Gravitational Potential Energy is demonstrated by a stationary ball put at the top of a ramp. The energy that a body has or acquires is known as gravitational potential energy.
because when something is in a gravitational field, it changes position. It is, to put it simply, energy that results from gravitational force or gravity. Taken two pencils is the most typical illustration. If one pencil is set down on a table and the other is raised above it, the pencil raised will have more gravitational potential energy than the pencil set down on the table. The equation U = mgh is used to compute it. The mass, m, is expressed in kilograms.
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Exposure to high doses of microwaves can cause tissue damage. Estimate how many photons with a wavelength = 12 cm, must be absorbed to raise the temperature of your eye by 3.0 C. Assume the mass of the eye is 11 g and its specific heat is 4.0 J/g K.
1.21 x 10^26 photons with a wavelength = 12 cm, must be absorbed to raise the temperature of your eye by 3.0 C. Assume the mass of the eye is 11 g and its specific heat is 4.0 J/g K.
λ = 12 cm = 0.12 m
T=3 C degrees.
m = 11 g, or 0.011 kg, and c = 4 J/g K, or 4000 J/kg K.
Suppose there are n photons.
One photon's energy is equal to hc/.
h is the Planck constant, and let c represent the speed of light.
n photons' energy, E = n h c /
Since this energy is used to increase the eye's warmth, n h c / = m c. Δ T\sn = m c T = (0.011 x 4000 x 3 x 0.12)/(6.63 x 10-34 x 3 x 108), where n = 1.21 x 1026.
The number of photons is 1.21 x 1026.
The term "photon" refers to an elementary particle that is a quantum of the electromagnetic field, which includes electromagnetic radiation like light and radio waves, as well as the force carrier for the electromagnetic force. The word "photon" is derived from the Ancient Greek "phôs, phtós," which means "light." The speed of light in a vacuum, which is 299792458 m/s (or 186,282 mi/s), is the only speed at which photons can travel because they have no mass[a]. The boson class includes the photon.
The behavior of photons exhibits wave-particle duality, exhibiting characteristics of both waves and particles. Like other elementary particles, photons are best understood by quantum mechanics. The contemporary photon theory was developed by Albert Einstein in the first two decades of the 20th century, building on the work of Max Planck.
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a 0.262 kg ball, containing a net charge of -151.9 mc, is thrown horizontally into a region of uniform magnetic field of field strength 10 tesla. the ball is traveling perpendicular to the b-field at the instant it is thrown, and at that moment, it is known to be traveling at v
At the instant it is thrown, the ball is known to be moving perpendicular to the b-field and is moving at velocity v and time taken is 1.259*10^-3 sec
F=Q(V*B)
V=velocity vector
B=magnetic field vector
q=charge
F=q(Vi*b-k)
=q|v||b|j
|Fb|=q|V|B|
t=D/v
t=2518/20000sec=1.259*10^-3sec
During the time t, the deflection of charge is negtive y direction
y=Vt+1/2at²
y=1/2ayt²
a=acceleration is -ve y direction
=Fb/m
m=mass of charge
Fb=magnetic force
ay=q|V||B|/m
q=-158.85 mc
ay=1.24*10⁵m/s
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The current in an RL circuit drops from 1.5 A to 13 mAin the first second following removal of the battery from thecircuit. If L is 14 H, find the resistance R inthe circuit. Number Units
The resistance of the circuit is 0.51ohm if the current in a RL circuit drops from 1.5A to 1.3 A in first second.
We know very well that in an RL circuit if a current is changing from one state to another state is given by the below formula
I[tex]_t[/tex] = I₀×[tex]e\frac{-t}{RL}[/tex]
where I[tex]_t[/tex] is current flowing in RL circuit at any time,
I₀ is the maximum current flows in R-L circuit.
R is defined as resistance of circuit
and L is inductance of circuit.
RL circuit works differently if battery is connected and it works differently if battery is disconnected. It works by charging the inductor when battery is applied.
