOLT - A unit of electrical pressure (or electromotive force) which causes current to flow in a circuit. One volt is the amount of pressure required to cause one ampere of current to flow against one ohm of resistance. VOLTAGE - That force which is generated to cause current to flow in an electrical circuit.
Voltage is the pressure from an electrical circuit's power source that pushes charged electrons (current) through a conducting loop, enabling them to do work such as illuminating a light. In brief, voltage = pressure, and it is measured in volts (V).
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Voltage is the unit that measures the pressure or force that pushes the flow of electrons forward through a conductor.
Voltage is the electrical potential, potential difference and electromotive force in meter , kilogram, second system.The standard unit of measurement used for the expression of voltage is volt which is represent by symbol "V".
High voltage cable is used for electric power transmission at high voltage.A cable that includes conductor and insulation. cable which are considered to be fully interested. That means that they have fully rated insulted system that will consist of insulation , semi-con layers.
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Martha is late for class, so she races her 75 kg body up a 4.0 meter flight of stairs in only 2.3 seconds. What is Martha’s power?
Group of answer choices
a. 1,300 W
b. 6,800 W
c. 130 W
d. 680 W
Martha's power is 1,300 W and is denoted as option A.
What is Power?This is defined as the amount of energy used or transferred per unit time and the S.I unit is Watts.
Power = Work/ time
Work = force × distance
= F = ma = 75kg× 10m/s² = 750N
Work = 750N × 4m = 3000J
Power = work/time = 3000J/ 2.3s ≈ 1300W
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Using the Left Hand Rule, if current points up and
the field is toward you, which way does the motion
point?
A. Left
B. Down
c. Up
D. Right
Using the left hand rule, if current points up and the field is toward you, the motion points up.
What is the left hand rule?The left hand rule states that if the thumb, the fore finger and the middle finger are held mutually perpendicular to each other, the thumb points in the direction motion, the middle finger points in the direction of current while the fore finger points in the direction of the magnetic field.
Thus using the left hand rule, if current points up and the field is toward you, the motion points up.
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How did the magma get from the volcanic center to the locations where the laccoliths formed?
Laccolith magma (molten rock) rising through the Earth's crust begins to spread out horizontally, prying aside the host rock strata.
Laccoliths are not unusual in the Pine Valley Mountain desert location close to St. George, Utah. The stress of the magma is high enough that the overlying strata are compelled upward, giving the laccolith its dome-like form.
A laccolith is a frame of intrusive rock with a dome-shaped top surface and a degree base, fed through a conduit from under. A laccolith bureaucracy when magma (molten rock) rising thru the Earth's crust starts to unfold out horizontally, prying aside the host rock strata. The stress of the magma is excessive enough that the overlying strata are pressured upward, giving the laccolith its dome-like form.
A laccolith is a type of igneous intrusion, shaped when magma forces its manner upwards via the Earth's crust however cools and solidifies before attaining the surface. Laccoliths are outstanding from other igneous intrusions by way of their dome-shaped upper floor and level base.
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Why is it so much easier to determine the length of the day on mars than on venus?
The thick cloud cover of Venus makes it difficulty in visibility because of impenetrable in visible light which has made it tough for astronomers to measure the length of the planet's day . Whereas Mars have clear atmosphere which do not hinder visibility
The most important reason of why is it difficult to measure the length of the day on Venus is tougher than in mars is that Mars' atmosphere is generally clear because of which their is no visibility issue on mars but due to the thick cloud covering of Venus makes it impenetrable in visible light , due which visibility is not that clear and it become tough to observe the length of the day on Venus.
Mars is much larger than Venus in size which makes easier to observe
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Two forces of magnitude 10n and 20n acting at an angle of 30 degree. what will be the x component of their resultant force?
The resultant of the forces is 29 N. Option D
What is the resultant force?The resultant force is the force that acts in a given direction. Now we have two forces as enumerated in the question.
Thus;
Resultant = √(10)^2 + (20)^2 - [2 * 10 * 20 * cos (60 - 30))
Resultant = 29 N
Thus, the resultant of the forces is 29 N.
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Missing parts;
Two forces of magnitude 10N and 20N act on a body in directions making angles 30° and 60° respectively with x-axis what is the resultant force
A.17N
B. 19N
C. 23N
D. 29N
E. 37N
A sky-diver jumps from a stationary balloon. His initial downwards acceleration is 10m/s².
Fig. 1.1 shows the directions of the air resistance and the weight of the sky-diver.
The mass of the sky-diver is 60 kg and his weight is 600 N.
(a) Explain, using ideas about the forces, why his initial downwards acceleration is 10m/s².
Explanation:
a. The force acting down is gravity, on Earth gravity is 10 m/s^2. When the skydiver jump, the acceleration will start out as -10 m/s^2, but it will eventually equals the air resistance , which is called terminal velocity.
The large, roughly circular, dark, and somewhat younger regions on the moon are called?
The large, roughly circular, dark, and somewhat younger regions on the moon are called Maria.
What is Maria?Lunar Maria are large, dark, basaltic plains on Earth's Moon. It was created by an ancient asteroid impacting the Moon on the far side and triggering some volcanic activity on the opposite side.
These are vast basins containing lava flows that are marked by craters, ridges, faults and straight and immersed valleys called rills. They are waterless. There are about 20 major areas of this type. Most of which include the largest located on the side of the Moon that always faces Earth.
These maria were the result of the melting and eruption of basaltic lava on the lunar surface 3.8 to 2.8 billion years ago. This type of lava was highly fluid under the Moon's weak gravitational field and spread over vast distances.
