In a circle with a radius of 10 millimeters, the area of a sector whose central angle is 102° is approximately 88.97 mm^2 (option b).
1. Calculate the fraction of the circle represented by the sector: Divide the central angle (102°) by the total degrees in a circle (360°).
Fraction = (102°/360°)
2. Calculate the area of the entire circle using the formula A = πr^2, where A is the area, π is 3.14, and r is the radius (10 millimeters).
A = 3.14 * (10 mm)^2
3. Multiply the area of the entire circle by the fraction calculated in step 1 to find the area of the sector.
Area of sector = Fraction * A
Calculating the values:
1. Fraction = (102°/360°) = 0.2833
2. A = 3.14 * (10 mm)^2 = 3.14 * 100 mm^2 = 314 mm^2
3. Area of sector = 0.2833 * 314 mm^2 ≈ 88.97 mm^2
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Which of the following areas takes visual information from one side of the body and conveys it to the opposite side
The optic chiasm is the point where the optic nerves cross the midline, allowing the opposite side of the brain to process sensory data from one side of the body.
What is the optic chiasm and where is it located?Since the optic nerves cross in the optic chiasm, also known as the optic chiasma, it plays a crucial role in the visual pathway. Within the suprasellar cistern, it is situated 10 mm above the pituitary gland and 10 mm beneath the hypothalamus near the base of the brain.
The optic chiasm's function is to make sure that visual impulses reach both hemispheres of the brain. The thalamus receives and processes the majority of brain impulses, which are then transmitted to various parts of the occipital lobe. Half of each divided optic nerve's fibers travel to the opposing side. Due to the anatomical configuration, injury to the optic nerve system results in particular patterns of vision loss.
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When a person is standing upright, the weight of anything being lifted and carried in the hands is first reflected onto the:
Pelvic girdle
In human anatomy, the pelvis is a complex of bones that connects the trunk and the legs, supports and balances the trunk, and houses and supports the intestines, the urinary bladder, and the internal organ. It is sometimes referred to as the bony pelvis or the pelvic girdle.
One is located on the left side of the body and the other is located on the right. They come together to make the pelvic girdle, a portion of the pelvis. The hip bones are attached to the upper portion of the skeleton at the sacrum.
The pelvic girdle's main function is to support the upper body's weight while seated and transfer that weight to the lower limbs while standing. For the muscles in the trunk and lower limbs, it functions as attachment point.
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A force does work on an object if a component of the force __________.
Group of answer choices
a. is parallel to the displacement of the object
b. is perpendicular to the displacement of the object
c. perpendicular to the displacement of the object moves the object along a path that returns to its starting point
d. parallel to the displacement of the object moves the object along a path that returns to its starting point
Option A. A force does work on an object if a component of the force is is parallel to the displacement of the object.
Work done by force
The force applied to an object to displace it from a given point to another point is known as work done on the object.
W = Fd cosθ
where;
f is the magnitude of applied forced is the displacement of the object.θ is the angle between the applied force and displacement.Thus, A force does work on an object if a component of the force is is parallel to the displacement of the object.
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Why is quantum computing potentially a better fit for weather forecasting than classical computers?.
Quantum computing is a better fit than classical computing because it can access advanced simulations for vast quantities of weather.
What is Quantum computing?
Quantum computing can process large number of data sets of weather for all the properties of quantum states. Unlike classical computers which contains only standard bits 0 and 1 , quantum computing use Qubit or Quantum bit in which there are more than two standard sets of bits. These Qubits can measure the light at any degrees of polarisation between 1 and 0.This is the spin attribute that corresponds to superposition. This can create a lot more possibilities beacuse we can run multiple tasks at once with only one bit of data beacuse of the superpositioned qubit. This unlike classical computers where the bit can be only 1 and 0 is more effectively used in breaking encryption tasks.
So, the analysis of vast quantities of weather data can be done in seconds using Quantum computing.