We have I[tex]_t[/tex]=1.3A,I₀=1.5A,R=?,L=14H
=>1.3=1.5×[tex]e\frac{-1}{R.14}[/tex]
=> [tex]e\frac{-1}{R.14}[/tex]=1.3/1.5
=>1.5/1.3=[tex]e\frac{1}{R.14}[/tex]
Taking ln on both sides of equation.
ln(1.5/1.3)=ln([tex]e\frac{1}{R.14}[/tex])
=>ln(1.5)-ln(1.3)= 1 / (R×14)
=>0.405-0.262=1/(R×14)
=>R×14= 1 /0.14
=>R=1/(0.14×14)
=>R=1/1.96
=>R=0.51ohm
Hence, resistance value is 0.51 ohm
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No astronomical object that produces a continuous visible spectrum of light has ever been observed. However, there are many astronomical objects that produce emission or absorption spectra. Read the following descriptions of astronomical objects, and then sort the labeled images into the appropriate bins according to the type of spectrum each object produces
Emission spectrum:
- Emission nebula
- Planetary nebula
Absorption spectrum:
- Sun
- Atmosphere on Titan
Spectroscopy is a highly valuable method of astronomical investigation. Astronomers can determine the composition, density, and temperature of celestial bodies by interpreting the light they emit or absorb.
Emission Spectra
- Emission Nebula
- Planetary Nebula
Absorption Spectra
- Titan's Atmosphere
- Sun
Astrophysics is the science that applies the methods and principles of physics and chemistry to the study of celestial bodies and phenomena. As one of the founders of astrophysics put it, astrophysics is about ``determining the nature of celestial bodies, not where they are, not their positions and movements. ”. Stars, galaxies, exoplanets, the interstellar medium, and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is such a broad subject, astrophysicists study classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear physics, particle physics, atomic physics, molecular It applies concepts and methods from many fields of physics, such as physics.
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two football players collide head-on in midair, moving along the same horizontal direction, while trying to catch a thrown football. the first player is 86.5 kg and has an initial velocity of 6.15 m/s (in the positive direction), while the second player is 118.5 kg and has an initi
Final Velocity = 4.65 m/s
From the question, we have
Mass of player one M1= 98.5kg
Initial Velocity U1= 6.05m/s
Mass of player two M2= 119kg
Initial velocity U2= -3.50m/s
Final Velocity = V
Utilizing the idea of linear momentum conservation,
M1U1 + M2U2 = (M1+M2)V
98.5*6.05 + 119*3.50 = (98.5+119)*V
595.925 + 416.5 = 217.5V
1012.425 = 217.5V
V = 1012.425/217.5
V = 4.65 m/s
Principle of conservation of linear momentum:
According to the conservation of momentum, the total momentum before and after a collision will be the same if there is no external force acting on the colliding objects.
Complete question:
Two football players collide head-on in midair while trying to catch a thrown football. The first player is 98.5 kg and has an initial velocity of 6.05 m/s, while the second player is 119 kg and has an initial velocity of −3.50 m/s. What is their velocity (in m/s) just after impact if they cling together? (Indicate the direction with the sign of your answer.)
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a man enters a tall tower, needing to know its height. he notes that a long pendulum extends from the ceiling almost to the floor and that its period is 19.7 s.
Time period of the pendulum, T = 19.7 s
The time period of the pendulum is given by :
T = [tex]2\pi \sqrt{\frac{l}{g} }[/tex], l is the length of the pendulum
substituting,
l = 174.32 meters
What is the time period?
Time period (plural time periods) is the amount of time that a behavior lasts or a condition persists. Depending on the type of activity or situation under consideration, it may be measured in seconds or in millions of years.
