a barrel will rupture when the gauge pressure within it reaches 350 kpa. it is attached to the lower end of a vertical pipe, with the pipe and barrel filled with oil \rho

Saturn's Atmosphere :-Proportionally less helium, Thinner Atmosphere, Most colorful in visible light, Composed of hydrogen and helium.

Jupiter's Atmosphere :- Oval stroma systems, Differential Rotation, Fewer observers features in light.

Electromagnetic radiation that the human eye can see is referred to as light or visible light. Typically, visible light is characterized as having wavelengths in the 400–700 nanometer (nm) range, which corresponds to frequencies of 750–420 terahertz, lying between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths) (with shorter wavelengths).

In physics, the term visible light" can more widely be used to refer to electromagnetic radiation of any wavelength, whether or not it is visible.

This definition of light includes gamma rays, X-rays, microwaves, and radio waves. The main characteristics of light include intensity, polarization, frequency or wavelength spectrum, and propagation direction. One of nature's basic constants is the speed of light in a vacuum, which is 299 792 458 meters per second (m/s). Visible light travels through space by, like all forms of electromagnetic energy,

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The qualitative sketch of the process on the PV plane is attached below:

The ideal gas law (also called the perfect gas law), the relationship between pressure P, volume V, and temperature T of a gas in the boundary region between low pressure and high temperature. Gas molecules move almost independently. each other. In such cases, all gases obey an equation of state known as the ideal gas law.

PV = nRT, where n is the number of moles of gas and R is the universal (or complete) gas constant, 8.31446261815324 joules/kelvin/mol (the universal gas constant is defined as Avogadro's number NA multiplied by Boltzmann's constant k) . ) In the International System of Units, energy is measured in joules, volume in cubic meters (m3), force in newtons (N), and pressure in pascals (Pa). where 1 Pa = 1 N/m2. A force of 1 Newton moving a distance of 1 meter does 1 Joule of work. Therefore, the dimension of both products PV and nRT is work (energy).

The qualitative sketch of the process is drawn on the PV plane.

At A,

P₁ = 100 kPa

V₁ = 0.50 m³
T₁ = 375 K

At B,

T₂ = 375 K

V₂ = 0.25 m³
P₁V₁ = P₂V₂

So, P₂ = (100× 10³ ×0.50)/ 0.25

= 200 kPa

At C,

P₃ = 200 kPa

V₃ = 0.75 m³

We know, V₂/ T₂ = V₃/ T₃

So,

T₃ = V₃T₂/ V₂

= (0.75 × 375)/ 0.25

= 1125 K

At D,

P₄ = 100 kPa

T₄ = 1125 K

V₄ = P₃V₃/ P₄

= (200 × 0.75)/ 100

= 1.5 m³

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The complete question is:

the rate at which the entropy of the two reservoirs changes is 0.004081 KW/K

Yes, the second law is satisfied.

claculation :

ΔS = Q/T (entropy formula)

ΔS1 = 2/300 = 0.006667 KW/K

ΔS2 = 2/715 = 0.002580

Δs = 0.006667 - 0.002580

Δs = 0.004081 KW/K

Yes, the second law is satisfied.

Entropy is a scientific concept and a measurable physical property most commonly associated with states of disorder, randomness, or uncertainty. The term and concept are used in a variety of fields, from classical thermodynamics, where it was first recognized, to microscopic descriptions of nature in statistical physics, to principles of information theory. It finds a wide range of applications in information systems, including information transmission in chemistry and physics, the relationship between biological systems and life, cosmology, economics, sociology, weather science, climate change, and communications.

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The formula to calculate mechanical energy is ME=PE+KE. If you are aware of the kinetic and potential energies of the vehicle.

The energy an entity has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.

The capacity to perform work is arguably the most significant characteristic of kinetic energy. Force flowing on an object while it is moving is referred to as work. Energy and work are interchangeable because of their tight relationship.

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The tension in a given rope may be thought of as T = (m g) + (m a), where "g" denotes the gravitational acceleration of any items the rope is supporting and "a" denotes any additional accelerations placed on those same objects.