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The spectral type of this star is B7V. The order of spectral types, from hottest to coolest, is OBAFGKM. How does the surface temperature of this star compare with the other stars we have observed
The hottest celebrity is this one.
The majority of stars fall under a select few spectral categories. The hottest to the coldest stars are listed in the spectral types of the Henry Draper and Bright Star Catalogues (see stellar classification). The letters O, B, A, F, G, K, and M are used to indicate these categories in decreasing order of temperature.
What is Spectral type of star ?Using spectral types, we can categorise stars based on their colour or the spectral lines that are visible in their light. The spectral types are OBAFGKM, with the hottest stars being O and the coldest being M. To humans, cooler stars appear redder and hotter stars appear bluer.
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Pearl labels a diagram of a charged capacitor as shown. Which change would correct the error in the diagram?
A) changing +2Q to +Q
B) changing +2Q to –2Q
C) reversing the direction of the arrows
D) reversing the labels for Conductors and Insulator
To correct the error in the diagram, we need to change +2Q to +Q in order for the charges to become balanced. Option A
What is a capacitor?A capacitor is device that is used for storing electric charge. We know that the capacitor is composed of two conductors separated by an insulator.
In order to correct the error in the diagram, we need to change +2Q to +Q in order for the charges to become balanced. Option A
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Answer:
A
Explanation:
A toy car is placed at 0 on a number line. It moves 9 cm to the left, then 4 cm to the right, and then 6 cm to the left. What is the total distance the toy car traveled?
1 cm
5 cm
11 cm
19 cmis the displacement of an object during a specific unit of time.
The total distance the toy car traveled is D. 19cm
Calculations and ParametersThe total distance of the toy car traveled in cm would be calculated
We would add the sum:
D = 9 + 4 + 6 cm
D = 19 cm
Therefore, the total distance the toy car traveled in cm is 19 cm.
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Consider vectors u and v, where u = ⟨1, –1⟩ and v = ⟨1, 1⟩. what is the measure of the angle between the vectors?
The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.
Angle between the vectorsThe angle between the vectors describes the direction of the vector and the value of the angle can be determined from the horizontal and vertical components of the vectors as shown below.
The sum of the horizontal components and vertical components of the vectors is calculated as follows;
Sum of the horizontal component of the vectors, x = 1 + 1 = 2
Sum of the vertical component of the vectors, y = -1 + 1 = 0
The angle between the vectors is calculated as follows;
θ = arc tan (y/x)
θ = arc tan (0/2)
θ = arc tan (0)
θ = 0⁰
The angle between the two vectors is 0⁰, thus the two vectors are parallel to each other.
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Answer: C. 90°
Explanation:
A uniform bar 15m long balanced on a pivot at its midpoint. A boy of mass 55kg sits on one arm of the bar at a point 5m away from the pivot. What mass can be placed 2m away from the other end of the bar to keep the bar horizontally
The mass at the other end of bar will be 50g .
what is mass
It is the fundamental property of matter , every single property which exist in this world has mass
Mass never can be 0 .
So , the system is in equilibrium
let mass of the body be m
55×5= m×5.5
m= 5 5 × 5 /. 5.5
m= 5 0g
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137.5 kg mass can be placed 2m away from the other end of the bar to keep the bar horizontally.
What does horizontal mean?Any straight line traveling from left to right or right to left is a horizontal line. If two points on a line share the same Y-coordinates, the line is said to be horizontal in coordinate geometry. It is derived from the word "horizon." In other words, the horizon or x-axis is always parallel to the horizontal lines.In the coordinate plane, a horizontal line is a straight line drawn from right to left or from left to right, perpendicular to the x-axis. In other words, a horizontal line is a straight line with an intercept solely on the y-axis, not the x-axis.To keep the bar horizontal, the right and left side torques must be equal:
[tex]F_{1} d_{1} =F_{2} d_{2}[/tex]
[tex]F_{2} =F_{1} \frac{d_{1} }{d_{2} }[/tex]
[tex]=(55.9.8)\frac{5}{2}[/tex]
=1347.5 N.
