(a) Calculate the ratio of the highest to lowest frequencies of electromagnetic waves the eye can see, given the wavelength range of visible light is from 380 to 760 nm. (b) Compare this with the ratio of highest to lowest frequencies the ear can hear.

The required angled is[tex]$\theta=33.4^{\circ}$[/tex].

What is angle is the first minimum?

The first minimum is going to be theta one is the inverse sine of one times 550 times ten to the minus nine meters divided by one times ten to the minus six meters giving an angle of 33.4 degrees

[tex]\begin{aligned}& \lambda=550 \mathrm{~nm} \\& D=1.00 \mathrm{~nm}\end{aligned}[/tex]

[tex]D \sin \theta=m \lambda, m=1,-1,2,-2, \ldots$$[/tex]

a) [tex]$\theta=\sin ^{-1}\left(\frac{m \lambda}{D}\right)$[/tex]

[tex]\theta_1=\sin ^{-1}\left(\frac{(1)\left(550 \times 10^{-9} \mathrm{~m}\right)}{1.00 \times 10^{-6} \mathrm{~m}}\right)=33.4^{\circ}[/tex]

b)The value of sine function can never be greater than 1, so second minimum does not exists for given wavelength of light and width of slit.

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Water Emerges Straight Down From A 1.50 Cm Diameter Faucet At A Speed Of 0.800 M/S has a 0.210 m below the faucet diameter of -0.918cm.

The speed of an object, also known as v in kinematics, is a scalar quantity that refers to the size of the change in that object's position over time or the size of the change in that object's position per unit of time. The distance travelled by an object in a time interval divided by the length of the interval gives the average speed of the object during that interval. A circle's diameter is defined as the distance between its opposing edges. Learn the diameter formulas and the connections between related metrics that are very significant.

H = (q/pi*v)^1/2

h = (141.37*10^-6/pi*2.1359

= 4.5905*10^-3m

d = 2h = 9.181*10^-3m

d = -0.918cm

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The complete question is -

Water emerges straight down from a 1.50 cm diameter faucet at a speed of 0.800 m/s. (Because of the construction of the faucet, there is no variation in speed across the stream.  What is the diameter of the stream 0.200 m below the faucet? Neglect any effects due to surface tension.

A body is free falling from height h now at the middle that is at h/2 the body's K.E. = P.E

What is kinetic energy?

An object's kinetic energy is the energy it has as a result of motion. Applying force is necessary if we want to accelerate an object. We have to put in work to apply force. After the work is finished, the object will be moving at a new, constant speed because energy has been transferred to it.

There are only two cases in this phenomenon to occur:-

Case 1 - Something is tossed upward

When is the change in kinetic energy equal to the change in potential energy for an object thrown upward at some beginning velocity v0? The total amount of kinetic and potential energy is constant due to energy conservation. We want to know when the kinetic energy has decreased by half because we define our potential energy as zero at the launch point.

Case 2 - Simple harmonic oscillator

A restoring force proportionate to the displacement of the mass from equilibrium distinguishes a simple harmonic oscillator (such as a mass on a spring) from other oscillators:

F=− kx

This equation's solution yields the position as x=Acos(ωt+Ф), where A denotes the oscillation's amplitude, frequency, and phase. The frequency is expressed as Ф= [tex]\sqrt{k/m}[/tex]. The derivatives of the location can be used to calculate the oscillator's velocity and acceleration, which are both sinusoidal functions.

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The creature died 5730 year ago by using the half-life decay equation.  

Half life decay equation is defined as a characteristic unit for the exponential decay equation and remains constant over the course of an exponentially decaying quantity. The appropriate metrics for defining the life of decaying material are provided by the half-life formula.

The half life decay equation is

N = N₀ ( 1/2 ) t/t ¹/²

Let N =  t/t ¹/²

So , N / N₀ = 1 / 2ⁿ

N₀ / N = 2ⁿ

N₀ / 0.50 N₀ = 2ⁿ

2ⁿ = 1 / 0.50

2ⁿ = nlog2

2ⁿ = log 1 - log 0.50

2ⁿ = 0 -( - 0.301 )

2ⁿ = 0.301

n = 0.301 / log 2

n = 0.301 / 0.301

n = 1

t1/2 = 5730

t = n x t1/2

t = 1 x 5730

t = 5730 years.