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The following are some properties of images formed by a plane mirror are; virtual, upright, left-right reversed, the same distance from the mirror as the object's distance, and the same size as the object.

When a ray of light hits a surface, then it can undergo one of the following reflection, refraction, or absorption. So mirrors are polished surfaces coated with mercury such that they reflect most of the light hitting them.

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The emf induced in the loop at t = 0 is

Part a)

[tex]$$\text { EMF }=14 \times 10^{-3} \mathrm{~V}$$[/tex]

The emf induced in the loop at t = 1.00 s

Part b)

[tex]$$E M F=15.67 \times 10^{-3} \mathrm{~V}$$[/tex]

What is emf induced ?

As we know that magnetic flux through the loop is given as [tex]$\phi=B . A$[/tex]

now we have

[tex]$$\phi=B \pi r^2$$[/tex]

now rate of change in flux is given as

[tex]\frac{d \phi}{d t}=B(2 \pi r) \frac{d r}{d t}$$[/tex]

now we know that

[tex]$$\begin{aligned}& A=\pi r^2 \\& 0.285=\pi r^2 \\& r=0.30 m\end{aligned}$$[/tex]

Now plug in all data

[tex]$$\begin{aligned}& E M F=(0.20) \times 2 \pi \times(0.30) \times(0.037) \\& E M F=14 \times 10^{-3} V\end{aligned}$$[/tex]

Now the radius of the loop after [tex]$t=1 \mathrm{~s}$[/tex]

[tex]$$\begin{aligned}& r_1=r_0+\frac{d r}{d t} \\& r_1=0.30+0.037 \\& r_1=0.337 m\end{aligned}$$[/tex]

Now plug in data in above equation

[tex]$$\begin{aligned}& E M F=(0.20) \times 2 \pi \times(0.337) \times(0.037) \\& E M F=15.67 \times 10^{-3} V\end{aligned}$$[/tex]

Complete question:The loop is in a magnetic field 0.40 T whose direction is perpendicular to the plane of the loop. At t = 0, the loop has area A = 0.285 square m.Suppose the radius of the elastic loop increases at a constant rate, dr/dt = 3.70 cm/s .

A) Determine the emf induced in the loop at t = 0.

B)Determine the emf induced in the loop at t = 1.00 s .

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(a) Refer to part (a)

(b) Refer to part (b)

(c) [tex]nr^{n-1}\bold{\hat{r}}[/tex]

To answer the questions, I will show the derivations of each part by applying vector calculus methods such as the gradient operator, denoted by '▽', to the given quantities. I will use the definition of the gradient operator in Cartesian coordinates to solve each part.

Given:

[tex]\bold{r} = (x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}; \ r=\sqrt{ (x-x')^2+(y-y')^2+(z-z')^2}[/tex]

Show that:

(a) [tex]\nabla (r^2)=2 \bold{r}[/tex]

(b)[tex]\nabla (1/r)=- \bold{\hat{r}}/r^2[/tex]

(c) What is the general formula for [tex]\nabla (r^n)[/tex]?

[tex]\hrulefill[/tex]

The gradient operator in Cartesian coordinates is:

[tex]\nabla = \hat{\imath}\dfrac{\partial}{\partial x}+ \hat{k}\dfrac{\partial}{\partial y}+ \hat{\jmath}\dfrac{\partial}{\partial z}[/tex]

The square of the vector length is given by:

[tex]\Longrightarrow r^2 = [(x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}]^2\\\\\\\\\Longrightarrow r^2 = (x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}[/tex]

Now, applying the gradient operator to 'r²':

[tex]\Longrightarrow \nabla r^2 = \\\\\bullet \dfrac{\partial}{\partial x}[(x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}]=2(x-x')\\\\\bullet \dfrac{\partial}{\partial y}[(x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}] = 2(y-y')\\\\\bullet\dfrac{\partial}{\partial z}[(x-x')^2\hat{\imath}+ (y-y')^2\hat{\jmath} + (z-z')^2\hat{k}] =2(z-z')\\\\\\\\\therefore \nabla r^2=2(x-x')\hat{\imath}+ 2(y-y')\hat{\jmath} + 2(z-z')\hat{k}\\\\\\\\[/tex]