Convert this force of gravity into mass:
[tex]F_{2} =m_{2} g,[/tex]
[tex]m_{2} =\frac{F_{2} }{g}[/tex]
[tex]=\frac{1347.5}{9.8}[/tex]
=137.5 kg.
The answer is 137.5 kg.
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A lightning strike can transfer as much as electrons from the cloud to the ground. if the strike lasts 2ms , what is the average electric current in the lightning?
The average electric current in the lightning will be 8 × [tex]10^{-17}[/tex] A
Why Lightning Conductors on top of a tower ?The lightning conductors are long metal strips running from the spike end of a conductor on the top of a building to the earth. They are used to prevent buildings from destruction when struck by thunder or lightning.
Given that a lightning strike can transfer as much as electrons from the cloud to the ground. if the strike lasts 2ms, to calculate the average electric current in the lightning, we will first consider the charge released.
one charge = 1.6 × [tex]10^{-19}[/tex] C
Average current I = Q/t
Where
Q = charge = 1.6 × [tex]10^{-19}[/tex] Ct = time = 2ms = 2 × [tex]10^{-3}[/tex] sI = current = ?Substitute all the parameters into the formula
I = 1.6 × [tex]10^{-19}[/tex] C ÷ 2 × [tex]10^{-3}[/tex]
I = 8 × [tex]10^{-17}[/tex] A
Therefore, the average electric current in the lightning will be 8 × [tex]10^{-17}[/tex] A
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The spectral type of this star is listed as K5V. (V means it is a main sequence star.) Based on the table below, how does the surface temperature of this star compare with that of HIP 87937
It turns out that the star in question belongs to the K5V star class. Thus, the surface temperature of this must be between 5200 K and 3700 K. It has a surface temperature of 6200 K to 5200 K and is a G2V class star, commonly known as Bernard's star. In other words, the star in question has a colder surface than HIP 87937. This is further explained below.
What is surface temperature?Generally, The temperature at a surface is referred to as the surface temperature. In particular, it may refer to the surface air temperature, which is the temperature of the air that is relatively close to the earth's surface.
In conclusion, The star in question is of the K5V type. Therefore, the temperature of the surface of this must be somewhere between 5200 and 3700 kelvin. The star with the designation HIP 87937, often known as Bernard's star, is of the G2V type. Stars of this type have a surface temperature that falls anywhere between 6200 and 5200 degrees Celsius. Therefore, it should come as no surprise that the surface temperature of the given star is lower than that of HIP 87937.
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Answer: It is hotter because K is before M
Explanation:
The actual surface temperature of this star is 4600 KK compared to 3100 KK for the M4 star in Parts A and B.
What was the role of gravity in the formation of the solar system?
A. Gravity caused the solar system to move closer to the Sun.
OB. Gravity caused the solar system to compress into one larger
mass.
OC. Gravity caused the solar system to separate into individual
celestial bodies.
D. Gravity caused the solar system to expand from a central point.
The role of Gravity in the formation of the solar system is that gravity caused the the solar system to move closer to the Sun.
This was possible because gravity attracted smaller particles together until they formed large particles and began to rotate around the sun.
What is Gravity?Gravity is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun.
Gravity can also be said to mean an attraction between objects objects with mass.
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A train is traveling at 30.0 m/sm/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 HzHz. The speed of sound in air should be taken as 344 m/sm/s .
frequency fapproach is heard by a passenger = 302.05 Hz
frequency frecede is heard by a passenger = 228.37433 Hz
Given :
speed of train to the ground = 30.0 m/s
frequency emitted by the train whistle = 262 Hz
speed of sound in air = 344 m/s
To Find :
(A) frequency fapproach (B) frequency frecede
Solution :
The frequency of approach is given by
f' = f v + v(relative)
v - v(air)
= 262x 344 + 18
344 - 30
f' = 302.05 Hz
The frequency of approach is 302.05 Hz
The frequency of recede is given by
f' = f v - v(relative)
v + v(air)
= 262 x 344 - 18
344 + 30
The frequency of recede is 228.37433 Hz
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A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is:
A long narrow solenoid has length l and a total of N turns, each of which has cross-sectional area A. Its inductance is μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
To find the answer, we need to know about the magnetic field due to a solenoid.