Thus, the creature died 5730 years ago by using the half-life decay equation.  

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The target temperature increase from pre-industrial levels is to keep global warming below 1.5 degrees Celsius.

The business also took part by signing the UN Global Compact Business Ambition for the 1.5° Pledge, which was signed by 1,100 companies.

They have sworn to uphold the Paris Climate Agreement and do our part to keep global warming below 1.5° Celsius.

They are dedicated to reducing emissions to zero.

Additionally, they emphasize neutrality by outlining the process of balancing their carbon emissions.

The warming of Earth's surface over time, seen since the pre-industrial era (between 1850 and 1900), is referred to as global warming.

This warming is a result of human activities, particularly the burning of fossil fuels, which raises the levels of heat-trapping greenhouse gases in the atmosphere. 'Climate change' should not be used in place of this phrase.

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Similarity which leads about most of the object to let the bulb light is their conducting materials.

The behaviour (ie., brightness) of the bulb when objects made out of various materials are inserted into the circuit is as-

The bulb glows when connected to conducting object but it does not glow when some objects like eraser, wood, plastic etc. are used to complete the circuit as it is the non-conducting objects.

Paper is a non-conducting object.

Coins are normally made up of silver, gold and metal alloys and we know all metals conduct electricity.

Pencil lead is made up of graphite which is non-metal still it conducts electricity as graphite contains delocalised electron (free electrons). These electrons can move through the graphite, carrying charge from place to place and allowing graphite to conduct electricity.

Human fingers are conductors as whole body of a human is an excellent conductor of electricity. This reply on the fact that our fingers is 3 parts salty water - which means it's got lots of loose electric charges floating around in it.

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Speed can be calculated using Kinetic energy and Potential energy. Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2.

How to calculate speed using Kinetic energy and Potential energy?

We know

Mass of the car = 300kg

G=9.8

Height = 16m

Thus, potential energy U =mgh and kinetic energy is 1/2mv²

0.5*m*v2 = m*g*h

v = √(2*g*h) = √(2*9.81*16)

v=17.71 m/s

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These speeds 4 s later is -20 m/s.

What is Acceleration due to Gravity?

The acceleration due to gravity would affect the radial component of an object at the surface of the earth. This would seem to us that the gravitational force acting on us on a vertical axis. This means that gravity would not affect any horizontal movement.

Determine the horizontal and vertical speeds, [tex]$v_x$[/tex] and [tex]$v_y$[/tex], of the baseball after t=4 seconds. We only recognize gravity as the force acting on the object, acting only on the vertical component. This means that the horizontal speed remains the same, such that

[tex]$$v_x=16 \mathrm{~m} / \mathrm{s}$$[/tex]

Now, we determine the vertical speed after the given time, t, by applying the kinematic equation,

[tex]$$v_y=v_{0 y}-g t$$[/tex]

where[tex]$g=9.81 \mathrm{~m} / \mathrm{s}^2$[/tex] is the acceleration due to gravity and t is the time. We proceed with the solution.

[tex]$$\begin{aligned}v_y & =v_{0 y}-g t \\& =18 \mathrm{~m} / \mathrm{s}-\left(9.81 \mathrm{~m} / \mathrm{s}^2\right)(4 \mathrm{~s}) \\& \approx-20 . \mathrm{m} / \mathrm{s}\end{aligned}$$[/tex]

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So moving the slit towards the laser will increase the slit and screen distance and the screen and the fringe will be bigger. The other factors such as the angle of diffraction, and wavelength will remain unaltered in this case.

What is Diffraction?

In order to enter the region of the geometric shadow cast by the obstruction or aperture, waves must interact with one another or bend around its edges, which is referred to as diffraction. A secondary source of the wave that is propagating is in fact created by the diffracting item or aperture.

What is Fringe?

The band of alternating light and dark material called a fringe is produced via interference.

The formula is used to calculate the fringe width

β=λDd

Where β represents the bandwidth, λ represents the wavelength of the light, D represents the distance between the source and the screen, d represents the distance between the two slits

Hence, moving the slit towards the laser will increase the slit and screen distance and the screen and the fringe will be bigger. The other factors such as the angle of diffraction, and wavelength will remain unaltered in this case.