Factoring out a 2:

[tex]\Longrightarrow \nabla r^2=2[(x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}]\\\\\\\\\therefore \boxed{\nabla r^2=2 \bold{r}}[/tex]

[tex]\hrulefill[/tex]

The length 'r' is given by:

[tex]r=\sqrt{ (x-x')^2+(y-y')^2+(z-z')^2}[/tex]

Now applying the gradient operator to 1/r:

[tex]\dfrac{1}{r}=((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}[/tex]

[tex]\nabla \dfrac{1}{r} =\\\\\bullet \dfrac{\partial}{\partial x}[((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}]=-(x-x')[(x-x')^2+(y-y')^2+(z-z')^2]^{-3/2}\\\\\bullet\dfrac{\partial}{\partial y}[((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}]=-(y-y')[(x-x')^2+(y-y')^2+(z-z')^2]^{-3/2} \\\\\bullet\dfrac{\partial}{\partial z}[((x-x')^2+(y-y')^2+(z-z')^2)^{-1/2}]=-(z-z')[(x-x')^2+(y-y')^2+(z-z')^2]^{-3/2}[/tex]

[tex]\Longrightarrow \nabla \dfrac{1}{r} = - \dfrac{(x-x')\hat{\imath}+ (y-y')\hat{\jmath} + (z-z')\hat{k}}{[(x-x')^2+ (y-y')^2 + (z-z')^2]^{3/2}}[/tex]

[tex]\Longrightarrow \nabla \dfrac{1}{r} = -\dfrac{\bold{r}}{r^3}; \ \text{Where:} \ \bold{\hat{r}} =\dfrac{\bold{r}}{r} \rightarrow \bold{r}=\bold{\hat{r}}\cdot r \\\\\\\\\Longrightarrow \nabla \dfrac{1}{r} = -\dfrac{ \bold{\hat{r}} \cdot r}{r^3}\\\\\\\\\therefore \boxed{\nabla \dfrac{1}{r} = \dfrac{\bold{-\hat{r}}}{r^2}}[/tex]

[tex]\hrulefill[/tex]

The general formula is as follows:

[tex]\Longrightarrow \nabla(r^n)=\dfrac{\partial}{\partial r}[r^n] \bold{\hat{r}} \\\\\\\\\therefore \boxed{\nabla(r^n)=nr^{n-1}\bold{\hat{r}}}[/tex]

Ao for a maraging steel (82 M Nm-, C= 0.15 10-11, m-41) is equal to 58.2*10^-6m, and for a medium-strength steel, it is 40.6*10^-6m (50 MN m1, C0.24x 10-", m 3.3). The second case can be more tolerant.

Ultra-high-strength steel alloys, or maraging steels, are a unique class of low-carbon steel that have comparable ductility while being stronger and tougher than most other steels. A structure's capacity to safely withstand  until repair can be made is known as damage tolerance. Based on the presumption that defects can exist in any building and that these problems spread with use, the approach to engineering design that takes damage tolerance into account.

9125 is equal to 2/c(1/stress)*pi1/2(2-m) (Afinal - A)

Ao = 58.2*10^-6m

9125 is equal to 2/c(1/stress)*pi1/2(2-m) (Afinal - Ao)

comparable to case two

Ao = 40.6*10^-6m

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The supply's output must have some sort of switching converter and must be electrically insulated from the source. Throughout the whole range of input voltages and frequencies, the system is to apply a feedback control to ensure proper output voltage.

Voltage, also referred to as electric tension, electric pressure, or (electric) potential difference, is the difference in electric potential between two places. It is equivalent to the labor required to transfer a test charge between two places in a static electric field. The derived unit for voltage in the metric system is referred to as a volt. One volt equals one joule (of work) for one coulomb, which is how to work per unit charge is defined in SI units (of charge). Power and current were employed in the earlier SI definition for the volt; starting in 1990, the quantum Hall and Josephson effect was applied; and most recently (as of 2019), fundamental physical constants were added to the definitions of all SI units and their derivative units.