What is the magnetic field due to a solenoid?A solenoid is an insulated wire wound in the form of a helix. Its length is very large compared to its diameter.The magnetic field due to solenoid carrying current [tex]I[/tex] can be written as,[tex]B=[/tex] μ₀n [tex]I[/tex]
[tex]n=\frac{N}{l}[/tex]
We have an expression for magnetic flux as,Φ [tex]= BA[/tex] Where, A is the area.
Substituting above value of magnetic field in the expression of magnetic flux, we get,Ф [tex]= \frac{NIA}{l}[/tex] μ₀
In terms of inductance, we can express the magnetic flux linked with the coil as,Ф [tex]= LI[/tex]
By equating above two equations of magnetic flux, we get the expression for inductance as,μ₀ ( [tex]\frac{N^2A}{l}[/tex] ) [tex]I[/tex] [tex]=LI[/tex]
[tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
Thus, we can conclude that the expression for inductance is μ₀ ( [tex]\frac{N^2A}{l}[/tex] ).
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The inductance of a solenoid having N number of turns, area A and a length l will be equal to μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
We need to understand the magnetic field created by a solenoid in order to determine the solution.
What does a solenoid's magnetic field look like?An insulated wire twisted into a helix is what makes up a solenoid.Compared to its diameter, its length is significantly larger.It is possible to express the magnetic field caused by a solenoid carrying current as,[tex]B=\frac{NI}{l}[/tex]×μ₀
We can express magnetic flux as follows:[tex]flux=BA[/tex] , A is the area.
In the formula for magnetic flux, we obtain by substituting the above magnetic field value:[tex]flux=\frac{NIA}{l}[/tex] times the μ₀.
The magnetic flux associated with the coil can be expressed in terms of inductance as follows:[tex]flux=IL[/tex]
We obtain the expression for inductance as, by combining the aforementioned two magnetic flux equations.μ₀ ( [tex]\frac{N^2AI}{l}[/tex])= [tex]LI[/tex]
[tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
As a result, we can say that the inductance expression is [tex]L=[/tex] μ₀ ( [tex]\frac{N^2A}{l}[/tex]).
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Monochromatic light with wavelength 590 nm passes through a single slit 2. 30 ?m wide and 1. 90 m from a screen. Find the distance between the first- and second-order dark fringes on the screen.
Answer:
The fringes are 4.7*10^-7 m apart, such that they are adjacent.
Explanation:
Using the formula for adjacent fringes given a single slit:
Δ[tex]x=\frac{(Wavelength)(Distance between slit and screen)}{Width}[/tex]
Δ[tex]x=\frac{(590/10^{9})(1.90) }{(2.30)}[/tex]
Δ[tex]x=0.000000487 m[/tex]
Hope this helps!
The distance between the first-order and second-order dark fringes on the screen will be 4.874 × 10⁻⁵ cm.
Given:
wavelength, λ = 590 nm = 590 × 10⁻⁹ m
Distance between the slit and screen, D = 1.90 m
Width of slit, d = 2.30 m
Calculation:
We know that the distance between two slits is given as:
Δx = λD / d
where λ is the wavelength of light
D is the distance between the slit and screen
d is the width of the slit
Applying values in the above equation we get:
Δx = (590 × 10⁻⁹ m)(1.90 m) / (2.30 m)
= 4.874 × 10⁻⁷ m
= 4.874 × 10⁻⁵ cm
Therefore, the distance between the first- and second-order dark fringes on the screen will be 4.874 × 10⁻⁵ cm.
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A stone ‘X’ of mass 2 kg is at the height of 20m in two minutes, calculate the power delivered. [g=10 m/s-2]
400 J power will be delivered by lifting a stone of mass 2 kg at the height of 20m in two minutes.
What is power?The quantity of energy transferred or transformed per unit of time is known as power. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as an activity in ancient writings. A scalar quantity is a power.