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Its top cruising speed is 90 miles per hour. (a) I discovered that the answer to the question, "What is the maximum distance the train can travel if it accelerates from rest till it reaches," was 22.665.

Given is the formula Acceleration=Deceleration=a

Maximum cruising speed: 1 mile = 5280 feet per hour (3600 s).

Time, t = 15 min = 1 min = 60 s

initial velocity, u=0

Replace the values

Distance=D

Distance total = s+d=2178+118800=120978 feet

Total distance = 22.665 miles, which is the furthest train can go.

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Due to her location within it, this is not possible. It can only be seen if the sky is clear and there is little to no light pollution, and as a result, environmental changes occur.

The Milky Way is crammed with anything between 100 billion and 400 billion more stars, many of which have their own planets. The Milky Way is so named because it appears from Earth like a streak of milk that has been spilled across the sky.

A galaxy is a sizable group of stars gathered in one place in the universe. The Milky Way galaxy, which contains the sun, Earth, and seven other planets, is where our solar system is located. Similar to our sun, the Milky Way is home to hundreds of billions of stars.

The Milky Way makes it possible to examine a medium-sized spiral galaxy's functioning in great detail.

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The speed of a wave with a frequency at 46 Hz as well as a wavelength = 1.7 meters is 78.2 m/sec.

The Greek letter λ is frequently used to represent wavelength. The name wavelength is also occasionally used to refer to modulated waves, their sinusoidal envelopes, or waves created by the interference of multiple sinusoids.

The distance between each trough or the difference between each wave's crest and the next one. One of "yardsticks" used to gauge radiation levels is this. The SI unit measuring wavelength is the metre, which is frequently abbreviated as m. The wavelength of an object is measured using its multiples and fractions.

Wavelength = 1.7 m

Frequency = 46 Hz

v denotes the wave's speed, w its wavelength, and f its frequency.

f = v/w,

= 46 =v/1.7

v = 78.2 m/sec

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Given that copper's electron mobility is 3 10-3 m2/v-s, there are 1.20 × 10⁷ conducting electrons per cubic meter in copper.

The mobility of holes and electrons in semiconductors and metals is the subject of this essay. See Electrical mobility for a broad explanation. The electron mobility in solid-state physics refers to how quickly an electron may move through with a metal or semiconductors when being drawn by an electric field. Hole mobility is the corresponding quantity for holes. Both electron / hole mobility are collectively referred to as carrier mobility. The electrical mobility if charge particles in a fluid under such an applied electric field includes electron / hole mobility as specific examples.

The equation =VdE allows us to mathematically demonstrate electron mobility. The SI symbol for electron mobility when subject to an external electric field is m2V1s1. We can see that [M1T2A] is its dimensional form when the SI unit's dimensions are calculated.

resistivity of the copper (p) = 1.73 × 10⁸ Ωm

η = σ/μe

Here, σ = electrical conductivity

σ = 1/ρ

e = charge on electrons = 1.6 × 10⁻¹⁹

μ = mobilty of electrons

n = σ/μe

n = 1/ρμe

n = 1/8.304 × 10⁻⁸

n = 10⁸/8.304

n = 1.20 × 10⁷ electrons/ m³

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Answer:

0.612 kilograms.

Explanation:

To solve this problem, we need to use the definition of work as the product of force and displacement.

(a) The work done on the book is the force applied to it multiplied by the distance through which it is moved. In this case, the force applied to the book is its weight, which is 6 newtons. The displacement of the book is 2 meters, because it is moved from one shelf to another shelf that is 2 meters higher. Therefore, the work done on the book is 6 newtons * 2 meters = 12 joules.

(b) The next person to take the book from the shelf accidentally drops it. When an object is dropped, it accelerates due to the force of gravity, which is 9.8 m/s². Since the force of gravity is the same for all objects, we can use the acceleration of the book to calculate its mass. Specifically, we can use the formula F = ma, where F is the force acting on the object (in this case, the force of gravity), m is the mass of the object, and a is its acceleration.

In this case, the force acting on the book is its weight, which is 6 newtons. The acceleration of the book is 9.8 m/s². Therefore, we can solve for the mass of the book using the formula F = ma: 6 newtons = m * 9.8 m/s². This simplifies to m = 6 newtons / 9.8 m/s² = 0.612 kilograms.