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In a two-slit interference and diffraction experiment, the fifth interference maximum and the first diffraction minimum can occur at the same angle relative to the center of the screen under certain conditions.

In a diffraction experiment, light waves passing through the two slits can also diffract and spread out, producing a pattern of bright and dark fringes on the screen. The position of the dark fringes, also known as diffraction minima, is determined by the wavelength of the light and the size of the slits.

If the fifth interference maximum and the first diffraction minimum occur at the same angle relative to the center of the screen, it means that the path difference between the waves passing through the two slits is equal to the wavelength of the light. This can be achieved by adjusting the separation between the slits, the distance between the slits and the screen, and the wavelength of the light.

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Answer: 22.63 m/s

Explanation:

Not sure if this is the right answer.

[tex]\frac{1}{2} m(v)^2=2(\frac{1}{2} m(16)^2 )[/tex]

[tex]\frac{1}{2} (v)^2=(16)^2[/tex]

[tex]v = 22.63 \frac{m}{s}[/tex]

The required length and compressed length of the spring at the given force values are 13 cm and 8 cm respectively.

Explanation:

F = ke

k = spring constant ;

e = extension;

e = (Final length - Initial length)

Initial length, l = 10

Final length = L1 = 11

F = k(11 - 10)

F = k;

Length for a restoring force of 3F ;

3F = k(Final length - Initial length)

k = F

3F = F(L1 - 10)

3F = - 10F + F(L1)

F(L1) = 3F + 10F

F(L1) = 13F

L1 = 13

Hence, required length ls 13 cm

B.)

Let compressed length = c

2F = F(initial length - compressed length)

2F = F(10 - c)

2F = 10F - F(c)

F(c) = 10F - 2F

F(c) = 8F

c = 8F / F

c = 8 cm

Therefore, the required compressed length ls 8 cm

Spring:

A spring is an elastic body that stores mechanical energy. Coil springs are often used in daily life, but there are many different types of springs. Modern quills are usually made of spring steel, but non-metallic items like bows are also quills.

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The term which is called as mechanical weathering always refers to the changes in a rock which are physical and there is no or very little chemical change. So, it's True.

Mechanical weathering (additionally known as bodily weathering) breaks rock into smaller portions. These smaller portions are similar to the larger rock, simply smaller. That means the rock has modified bodily with out converting its composition. Mechanical weathering is likewise called bodily weathering. In this kind of weathering, a huge rock is disintegrated into smaller portions of rocks.

When rocks crumble or split with out experiencing any alternate of their chemical composition, it's far called mechanical weathering. The assertion approximately mechanical weathering that isn't genuine is includes a chief alternate withinside the mineral composition of the weathered material. Mechanical weathering breaks rocks down into smaller fragments, and will increase the floor location of the over all material. By growing the floor location, chemical strategies may also act extra without problems upon the rock floor.

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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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The acceleration versus time graphs are the mathematical representation of the variation of acceleration with time.

There are several methods of representing the variation of two quantities one such method is graphs.

When the variation of the acceleration of the object and the time taken by the object to reach at acceleration are plotted on a graph the provides us with a few certain quantities.

For an example the slope of the acceleration-time graph tell us about the sudden change in acceleration at that particular instant.

Also the area under the acceleration vs. time graph represents the change in velocity of the object.

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The two planets are similar in size, inclination, structure, composition, and the presence of water on their surfaces. They also have many key differences.

While Earth has 23h 56m and 4 s period of rotation, Mars's period of rotation is about 24 hours and 40 minutes. Mars is inclined on its axis, similar to Earth., It is inclined at 25.19° to its orbital plane.

They are both terrestrial planets. This means that both have a dense metallic core and also an overlying mantle and crust, which is composed of less dense materials (like silicate rock).

Mars also has a surface covered by a mountain range. Ice water exists beneath much of the Martian surface. Radar data and soil samples have confirmed the presence of shallow subsurface water at the middle latitudes as well.

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a)When the metal ball leaves the tray, the tray will be 10.78 cm above point A.

b) The total time between the system being released at point A and the ball leaving the tray is 0.086 seconds.

c) The speed of the ball as it exits the tray is 1.175 m/s.