Work completed and time is linked in the power equation. Since forces may move objects and we know that forces perform work, we might anticipate that by understanding the power, we can gain insight into how a body moves through time. This outcome may be especially beneficial.
Given that, a stone ‘X’ of mass 2 kg is lifted to the height of 20m in two minutes, and g=10 m/s-2
Power Delivered = Work done in lifting the stone
Work Done = Potential energy = mgh
Work done = 2 × 10 × 20
Work done = 400 J
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What must the charge (sign and magnitude) of a 3.45 g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 590 N/C
charge must be equal to 5.74 ×10⁻⁵
In the question it is said that the particle remains stationary which means the the net force on the particle is zero. So, the counterbalancing forces must be equal which means weight is equal to upward electric force.
→ Fnet =0
→ mg = qE
substituting the values we get :
0.00345 × 9.81 = q × 590
→ q = 5.74 ×10⁻⁵
Hence the charge must be equal to 5.74 ×10⁻⁵.
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A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens
The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
What is convex lens?A convex lens is the name given to any converging lens.
A converging lens or convex lens is a lens that converges rays of light that are traveling parallel to its principal axis.
What is focal length?The focal length, f of a lens is the distance between the center of a lens and its focus.
Object placed between infinity and 2fFor an object that is placed between infinity and double of the distance from focal point, along a line perpendicular to the center of the lens,
The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
Thus, for an object placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image formed will be located between the focal point, f and double of the distance from focal point, 2f.
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It is advisable to place room heater at the ground level for effective heating
Answer:
yes
Explanation:
The heater is placed near the floor because the air currents move upwards so the hot air fills up the whole room. Whereas, an air conditioner is placed near the ceiling because the cold breeze tends to settle down. If it is placed near the floor then it will fill just the bottom of the room with cool air.
A 7.55 × 1014 hz electromagnetic wave travels in carbon tetrachloride with a speed of 2.05 ×108 m/s. what is the wavelength of the wave in this material?
Answer:
2.72×10^-7
Explanation:
velocity = frequency × wavelength
2.05×10^8=7.55×10^14 wavelength
wavelength = 2.05×10^8/7.55×10^14
wavelength = 2.72×10^-7
An astronomical telescope is designed with over magnification of 35x if the object has a focal length of 100 cm what should be the focal length of the eyepiece and how far should the eyepiece be from the objective
The focal length of eyepiece is 2.85.
It is given that astronomical telescope is designed with over magnification of 35.
The object has a focal length of 100 cm.
We need to determine the focal length of the eyepiece.
The formula to be used here is for astronomical telescope is:
[tex]m=\frac{f_{0} }{f_{e} }[/tex]
Using values here, we get
[tex]35=\frac{100 }{f_{e} }[/tex]
[tex]f_{e}=100/35=2.85[/tex]
Hence, the focal length of eyepiece is 2.85
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A 36.5-g glass thermometer reads 23.6 ∘C before it is placed in 145 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 40.8 ∘C. Ignore the mass of fluid inside the glass thermometer. The value of specific heat for water is 4186 J/kg⋅C∘, and for glass is 840 J/kg⋅C∘.
The initial temperature of the water was [tex]41.6688^{0} C[/tex].
Given,
Weight of glass 36.5g
specific heat for glass is 840 J/kg⋅C∘.
Initial temperature of glass was [tex]23.6^{0} C[/tex].