Hence, the answer is 174.32 m
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bob's car ran out of gas 3.4 km from the nearest gas station. if it requires a 500 n force to push his car, how much work will bob do to get his car to the gas station? (1.7 MJ or 1.7 10 j)
The mileage of the car is calculated by dividing the number of miles traveled by the amount of gas used. Car's Gas Mileage is 147.0
How do you calculate how far you can go on a tank of gas?Gas Run Out.Turn on your hazard lights and safely pull your car over to the right shoulder.If you have emergency gear, such as a reflective triangle, set it up as needed.Go for a stroll to the closest gas station.Place a roadside assistance call.How to Calculate Your Car's Gas MileageThe outcome is your car's normal miles per gallon, which you can calculate by dividing the distance traveled by the number of petrol tanks you filled up.For instance, your car would average 25 miles per gallon if you traveled 200 miles on 8 gallons of gas.Car's Gas Mileage = 500/3.4
=147.0
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An electron is released from rest in a uniform electric field. If the electric field is 1.25 kN/C, at the end of 20 ns
the electron's velocity will be approximately
At the end of 20 ns, the electron's velocity will be approximately 5.2 × 10⁶ m/s.
What is electric field?The force per unit charge exerted on a positive test charge that is at rest at a given position is the force per unit charge that is used to define the electric field analytically.
Electric charge or magnetic fields with variable amplitudes can produce an electric field. The attraction forces that keep together atomic nuclei and electrons at the atomic scale are brought on by the electric field.
Given that:
the electric field is 1.25 kN/C
So, acceleration of the electron: a = eE/m
= (1.6 × 10⁻¹⁹×1.25×10³)/(9.1×10⁻³¹) m/s²
= 2.6 × 10¹⁴ m/s².
Hence, after the end of 20 ns the electron's velocity will be = at
= 2.6 × 10¹⁴ × 20 × 10⁻⁹ second
= 5.2 × 10⁶ m/s.
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A 215-g object is attached to a spring that has a force constant of 77.5 N/m. The object is pulled 7.25 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. Calculate the maximum speed of the object.Find the locations of the object when its velocity is one-third of the maximum speed. Treat the equilibrium position as zero, positions to the right as positive, and positions to the left as negative.
(a) The maximum speed of the object is 1.37 m/s.
(b) The locations of the object when its velocity is one-third of the maximum speed is 5.87 cm.
In easy words, speed is the rate at which some thing actions in a specific direction. For instance as the rate of a vehicle journeying north on a highway, or the rate a rocket travels after launching. The scalar method absolutely the cost value of the rate vector is constantly be the rate of the motion.
Velocity is a vector expression of the displacement that an item or particle undergoes with appreciate to time . The preferred unit of speed value (additionally called speed ) is the meter according to second (m/s). Alternatively, the centimeter according to second (cm/s) may be used to specific speed value.
Maximum speed for the object:
[tex]w=\sqrt{ \frac{k}{m}\\\\\\w=\sqrt{ \frac{77.5}{0.215}\\\\\\\\\\\\\w=\sqrt{ 360.46}\\\\\\\\w=18.98[/tex]
Maximum velocity = ωr
v= 18.98*0.0725
v= 1.37.
Maximum velocity = ωr = 1.37.
The speed of the object at a distance x from its mean position is given as:
[tex]v=w\sqrt{a^2- x^{2} } } \\so,\\ v=x\\x=\sqrt[]{8(*7.25} \\x= 5.87[/tex]
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a drum rotates around its central axis at an angular velocity of 11.00 rad/s. assume that the drum then slows at a constant rate of 4.30 rad/s2. (a) how much time does it take and (b) through what angle does it rotate in coming to rest?
The time taken by the drum to come to rest is 2.55 seconds and the angle that it makes is 14π.
The drum rotates around the central axis with angular velocity of 11 rad/s. After that it slow down with constant rate of 4.3 rad/s².
(a) The time taken by the drum to come at rest will he given by,
W' = W + at
W is initial angular velocity,
W' is final angular velocity,
a is the rate of slowing down,
t is the time taken.
Putting values,
11 = 4.3t
t = 11/4.3
t = 2.55 seconds.
(b) The angular displacement will be given by,
2aS = W'² - W²
S is the angles made while slowing down,
Putting values,
2(4.3)S = (11)²
S = 14 rad.
So, the angle made is 14π.
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a workstation is connected to a switch on the gi 0/2 interface using a straight-through cable. the ethernet interface in the workstation has been manually configured to use a 100 mbps link speed in full-duplex mode. which of the following are true in this scenario? (select three.)