Given,

Mass of tray , m_t=1.90 kg

spring of force constant, k = 200N/m

mass of the ball, m_b = 300 g

Height below the equilibrium point A = 16.4 cm

a)

The tray's height above point A when the metal ball leaves it- The total mass of the tray and ball is 2.2 kg (1.90kg+0.3 kg). The spring force is equal to the product of the spring constant and displacement.Thus,

f=kx

but we know that, f=mg

equating both the equations

[tex]mg=kx\\\\2.2*9.8=200*x\\\\21.56=200x\\\\x=\frac{21.56}{200}\\\\x=0.1078 m=10.78 cm[/tex]

As a result, the tray is pushed down 17.4 cm below its equilibrium point (point A) and released from rest. Thus, the tray's position above point A is h=16.4+10.78=27.18 cm.

b)

The total amount of time that passes between releasing the system at point A and the ball leaving the tray.

The formula for the simple harmonic function of a spring is as follows:

[tex]y=Acos(\sqrt{\frac{k}{m}}-\phi)[/tex]

Here,

y= displacement = 10.78 cm

A=amplitude i.e 16.4 cm

k= spring constant = 200 N/m

m= total mass = 2.2 kg

and [tex]\phi = 0 \degree[/tex]

[tex]10.78=16.4cos(\sqrt{\frac{200}{2.2}}t-0)\\\\\frac{10.78}{16.4}=cos(\sqrt{90.909}t)\\\\0.657=cos(9.534t)\\\\cos^{-1}(0.657)=9.5434t\\\\0.829=9.543 t\\t=\frac{0.829}{9.543}\\\\t=0.086 s[/tex]

c)

The speed at which the ball moves as it exits the tray

The total mechanical energy for simple harmonic motion of a spring can be given as,Here, take the distance measurements in meters

[tex]\frac{1}{2}mv_y^2+\frac{1}{2}ky^2=\frac{1}{2}kA^2\\\\v_y^2=k\frac{A^2-y^2}{m}\\\\v_y^2=200*\frac{0.164^2-0.1078^2}{2.2}\\\\v_y^2=90.909(0.0268-0.0116)\\\\v_y^2=1.38\\\\v_y=1.175 m/s[/tex]

Thus, the speed of ball is 1.175 m/s

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the apex half-angle of the cone is  [tex]\frac{V^{2} }{g}[/tex]

Calculation :

Ncosθ = mg   ---1

Nsinθ =[tex]\frac{mv^{2} }{r}[/tex]

divide eqn 1 and 2

tanθ = V²/rg ---3

now tan θ = h/r ---4

fro eqn 3 and 4

h=  [tex]\frac{V^{2} }{g}[/tex]

A cone is a three-dimensional geometric shape that tapers from a flat base (often not necessarily circular) to a point called the vertex or apex.

A cone is formed by a series of line segments, half-lines, or lines that connect a point (vertex) common to all points on the base in a plane that does not contain vertices. Depending on the author, the basis may be restricted to a circle, a one-dimensional square in the plane, a closed his one-dimensional figure, or any of the above plus all enclosed points. A cone is a solid object if the base contains the enclosed points. Otherwise, it is a 2D object in 3D space. For solids, the boundaries formed by these lines or partial lines are called faces. If the sides are unlimited, it is a conical surface.

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The physical quantity that does the slope of the v2/2 v/s h graph represent is the slope-g. The slope is representing the change in v over the change in time.

By definition, that is the acceleration. Also extra than only a gimmick, it is geometry's manner of displaying us how variables now no longer most effective relate to 1 another, however how they are able to constitute the fee of alteration among the variables.

The slope of the displacement time graph offers us the bodily amount called pace. The slope of a pace graph represents an object's acceleration. As a result, the cost of the slope at a given time represents the object's acceleration at that time. The fee of changing of an object's pace with admire to time is described as acceleration.