In summary, the work done on the book when it is picked up and moved to a higher shelf is 12 joules, and the mass of the book is 0.612 kilograms.

The factory without exceeding the 85 dB limit n  =10.

A factory is described as a building, or a group of buildings wherein goods are synthetic via a system. however, the industry is defined as the branch of economics wherein raw substances, goods, and offerings are produced.

The sound level in decibels is

β dB = 10 log ( I / Io )

where I am the intensity of sound

It is the relative intensity

80 = 10 log ( I / 10-12 )

8  = log ( I / 10-12 )

10 8  =  I / 10-12

I  =  10 8 . 10 -12 =  10 -4 W /m2

if the sound level is 90 dB, the number of identical machines is n.

90 = 10 log ( n I / Io )

=  10 logs ( n . 10-4 / 10 -12 )

9  =  log ( n . 108 )

10 9 = n. 10 8

n = 10.

so  n  =10 .

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The total width of the central maximum be 1.266 cm.

Given data :

So,  the total width of the central maximum = 2λD/a

= ( 2 × 633 nm × 2.00 m)/ 0.200 mm.

= 0.01266 m = 1.266 cm.

Hence, the total width of the central maximum be  1.266 cm.

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The standard way to express an order of magnitude is as 10 to the nth power where q/h is 0.01.

An order of magnitude is an exponential change of plus or minus 1 in the value of a quantity or unit. The term is generally used in conjunction with power-of-10 scientific notation. Order of magnitude is used to make the size of numbers and measurements of things more intuitive and understandable.

The order of magnitude is the power of 10 a number is raised to when it's in scientific notation. For example, the order of magnitude for 19,400 would be 4. This is because when we convert it into scientific notation, 1.94×104, the 10 is being raised to the 4th power.

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If the loops are moved closer to and farther from the magnets in exactly the same way then the emf generated around the wooden loop is equal to the emf generated around the wire loop.

Electromotive force (emf) can be described as the electric potential that is produced by either changing the magnetic field or is produced by an electrochemical cell.

The emf generated around the wooden loop is equal to the emf generated around the wire loop because Faraday's law is only concerned about how the flux is changing and is therefore independent of the material involved. The loop material is not involved in the magnetic flux expression, so an emf is generated anyhow as long as it experiences a change in magnetic flux since it moves near the end of the bar magnet, changing the magnetic flux through the loop.

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The final temperature of the copper cup is found to be 409.19° K.

The mass of the copper cup is 0.500 Kg and it is at a temperature of 280°K.

A total of 2.5 x 10⁴ J of energy is added to the system.

The final temperature of the system is let us say T.

Now, the change in energy will be given by,

∆Q = mC∆T

Where,

C is the specific capacity of copper.

Putting values,

2.5 x 10⁴ = 0.5 x 387 x(T - 280°)

T = 409.19°K.

So, the final temperature of the copper cup is 409.19°K.

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The work done on the ball during one period is 66.67 J.

What is acceleration?
The rate at which the speed and direction of a moving object change over time. A point or object moving straight ahead is accelerated when it accelerates or decelerates. Even though the speed is constant, motion on a circle accelerates because the direction is constantly shifting. Both effects contribute to a acceleration for all other motions. Acceleration is a vector quantity because it has both a greater acceleration. A vector quantity is also velocity. The velocity vector change over a time interval divided by time interval is the definition of acceleration.

The amount of work done on the ball during one period is equal to the force times the distance traveled, which is equal to the mass times the centripetal acceleration times the distance traveled. Thus, the work done on the ball during one period is equal to 4 kg x (5 m/s)2 / 1.5 m = 66.67 J.

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The majority of alpha particles were found to pass directly through gold foil, suggesting free space makes the majority of atoms. Due to interactions with other + charged molecules inside atom are slightly deflected.

The majority of a alpha particles were absorbed without being rejected by positively particles (protons) inside the nucleus, although some of them rebounded back. Positive attracts positive and vice versa.

The majority of alpha particles passing right through to the foil is proof that the atom is primarily made up of empty space. There is an concentration of alpha particles since only a limited number of them were deflected at great angles The atom has a positive charge.

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The current flowing through the resistors is 0.229 A

A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device.

A specified voltage can be supplied via resistors to an active device like a transistor.