The following are true in this scenario:
1. If the link speed is 10 Mbps or 100 Mbps, half- duplex is used.
2. If the link speed is 1000 Mbps or faster, full-duplex is used.
3. The switch attempts to sense the link speed. If it can't, the lowest link speed supported on the interface is selected.
Interfaces can work in the following two duplex modes. They are half duplex mode and full duplex mode.
Half- duplex mode: An interface in this mode can send data only when it is not received data and conversely, it can receive data only when it is not sending data. There is a limit on transmission distance in this mode.
Full-duplex mode: An interface in this mode can send and receive data simultaneously. The maximum throughput in full-duplex mode is theoretically double than in half duplex mode. There is no limit on transmission distance in this mode.
You can configure the rate and duplex mode of an Ethernet interface working in either auto-negotiation or non-auto negotiation mode.
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________is a measure, an actual measurable number of the average kinetic energy of the particles of one substance.
A) heat
B) energy
C) matter
D) temperature
Answer:
d) temperature
Explanation:
Answer:
D) temperature
Explanation:
Temperature is a measure, an actual measurable number of the average kinetic energy of the particles of one substance.
What are the interactions of sound waves?; What best describes a sound waves?; What are three interactions of sound waves?; What is wave interaction?
1. Sound waves interact with other objects by transmitting energy and causing vibrations. Examples include sound waves reflecting off of walls and objects, sound waves interfering with one another, and sound waves bouncing off of surfaces and producing echoes.
2. Sound waves are waves of pressure that travel through a medium, such as air or water, and can be heard when they reach a person's ear.
3. Three interactions of sound waves include reflection, interference, and reverberation.
4. Wave interaction is the process in which two or more waves interact with each other to produce an effect. This effect can be a change in amplitude, frequency, or direction.
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Suppose you hear an echo 0.15 seconds after banging. How long
is the barn? (Remember the relationship between distance, time, and speed from sections on motion.)
If you hear an echo 0.15 seconds after banging, the barn is 25.725 m long.
What is echo?
An echo is a sound that results from the return of sound waves to the listener from a surface. It is the reflection of sound, which reaches the listener after the direct sound has passed.
Given data:
you hear an echo 0.15 seconds after banging.
we know that speed of sound in air is 343 m/s.
As in this time sound waves goes to the barn and returns back.
Hence, the barn is = 343×0.15/2 m long = 25.725 meter long.
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The number in the box is ___ and this is a form of ____ decay.
Nuclear/Radioactive Decay: occurs when the nucleus of an atom becomes unstable and spontaneously loses energy in the form of radiation emission.
Gamma Decay: a form of radioactive decay that a nucleus may undergo. This type of decay differs from other because no particles are ejected from the nucleus. Instead, a high energy electromagnetic radiation (gamma ray) photon is released.
The number in the box will be 225.
This example displays the form of gamma decay.
Without collecting any data, describe the motion of the puck while it is on the curved portion of the ramp - is it more similar to motion with constant velocity or motion with constant acceleration? Explain your reasoning. Assume we can ignore friction.
A constant acceleration for an object guarantees that its velocity will change continuously throughout time and not remain constant.
What parallels exist between acceleration and speed?Similarities.Acceleration and velocity are both vector quantities, meaning they have both a magnitude and a direction.Both expressions are capable of being zero, positive, or both.
What are the parallels and differences between acceleration and velocity?The rate at which in displacement is known as velocity.The rate at which velocity changes is called acceleration.Due to the fact that it includes both magnitude and direction, velocity is an vector quantity.As the rate at which velocity changes, acceleration is likewise a vector quantity.
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a flat, circular loop has 17 turns. the radius of the loop is 11.0 cm and the current through the wire is 0.58 a. determine the magnitude of the magnetic field at the center of the loop (in t).
The magnitude of the magnetic field at the center of the loop is 3.31 x 10⁻⁶ T.
What is the magnitude of the magnetic field?The magnetic field is the region of space around which the influence an magnetic force is felt.