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= [ 4 (C-H) + 1 (C=C) + 1 (X2) ] - [ 2 (C-X) + 1 + (C-C) + 4 (C-H)

= [ (C=C) +(X2) ] - [ 2 (C-X) + 1 (C-C) ]

= [ 604 +151.9 ] - [ 2 (276.3) + (338)]

= -134.7 KJ

= -135 KJ

Bond energies depend on the number of bonds between atoms. Even though π bonds are weaker than σ bonds, a double bond, which consists of a σ and π is bond, is stronger than a single bond because there are  bonds.

A quantity of strength, equal to the distinction among the energies of the Bond energies depend on the number of bonds between atoms. Atoms and the energies of the separated atoms, is released, usually as warmness. that is, the bonded atoms have a lower strength than the character atoms do.

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The time taken should be 0.399 ns.

What is the refractive index?

The refractive index is the measure of bending of a light ray when passing from one medium to another. It can also be defined as the ratio of the velocity of a light ray in an empty space to the velocity of light in a substance, n = c/v.

We know that

Time  taken = Thickness of the layer / speed of the light

Also,

v = speed of sound/refractive index.

Now

T1  = 0.05*1.46/3*10^8 = 2.43*10^-10 s

t2 = 0.01*1.5/3*10^8 = 5*10^-11 s

t3 = 0.02*1.59/3*10^8 = 1.06*10^-10 s

So,

total time is

=  2.43*10^-10 + 5*10^-11 + 1.06*10^-10 = 0.399*10^-9 s

= 0.399 ns

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The wavelength λ of the laser is 632.8 nm and the index of refraction for this mystery fluid is 1.329.

Refraction can change the wavelength of light or sound as it travels through a medium with a density greater than that of air. The wavelength reduces as a result of the wave's decreasing speed as it moves through the denser medium. If the wave travels faster when in a rarer medium, the wavelength rises. Because the speed and, consequently, the wavelength of the wave are lowered while traveling through the denser media, the index of refraction is greater for the denser medium than the rarer one.

An interferometer is a device that employs the interference phenomena to calculate the wavelength of light in terms of a standard length or the distance in terms of the wavelength of light that is already known. Through partial reflection and transmission, light from an extended source is split into two halves. The two directions in which these two beams are transmitted are at right angles to one another. They are noticed and studied as interference fringes that are created when they are reflected off the mirror.The angle between mirrors M1 and M2 determines how the fringes in the Michelson interferometer are shaped. Let S' be the replica of the source S, and let M2 be the virtual replica of mirror M1.Let D represent the distance between the mirror M1 and its virtual counterpart, M2'. As a result, the air film that is enclosed between M1 and M2' is what will cause the interference pattern to appear. Let S1' and S2' represent the respective Saras M1 and M2's photos.As a result of the amplitude division process, we are able to produce two coherent sources, S1' and S2'.

A)

2D = nλ

2 x 0.03164 x 10^-3 = 100 x λ

Wavelength, λ = 632.8 nm

B)

2D = n λ

2 x 0.02381 x 10^-3 = 100 λ

Wavelength,λ = 476.2 nm

Refractive index =λ₁/λ₂

Thus,

Refractive index = 632.8/476.2 = 1.329

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Answer:When a rocket is fired horizontally at 50 m/s and breaks into two equal masses, m1 and m2, the velocities of the two masses at the moment of separation can be determined using the principles of conservation of momentum and conservation of kinetic energy.

According to the principle of conservation of momentum, the total momentum of an isolated system remains constant, unless an external force is applied. This means that the total momentum of the two masses before and after the separation must be the same. Since the two masses are equal and the initial velocity of the rocket is 50 m/s, the total initial momentum of the system is 50 m/s x 2 masses = 100 m/s.

After the separation, the momentum of m1 is equal to the initial momentum of the system, since the direction of motion has not changed. This means that the velocity of m1 is 50 m/s.

The momentum of m2, however, has changed due to the deflection of 60ᴼ below the horizontal. The direction of motion of m2 is now perpendicular to the initial direction of the rocket, and the magnitude of the momentum is equal to the initial momentum of the system. Using the law of cosines, we can determine the magnitude of the velocity of m2 as follows:

v2 = (100 m/s) / (cos 60ᴼ)

v2 = 50 m/s

Therefore, the velocities of m1 and m2 at the moment of separation are 50 m/s and 50 m/s, respectively.