Thus, the large, roughly circular, dark, and somewhat younger regions on the moon are called Maria.
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An airplane is flying on a bearing of 170° at 495 mph. Find the component form of the velocity of the airplane. Be sure to show and explain your work.
The horizontal component of the plane's velocity is 85.96 mph and the vertical component of the plane's velocity is 487.5 mph.
Component form of the velocity of the airplane
The component form of the velocity of the airplane includes both horizontal and vertical velocity and it is calculated as follows;
Vx = V cosθ
Vy = V sinθ
where;
Vx is horizontal component of the velocityVy is vertical component of the velocityθ is the angle of the velocity measured with respect to horizontal axisθ = 170 - 90 = 80⁰
Horizontal component of the velocityVx = 495 mph (cos 80)
Vx = 85.96 mph
Vertical component of the velocityVy = 495 mph (sin 80)
Vy = 487.5 mph
Thus, the horizontal component of the plane's velocity is 85.96 mph and the vertical component of the plane's velocity is 487.5 mph.
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Earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.
a) Determine the Earth’s average orbital speed expressed in kilometers per hours.
b) Based on the information given in this question, calculate the approximate mass of the Sun.
The Earth’s average orbital speed is 107226 Km/hr and the mass of the sun is 2.6 x [tex]10^{24}[/tex] Kg
What is angular speed ?
Angular speed is the rate of change of the angle turned through by the body with time taken. That is W = Ф / T
And the relationship between linear speed and angular speed is V = wr
Where
V = Linear speedW = Angular speedr = RadiusGiven that the earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.
a) To determine the Earth’s average orbital speed, we will make use of the below formula to calculate angular speed
W = 2[tex]\pi[/tex]/T
W = (2 x 3.143) / (365.26 x 24)
W = 6.283 / 876624
W = 7.2 x [tex]10^{-4}[/tex] Rad/hr
The Earth’s average orbital speed V = Wr
V = 7.2 x [tex]10^{-4}[/tex] x 149.6 x [tex]10^{6}[/tex]
V = 107225.5 Km/hr
b) Based on the information given in this question, to calculate the approximate mass of the Sun, we will use Kepler's 3rd law
M = (4[tex]\pi ^{2}[/tex][tex]r^{3}[/tex]) / G[tex]T^{2}[/tex]
M = (4 x 9.8696 x 3.35 x [tex]10^{24}[/tex] ) / (6.67 x [tex]10^{-11}[/tex] x 7.68 x [tex]10^{11}[/tex])
M = 1.32 x [tex]10^{26}[/tex] / 51.226
M = 2.58 x [tex]10^{24}[/tex] Kg
Therefore, the Earth’s average orbital speed is 107226Km/hr approximately and the mass of the sun is 2.6 x [tex]10^{24}[/tex] Kg
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An object moving with 108 km/h moves 400 m in 8 seconds. find the velocity attained by the object.
Answer:50ms-1
Explanation:use the formula v=d/t
in order to find the velocity,devide the distance with time taken.
since distance is 400 meters devide it with seconds whiuch gives us 50.
A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with magnitude that is changing linearly with time. If r is the radial distance from the cylinder axis, the magnitude of the induced electric field inside the cylindrical region is proportional to:
The induced electric field inside the cylindrical region is directly proportional to r
What is the electric field?
An electric field is the physical field that surrounds electrically charged particles and exerts a force on all other charged particles in the field.
When a loop of wire is placed in a time-varying magnetic field, an induced electric field arises. This induced electric field allows the flow of current in the loop. There is no potential associated with this induced electric field.Here. a magnetic field with magnitude linearly varies with time.
Radial distance = r
Area of this region, A = π*r^2
Let the induced electric field be E.
Magnetic flux:
∅(B) = B*A
Let the magnetic field be kt,
where k is some constant and t is time.
(B) = kt * (πr^2)
Using Maxwell's equation of electromagnetism,
[tex]\int\limits^a_b {E} \, dr = -\frac{d∅}{dt}[/tex]
[tex]E* 2\pi r = - \frac{d}{dr}(\pi k tr^{2} )[/tex]
[tex]E*2\pi r = -\pi kr^{2}[/tex]
[tex]E = - \frac{kr}{2}[/tex]
Hence
E ∝ r
The induced electric field is directly proportional to r
So, option 2 is correct.
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In a series lrc circuit, the frequency at which the circuit is at resonance is f0. If you double the resistance, the inductance, the capacitance, and the voltage amplitude of the ac source, what is the new resonance frequency?.
When you double capacitance and inductance, the new resonance frequency becomes halved.
What is Resonance frequency?
It is the natural frequency of an object where it tends to vibrate at a higher amplitude.
The resonance frequency of the LC series circuit is the frequency at which the capacity reactance is equal to inductive reactance.
The formula resonance frequency:
[tex]f_{0} = \frac{1}{2\pi \sqrt{LC} }[/tex]
where;
f0 is the resonance frequency
L is the inductance
C is the capacitance
here, if the capacitance and inductance are doubled, the new resonance frequency becomes;
[tex]f = \frac{1}{2\pi \sqrt{2L2C} }\\f = \frac{1}{2\pi \sqrt{4LC} }\\f = \frac{1}{2*2\pi \sqrt{LC} }\\f=\frac{1}{2} \frac{1}{2\pi \sqrt{LC} }\\f = \frac{1}{2} f_{0}[/tex]
Thus from the above equation for frequency,
When you double capacitance and inductance, the new resonance frequency becomes f(0) / 2.
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