Mathematically, the formula for magnetic field at the center of a loop is given as;
B = μ₀I / 2r
where;
μ₀ is permeability of free spaceI is the currentr is the radius of the wireThe magnitude of the magnetic field at the center of the loop is calculated as;
B = ( 4π x 10⁻⁷ x 0.58 ) / ( 2 x 0.11 )
B = 3.31 x 10⁻⁶ T
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An inexperienced researcher runs an experiment and sets his alpha level at .40 because he can't wait to get his firstsignificant result.While he may indeed get a significant result, what are the potential problems?
A potential problem is that you are willing to accept a 5% chance of being wrong if you reject the null hypothesis.
The significance level is the probability of rejecting the null hypothesis if it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that there is a difference when there is actually no difference. Rejecting the true null hypothesis results in a Type I error.
The smaller the value of α the more difficult it is to reject the null hypothesis. Therefore, choosing a low value for α can reduce the likelihood of Type I errors. The result here is that if the null hypothesis is false, it may be more difficult to reject using a lower value for α. The alpha value or statistical significance threshold is arbitrary. Which value to use depends on your field of study.
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what will the pressure inside the container become if the piston is moved to the 1.20 l mark while the temperature of the gas is kept constant?
The new pressure of the system when we move the piston to the 1.20 L mark is obtained as 0.833 atm.
What is the pressure inside the container?We know that if we want to obtain any of the parameters that has to do with a gas we have to apply any of the gas laws that pattern to the ideal gas and in this case we are looking at an ideal gas.
We are told that;
Initial pressure [tex]P_{1}[/tex]= 1 atm, Initial volume [tex]V_{1}[/tex]= 1 L
Final pressure [tex]P_{2}[/tex] = ? , Final volume [tex]V_{2}[/tex]= 1.20 L
By the use of the formula;
[tex]P_{1}[/tex] [tex]V_{1}[/tex] = [tex]P_{2}[/tex] [tex]V_{2}[/tex]
[tex]P_{2}[/tex] = 1 atm * 1L/1.20 L
= 0.833 atm
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Missing parts;
Inside the container is an ideal gas at 1.00 atm, 20.0 ∘C, and 1.00 L. This information will apply to the first three parts of this problem.
A) What will the pressure inside the container become if the piston is moved to the 1.20 L mark while the temperature of the gas is kept constant?
❧ What is the Refraction of Light?
Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent substance into another.
detemine the shear force v and bending moment m at a section of thge loaded beam 200mm to the right of a
The shear force V and bending moment M is 0.15 kN and 0.15 kNm respectively.
What is shear force?
A force acting in a direction parallel to (over the top of) a surface or cross section of a body is known as a shear force. It is determined as the algebraic total of all transverse forces operating on either side of a beam or frame section.
What is bending moment?
A bending moment is the reaction in a structural element caused by an external force or moment that causes the element to bend.
In this question,
Moment about A,
[tex]B_y[/tex] * 0.6 = (6 kN/m * 0.3m) * (0.15m)
[tex]B_y[/tex] = 0.45 kN
Force balance along Y direction,
[tex]A_y[/tex] + [tex]B_y[/tex] = 6 kN/m * 0.3 m = 1.8 kN
[tex]A_y[/tex] + 0.45 = 1.8
[tex]A_y[/tex] = 1.35 kN
At a section 200mm (or 0.2m right of A)
V = [tex]A_y[/tex] - (6*0.2) = 1.35 - 1.2 = 0.15 kN
M = -[[tex]A_y[/tex] * 0.2] + [6*0.2*(0.2/2)] = 0.27-0.12 = 0.15 kNm
The shear force V and bending moment M is 0.15 kN and 0.15 kNm respectively.
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The nearly edge-on view of the spiral galaxy shown gives us some clues as to why the level of recent star formation is different between bulges and disks. Consider the type of environment in which new stars form, and use your observations of the picture to choose the statement that best describes why there is more star formation in the disk.
A. There is more cold, dense gas in the disk than in the bulge.
B. It is too bright in the bulge for new stars to form.
C. Stars can only form in flattened disks.
D. There is more hot gas in the disk than in the bulge.
A. There is more cold, dense gas in the disk than in the bulge.
The best statement is option A.There is more cold, dense gas in the disk than in the bulge.