An electrical component with two terminals that provides electrical resistance is called a resistor.

Resistors are frequently used in electronic circuits to reduce current flow, divide voltages, block transmission signals, and bias active elements.

Given; The value of the resistors are :

R1 = 41 ohm

R2 = 41 ohm

R3 = 71 ohm

R4 = 64 ohm

V = 24 V

At t = 0 sec when there is no flow of current through resistors R2 and R3

therefore the equivalent resistance is = R1 + R4

Thus V = I * R

24/ 41 + 64 = I

I = 0.229 A

thus the current flowing through the resistors is 0.229 A

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4P₀V₀ is the work done by the gas during process 1→2→6→5→1.

Therefore, the work performed by a gas expanding against an external pressure is negative, analogous to the work performed by a system on its surroundings. In contrast, when a gas is compressed externally, V₀ and the work is positive because the environment exerts force on the system.

The gas must release some energy into the environment when it expands in response to an external pressure. The overall energy of the gas is thus reduced as a result of the negative work. When a gas is compressed, energy is transferred to it, increasing its energy as a result of positive work.

Let's consider,

Work done = -W (As the energy is released)

External pressure = P₀

Volume of gas = V₀

So, the work done can be calculated as follows:

W = P x (dV)

-W = P₀ × V₀

Now according to the process given:

1→2→6→5→1

Energy flow increases up to 6 eventually decreases with loss of factor 4.

Hence, the energy of the system (work done) is:

-W = 4 × P₀ × V₀

-W = 4P₀V₀

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The total torque required to accelerate the wheel is 0.054 Nm.

The moment of inertia of the uniform cylinder is calculated  by applying the following formula.

I = ¹/₂MR²

where;

I = ¹/₂(0.38)(0.085)²

I = 1.37 x 10⁻³ kgm²

The angular acceleration of the grinding wheel or uniform cylinder is calculated as follows;

α = ω/t

where;

ω = 1750 rev/min x 2π rad/rev x 1 min / 60 s = 183.26 rad/s

α = (183.26 rad/s) / (5s)

α = 36.65 rad/s²

The torque required to accelerate;

τ = Iα

τ = (1.37 x 10⁻³ kgm²) x (36.65 rad/s²)

τ = 0.05 Nm

The frictional torque that is slowing down the wheel;

ω = 1500 rev/min x 2π rad/rev x 1 min / 60 s = 157.1 rad/s

α = (157.1 rad/s) / (55 s)

α =  2.86 rad/s²

τ = Iα

τ = (1.37 x 10⁻³ kgm²) x (2.86 rad/s²)

τ = 0.004 Nm

The total torque required to accelerate the wheel is calculated as;

τ(total) = 0.05 Nm + 0.004 Nm

τ(total) = 0.054 Nm

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it take for the radiation level of potassium-42 to drop to 1/16 of its original level is 48 hours.

Radiation can be divided into four main categories: alpha, beta, neutrons, and electromagnetic waves like gamma rays.The mass, intensity, and depth to which they pierce persons and things varies between them.

A beta particle is the first.Although they can exceed 50 mSv/yr, they normally fall between 1.5 and 3.5 millisievert per year.

The worst external risk is gamma radiation.Beta burns can occur when beta particles partially penetrate the skin.Alpha rays can't go through skin that is still intact.The cells in their route can be damaged by gamma and x-rays that travel through a person.

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If we were to move a detector along the x-axis starting at S1, it would have to be moved 11.6m far before it detects no sound at all.

A sound wave is what?

A sound wave is a pressure wave, which may be conceptualized as variations in pressure over time. Transverse waves include sound waves. The tines of a tuning fork must transfer air from the fork to one's ear in order for one to hear the sound of the fork. The majority of sound waves, although not all of them, are produced by some sort of vibrating object.

What two forms of sound waves are there?

The characteristics of sound waves should be the starting point for studying sound. Transverse and longitudinal waves are the two fundamental forms of waves, and they are distinguished by how they move through space.