Weight of water is 145*1=145g (Density*Volume=145ml*1g/ml)
Temperature final was [tex]40.8^{0} C[/tex].
specific heat for water is 4186 J/kgâ‹…Câˆ
(m of glass)(Cp of glass)(Tf_glass-Ti_glass) = (m of water)(Cp of water)(Ti_water - Tf_water)
36.5*840*(40.8-23.6)=145*4186*(Ti_water - 40.8)
Ti_water=[tex]41.6688^{0} C[/tex]
Specific heatIn thermodynamics, a material's specific heat capacity, or massic heat capacity as it is sometimes known, is equal to the heat capacity of a sample of the substance divided by the mass of the sample (symbol cp). Informally, it is the quantity of heat needed to raise a substance's temperature by one degree for every unit of mass that is added to it. joule per kelvin per kilogram, or Jkg1K1, is the SI unit for specific heat capacity. For instance, the amount of energy needed to increase the temperature of 1 kilogram of water by 1 K is 4184 joules, making water's specific heat capacity 4184 J kg 1 K 1.
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When a voltage of 12 V is applied to a resistor, a current of 2.5 A passes through it. What is the resistance of the resistor
Answer:
4.8 Ω
Explanation:
Ohm's law
V = IR
or V/I = R
12/2.5 = R = 4.8 Ω
what is the frequency of a wave that has a wavelength of 0.20m and a speed of 22 m/s?
Answer:
f=110HZ
Explanation:
Calculate the frequency of a wave
Based on equation λ= VT but T= 1/f
=> λ=V/f
=> f= V/λ
by V=22m/s
λ= 0.20m
=> f= 22/0.20= 22/(2×10-¹) = 110Hz
So the frequency of a wave is f=110Hz
Answer:
110
Explanation:
velocity=wavelength×frequency
22=0.20f
divide both sides by 0.20
22/0.20=0.20f/0.20
f=22/0.20
f=110
Describe and explain your observations using the law of conservation of charge and the properties of the conductors.
What is Law of conservation of charge?
Law of conservation of charge states that, "the total electric charge in an isolated system is always constant".
It can also be stated as, "Charge can neither be created nor destroyed but can only be converted from one form of energy to another".
What are the properties of conductors?
There is movement of electrons and ions in the conductor. Free charges exist on the surface of the conductor.The charge density of a conductor is zero.All points of a conductor are at the same potential.The electric field of a conductor is zero. This allows the electrons to flow within them.To learn more about Law of conservation of charge: https://brainly.com/question/4158552
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Radiation in the ultraviolet region of the electromagnetic spectrum is quite energetic. It is this radiation that causes dyes to fade and your skin to develop a sunburn. If you are bombarded with 1. 00 mol of photons with a wavelength of 370. Nm, what amount of energy, in kilojoules per mole of photons, are you being subjected to? energy mol submit answer try another versiorn 2 item attempts remaining.
The energy of photon in kJ/mol is 329kJ/mol.
Wavelength of radiation is 370nm. The frequency of given wavelength is
ν = c / λ
ν = 3×10^8 / 370×10^-9
ν = 8.11 × 10^14 s^-1
Now the energy of photon is:
E = hν
E = 6.63×10^-34 J.s/photon × 8.11×10^14s^-1
E = 5.41× 10^-19 J/photon
To find in mole
E = 5.41× 10^-19 × 6.022×10^23
E = 3.29 ×10^ 5 J/mol
So, the energy of mole of photon is equal to 329 kJ/mol.
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A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod:.
After the rod is charged and then touched on the neutral metallic sphere and then separated from it, the rod is repelled by the sphere. Option A
What is a static charge?There are very ways in which a static charge could be built up in an object. The ways include;
FrictionElectrostatic induction and ContactNow, after the rod is charged and then touched on the neutral metallic sphere and then separated from it, the rod is repelled by the sphere.
Missing parts;
A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from the ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod
A. is attracted by the sphere
B. is repelled by the sphere
C. feels no force due to the sphere
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Three charges, qA is +6.0 μC, qB is –5.0 μC, and qc is +6.0 μC, are located at the corners of a square with each
side length at 5.0 cm as shown in the diagram. Calculate the electric field at point D.
The net electric field at point D is determined as 3.95 x 10⁷ N/C.