Star-forming regions are concentrated in galaxies with high concentrations of the material that stars are made of: gas and dust. These concentrations of gas and dust can be "pushed" to the point where they collapse to form stars, depending on the type of galaxy and the types of gravitational interactions it may encounter. Gravity pushes gas and dust to form stars more efficiently in spiral arms than in other parts of the spiral galaxy. This is why spiral arms have more star-forming regions and collections of young stars (open clusters) than other parts of a spiral galaxy.
Thus, due to heavy gravity, gas are more cold and dense in the disk.
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What fraction of the 600 g sample of lodine-125 is left after 4 half-lives?
O 1/64
O 1/4
O 1/2
O 1/16
HELP PLEASEEE
Answer:1/64. im glad i could at least try to help lol im in middle school and i just ran through a bunch of articles 4 u
What kind of energy does the skier have at the top of the slope?
Potential energy is the energy that the skier have at the top of the slope as there will be a equillibrium which means zero velocity and maximum height.
The skier has potential energy at the top of the slope, which he will primarily transform into kinetic energy as he descends the hill. His body and the air, as well as his skis and the snow, will cause some of his PE to be transformed into thermal energy.
The ski lift, which elevated him against gravity, gave him his PE. In an electric motor, the lift transformed electrical energy into kinetic energy. A little portion of this energy was also converted to heat energy by friction in all of the moving elements.
The first law of thermodynamics is exemplified by the energy transformations. Examples of the second law include the losses caused by thermal energy diffusion.
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A ramp is 10 m high and 20 m long. What is the IMA of the ramp?
The IMA of the ramp is 2.
How do you calculate a mechanical advantage?The force amplified by utilising a tool, mechanical device, or machine system is known as mechanical advantage. To achieve the necessary output force amplification, the gadget trades off input forces against movement. The law of the lever serves as a paradigm for this. Mechanisms are machine parts made to control forces and motion in this way. An ideal transmission system does not increase or decrease power. Consequently, the ideal machine is devoid of a power source, frictionless, and built from inflexible materials that do not flex or wear. Efficiency factors that account for deviations from the ideal are used to express how well a real system performs in comparison to the ideal.The length of the effort arm of a lever divided by the length of the resistance arm represents the optimal mechanical advantage. The IMA is typically calculated as the resistance force (Fr) divided by the effort force (Fe). IMA is also equal to the product of the load's travel distance (dr) and the distance over which the effort is applied (de).Given data :
L = 20 mH = 10 mBy using the formula,
MA = L / H
= 20 / 10
= 2
IMA = 2
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two objects, t and b, have identical size and shape and have uniform density. they are carefully placed in a container filled with a liquid. both objects float in equilibrium. less of object t is submerged than of object b. which of the following statements is true
The correct statement about the given two object when placed in a container is b)Object B has a greater density than object T. So, correct option is b.
At the point when an item stay balance while lowered, its gravity should be equivalent to the lightness force, which is equivalent to the fluid weight dislodged by the lowered volume:
[tex]V_s[/tex]ρ[tex]_l[/tex]g=mg=Vρ₀g
=>[tex]V_s[/tex]ρ[tex]_l[/tex]=Vρ₀
=>ρ₀=([tex]V_s[/tex]ρ[tex]_l[/tex])/V
where ρ₀,ρ[tex]_l[/tex] are densities of the object and liquid, separately. are the volume lowered and the item volume, separately.
In the event that object B is completely lowered, the thickness of article B is equivalent to the fluid thickness (on the grounds that ).
With respect to protest T as it's just to some extent lowered, the mass of the fluid dislodged is same as mass of article. And keeping in mind that the volume uprooted is just a piece of the entire item volume (), this implies that the fluid thickness is more noteworthy than object T's thickness.
Hence, correct option is b.
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(Complete question) is:
Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true?
a. Object T has a greater density than object B.
b. Object B has a greater density than object T.
c. Both objects have the same density
which of the following is not an input that the lifted index uses? view available hint(s)for part a which of the following is not an input that the lifted index uses? predicted max temperature of the day at the surface temperature at 500 mb average humidity in the lowest kilometer predicted max humidity of the day
The predicted max humidity of the day is not an input that the lifted index uses. LI is easier and faster to calculate. the lifted index can be used to forecast thunderstorms.