Explanation:

The time of flight is 2.44 seconds.

We know that third equation of motion is  [tex]S = ut + \frac{1}{2} at^{2}[/tex] where,

S = distance = 29.3 m

u = initial speed

t  = time

a = acceleration = 9.8 [tex]m/s^{2}[/tex]

In this case, the ball is fired horizontally, so vertical initial velocity is 0.

i.e. u = 0

Putting these values in above equation, we get

      29.3 = 0 + [tex]\frac{1}{2} (9.8)t^{2}[/tex]

  ⇒ t = 2.44 seconds

So the time of flight is 2.44 seconds.

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The Gravitational potential energy depends on mass , acceleration and path and potential also as G=V/m.

a).  As you can imagine, gravitational energy is the energy associated with gravity. This is the potential energy stored due to an object being in a higher position compared to a lower position. (e.g. far from the ground or close to the ground).

Gravitational energy is the energy associated with gravity.

b). Systems can increase their gravitational energy as their mass moves away from the center of the Earth and away from other bodies (such as the sun, planets, and stars) large enough to generate a large amount of gravity. there is.

Potential energy can be defined as the amount of work expended to lift an object from the ground to its current height. In another sense, this is the amount of work the body does before returning to ground level (the position of maximum stability) when translated from its current level. Therefore, potential energy can be related to work.

c). A negative sign indicates that gravity is doing positive work as the mass approaches. A negative potential indicates a bonding state. That is, when mass is placed under its influence, it becomes trapped in its potential, and if something can provide the energy to escape the clutches of gravity, it must not escape.

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The force applied due to friction is 32.2 N.

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact.

Coefficient of friction, ratio of the frictional force resisting the motion of two surfaces in contact to the normal force pressing the two surfaces together. It is usually symbolized by the Greek letter mu (μ). Mathematically, μ = F/N, where F is the frictional force and N is the normal force.

To solve for the minimum force, let us assume it to be F (N)

So

F=mg sin A

But

=>>>> coefficient of static friction x (F + mg cos A

=>3 x 9.8 x sin35 = 0.3 x (F + 3 x 9.8 x cos35)

So making F subject of formula

F + 24.0 = 56.2

F = 32.2N

Therefore, the force applied due to friction is 32.2 N.

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Thrust, drag, lift, and weight is the forces that act on all aircraft in flight.

Thrust is the forward force produced by the propulsion unit/propeller or rotor.

Drag is the backward force caused by the disturbance of airflow by the wing, rotor, fuselage, and other objects.

When the plane is flying at a constant height, the force of thrust must equal the opposite force of drag, then only the airplane can experience uniform motion in one direction.

All four forces act on an airplane must equate to each other for an airplane to fly straight and level at a constant speed, the lift it creates balances its weight, and the thrust it creates balances its drag.

An unbalanced force changes the equilibrium state of a body. As with an aircraft cruising in level flight, the weight of the aircraft will equally lift and thrust will equal drag. So, the plane experiences a balanced force.

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Speed of the spacecraft right before the collision:[tex]\sqrt{} \frac{2G.Me}{Re}[/tex] .

Assumption: the earth is exactly spherical with a uniform density.

This question could be solved using the conservation of energy.

The mechanical energy of this spacecraft is the sum of:

the kinetic energy of this spacecraft, and

the (gravitational) potential energy of this spacecraft.

[tex]GPE=\frac{G.Me.M}{R}[/tex]

[tex]\sqrt{} \frac{2KE}{M}[/tex]=[tex]\sqrt{\frac{2G.Me}{Re} }[/tex]

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.

The floor's force on the block, measured in terms of its vertical component, is expressed as follows: mg- t sin theta

The resistive friction force (Fr) multiplied by the normal or horizontal force (N) forcing the objects together yields the coefficient of friction (fr), which is a numerical value. It can be represented by the equation fr = Fr/N.

A push or pull that an object experiences as a result of interacting with another item is known as a force. Every time two items interact, a force is exerted on each of the things. Newton(N) F=ma stands for the Si system of force.

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