Given,

The two sources, [tex]S_{1}[/tex] and [tex]S_{2}[/tex] separated by a distance is d = 2.0m

[tex]S_{2}P = \sqrt{x^{2} +2.0^{2} }[/tex]

       = [tex]\sqrt{x^{2} +4}[/tex]

For destructive interference

[tex]S_{2}P - S_{1}P[/tex] = λ/2                                                    

 λ=ν/f

Given:

frequency  f = 1000hz

speed of sound ν = 343m/s

   =[tex]\frac{343}{1000} = 0.343m[/tex]

[tex]\sqrt{x^{2} +4} -x[/tex] = [tex]\frac{0.343}{2}[/tex] = 0.1715

⇒ [tex]\sqrt{x^{2} +4}[/tex] = 0.1715 + x

⇒ [tex]x^{2}[/tex]+4 = [tex](0.1715+x)^{2}[/tex]

           =      [tex](0.1715)^{2} + x^{2} + 2(0.1715)(x)[/tex]

⇒ 4 = [tex](0.1715)^{2}[/tex]+ 0.343 [tex]x[/tex]

⇒ [tex]x = \frac{4-0.1715^{2} }{0.343}[/tex]

       = 11.6m

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Electrons flow continuously through a circuit when current is present.

A static discharge is a very quick, irregular transfer of charge.

Static discharge is the abrupt movement of electrons from one charged object to another.

Static discharge is the abrupt passage of electrons. The spark you see and the jolt you experience are both caused by an electron discharge.

For the circuit, the charge travels through a wire.-True

For a static discharge, the charge is transferred from one object to another.-True

The basic unit of electricity is charge (or, more precisely, electric charge).

Everything in electricity is a charge.

The physical characteristic of matter that causes it to feel a force when exposed to an electromagnetic field is called electric charge. The two types of electric charges that protons and electrons most frequently carry are positive and negative charges.

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The weight on the even stranger planet, quoozeptinaletina, that is 226 times more massive than zorgg and has a radius 17.1 times larger will be

991.759N

In science and engineering, the weight of an object is the same as the force that acts on the object because of the gravity. Some books define weight as a vector quantity, some as the gravitational force acting on the object, and others define as a scalar quantity, the magnitude of the gravitational force.

Weight -> F = m * g

m = mass of object (constant for non relativistic speed)
F = Force

g = Gm / R^2

where

m = mass of planet

R = radius of planet

G = gravitational constant

at Zorgg planet, Fz = 1283N = m* gz,

gz = G*Mz / Rz^2

at Quoozeptinaletina,

Rq = 17.1Rz

Mq = 226Mz

Fq = m*gq

gq = G * Mq / Rq^2

226GMz / 17.1^2 Rz^2

gq = 226 / 17.1^2 gz

Fq = 226 / 17.1^2 Fz

= 0.773Fz

= 0.773 * 1283N

= 991.759N

Therefore, your weight at planet quoozeptinaletina is 991.759N

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The internal energy of a system is 1542.52 J.

What is internal energy?

The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state and includes the contributions of potential energy and internal kinetic energy.

First we convert calories into joules, 530 calories =530 calories × 4.184                                                                        = 2217.52 J

Formula, ΔE = q + w

Here, the system releases heat, so q is negative

Therefore, ΔE = -q + w

Now, put the values of q and w

ΔE = -675 + 2217.52 J

ΔE = 1542.52 J

Internal energy is the sum of ability power of the gadget and the machine's kinetic strength. The alternate in internal energy (ΔU) of a response is equal to the heat gained or lost (enthalpy trade) in a reaction whilst the reaction is administered at steady pressure. inside the study of thermodynamics, a usually perfect gasoline is taken into consideration as a running substance. The molecules of an ideal gasoline are mere mass points that exert no force on each other.

The SI derived unit used to degree strength or paintings. One joule is identical to the electricity used to accelerate a body with a mass of 1 kilogram using one newton of force over a distance of one meter. One joule is also equal to one watt-second.

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The statement that is correct is that all the carbon atoms in the glucose would end up in the palmitic acid. Option C.

In science a model is used for the purpose of explanation. The model could be used to describe what is going on in the reaction system. We can see from the model that there is a combination of the molecule of glucose with the molecule of oxygen in the molecule.

Now, we can see that the bonds in the glucose that are carbon to carbon bonds are broken and then recombined in such a way that they now lead to the formation of the palmitic acid molecule.

By the law of the conservation of mass, the number of atoms of the reactant is equal to the number of atoms in the product. This would play out as we carry out an atom count of the reactants and the products.

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