The lifted index (LI) is the temperature differential between the environment Te(p) and an adiabatically raised air parcel Tp(p) at a certain pressure height in the troposphere (the lowest layer of the atmosphere where most weather occurs), typically 500 hPa (mb). The temperature is expressed in degrees Celsius. When the value is positive, the atmosphere (at that height) is stable; when it is negative, the atmosphere is unstable. Although the lifted index can be used to forecast thunderstorms, convective available potential energy (CAPE) is widely regarded as a superior metric of instability and is favored by many meteorologists for convection forecasting. However, LI is easier and faster to calculate without a computer, whereas CAPE involves integration from one level to the next.
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How many possible outcomes are there in rolling a spinner 1 to 8?; What is the probability of spin an even number on a 1 to 8 spinner?; What is the probability of getting a prime number in spinner with numbers 1/8 is spun?; How many different outcomes are possible for spinning the spinner and tossing the coin?
The probability of getting a prime number ( 2, 3, 5, 7) between 1 to 8 is 1/2. The total outcomes possible for spinning the spinner and tossing the coin is 16.
What is probability?Branch of mathematics concerning numerical descriptions of how likely an event is to occur is called probability.
Total number of outcomes = 8.
Let, the probability of getting a prime number ( 2, 3, 5, 7) between 1 to 8
P(E) = (no. of outcomes) /( total no. of outcomes)
=4/8
=1/2
When a coin is tossed, there are two possible outcomes that are H(head), and T(tail).
If you spin the spinner , there are 8 possibilities.
Total outcomes = 8 * 2
=16
There are 16 outcomes, when spinning a spinner numbered from 1 to 8 and tossing a coin.
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An object is thrown vertically up in the air. Its initial velocity is 6 m/s. What is the object's maximum height? (use g=9.8 m/s^2)
An object is thrown vertically up in the air. Its initial velocity is 6 m/s. The object's maximum height is 1.83673 m.
What is Projectile motion?
Projectile motion can be regarded as a form of motion that can be experienced by an object when its been projected near the Earth's surface and follows curved path under the action of gravity only.
Given, the velocity of ball, u= 6 m/s
Here, v be the final velocity, u be the initial velocity and H be the height.
Velocity of the ball at maximum height is zero, v=0
v² - u² =2aH
0−(6)²=2×(−9.8)×H
⟹H= 1.83673 m
Thus, the object's maximum height is 1.83673 m.
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a uniform rod of length l oscillates as a pendulum about a pivot that is a distance x from the center.
According to the given statement x = L / 2√3 in terms of l, is the oscillation period a minimum.
What is oscillation formula ?
In systems that can be characterized by Hooke's law, F = kx, where x is the displacement from equilibrium or deformation and k is the system's force constant, the simplest oscillations occur.
Briefing:
T = 2π√I/mgx
I stands for the moment of inertia about the oscillation axis.
m is the bodily mass.
x is the separation of the mass center from the pivot point.
g stands for gravitational acceleration.
Here , Moment of inertia of a rod about the axis through pivot is given by
I = ML²/12 + Mx²
As the axis of rotation passes past the pivot, we have measured the rod's moment of inertia with respect to it.
The Pendulum's Time Period is shown by
[tex]$$T=2 \pi \sqrt{\frac{\frac{M L^2}{12}+M x^2}{M g x}} \Rightarrow T=2 \pi \sqrt{\frac{L^2+12 x^2}{12 g x}}$$[/tex]
Time period will be minimum if [tex]$\mathrm{L}^2+12 \mathrm{x}^2 / 12 \mathrm{gx}$[/tex] is minimum
[tex]$$\begin{aligned}& \frac{d}{d x}\left(\frac{L^2+12 x^2}{12 g x}\right)=0 \\& \frac{12 g x(24 x)-\left(L^2+12 x^2\right) 12 g}{144 g^2 x^2}=0\end{aligned}$$[/tex]
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