Electric field at D due to charge A
E = kq/r²
where;
r is the distance between A and Dq is charge AE(AD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(AD) = 2.16 x 10⁷ i N/C
Electric field at D due to charge B
E = kq/r²
where;
r is the distance between A and Bq is charge Br² = 5² + 5²
r² = 50
r = √50
r = 7.07 cm
E(BD) = (9 x 10⁹ x 5 x 10⁻⁶)/(0.0707²)
E(BD) = 9 x 10⁶ N/C
in x - direction = 9 x 10⁶ N/C x cos(45) = 6.36 x 10⁶ i N/C
in y - direction = 9 x 10⁶ N/C x sin(45) = 6.36 x 10⁶j N/C
Electric field at D due to charge CE = kq/r²
where;
r is the distance between C and Dq is charge CE(CD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(CD) = 2.16 x 10⁷ j N/C
sum of electric field in x directionEi = 2.16 x 10⁷ i N/C + 6.36 x 10⁶ i N/C
Ei = 2.796 x 10⁷ i N/C
sum of electric field in y directionEj = 2.16 x 10⁷ j N/C + 6.36 x 10⁶j N/C
Ej = 2.796 x 10⁷ j N/C
Resultant electric field at DE = √Ei² + Ej²
E = √[(2.796 x 10⁷)² + (2.796 x 10⁷)²]
E = 3.95 x 10⁷ N/C
Thus, the net electric field at point D is determined as 3.95 x 10⁷ N/C.
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Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses:________
A. increases by a factor of 4.
B. increases by a factor of 2.
C. increases by a factor of 16.
D. decreases by a factor of 4.
E. decreases by a factor of 16.
Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses: C. increases by a factor of 16.
Gravitational force is an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.
Force between two masses = G M1 M1 / [tex]R^{2}[/tex]
since , gravitation force d follows an inverse square law
F is directly proportional to 1/[tex]R^{2}[/tex]
If distance between two masses is decreased by a factor of 4
Let initial distance : R
when distance between two masses is decreased by a factor of 4 = 4R
Force = G M1 M1 / [tex](4R)^{2}[/tex]
Force = G M1 M1 / [tex]16R^{2}[/tex]
16 Force = G M1 M1 / [tex]R^{2}[/tex]
since , there is an inverse relation , so if distance is decreased , gravitation force will increase .
hence, gravitational force will increase by factor of 16
correct option C. increases by a factor of 16.
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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 spring constant k?
Group of answer choices
130 N/m
33 N/m
13 N/m
330 N/m
Answer:
Approximately [tex]13\; {\rm N \cdot m^{-1}}[/tex] (assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].)
Explanation:
Let [tex]F_{\text{s}}[/tex] denote the force that this spring exerts on the object. Let [tex]x[/tex] denote the displacement of this spring from the equilibrium position.
By Hooke's Law, the spring constant [tex]k[/tex] of this spring would ensure that [tex]F_\text{s} = -k\, x[/tex].
Note that the mass of the object attached to this spring is [tex]m = 540\; {\rm g} = 0.540\; {\rm kg}[/tex]. Thus, the weight of this object would be [tex]m\, g = 0.540\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \approx 5.230\; {\rm N}[/tex].
Assuming that this object is not moving, the spring would need to exert an upward force of the same magnitude on the object. Thus, [tex]F_{\text{s}} = 5.230\; {\rm N}[/tex].
The spring in this question was stretched downward from its equilibrium by:
[tex]\begin{aligned} x &= (70\; {\rm cm} - 110\; {\rm cm}) \\ &= (-40)\; {\rm cm} \\ &= (-0.40) \; {\rm m}\end{aligned}[/tex].
(Note that [tex]x[/tex] is negative since this displacement points downwards.)
Rearrange Hooke's Law to find [tex]k[/tex] in terms of [tex]F_{\text{s}}[/tex] and [tex]x[/tex]:
[tex]\begin{aligned} k &= \frac{F_{\text{s}}}{-x} \\ &\approx \frac{5.230\; {\rm N}}{-(-0.40)\; {\rm m}} \\ &\approx 13\; {\rm N \cdot m^{-1}}\end{aligned}[/tex].