An object of an unknown mass is attached to an ideal spring with force constant 120 N/m and is found to vibrate with a frequency of 6.00 Hz.
Find:
(a) the period
(b) the angular frequency
(c) the mass of this object.

A horizontal ideal spring with a spring constant of k is linked to a mass m object that is at rest on a frictionless surface. By lowering m, the system's oscillation frequency can be raised.

What is an example of frequency?

The number of times that a specific data value occurs is its frequency. A data value's frequency is represented by the letter f. In the event that five students achieve The grade A was said to have a frequency of five, much like in science.

What does frequency serve to accomplish?

The frequency, a crucial factor in science and engineering, describes the temporal rate of change observed in oscillatory and periodic phenomena, including mechanical vibrations, audio signals (sound), radio waves, and light.

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The molar mass of the gas is

43.008 g/mol

Avogadro stated that "Equal volumes of all gases at the same temperature and pressure contain the same number of molecules". Hence at standard temperature and pressure 1 mole of a gas occupies 22.4 liters of volume.

1 mol = 22.4 liters

Given a gas with 1 L and mass of 1.92 g at STP

Number of moles = 1 L / (22.4 L/mol) = 0.0446 mol

The molar mass = mass of gas / number of moles

molar mass = 1.92 g / 0.0446 mol

molar mass = 43.008 g/mol

Hence, molar mass of the gas is

43.008 g/mol

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The energy absorbed by Hydrogen atom to transit an electron from n = 3 to n = 6 is 1.815x10-19 Joules

Energy Level: According to the Bohr atomic model, energy levels—also known as electron shells—are thought of as the orbits that electrons in an atom's nucleus take. Electrons must always be in one of the energy levels and never in the space between them since the energy levels represent defined distances.

According to the given information

Change in energy = [tex]-13.6eV \frac{1}{n_{f} ^{2} }-\frac{1}{n_{i} ^{2} }[/tex]

                              = -13.6 × 1.6 × [tex]10^{-19}[/tex] ( [tex]\frac{1}{6^{2} }[/tex] - [tex]\frac{1}{3^{2} }[/tex] )

                              = 21.76 × [tex]10^{-19}[/tex] × 0.084

                              = 1.815 × [tex]10^{-19}[/tex] J

Change in Energy level = 1.815 × [tex]10^{-19}[/tex] J

The energy absorbed by Hydrogen atom to transit an electron from n = 3 to n = 6 is 1.815x10-19 Joules

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The reading of the scale due to the two masses, massless string and the frictionless pullies is 0.

When the strings have frictionless pullies, they perform a rotary motion with the pulleys.

Net force of the masses

The two masses are connected by massless spring.

Since the masses are at rest, the sum of all the forces acting on the scale will be zero.

Fnet = o

T + M1g - M2g = 0

M1 and M2 are the masses at rest respectively.

T = M2g - M1g

Reading on the scale

Since the two given masses have same mass then their product with 'g' is  and their difference is zero.

The reading of the scale is equal to the tension in the pulley connecting the two masses.

The tension on the pulley is calculated as follows;

T = Mg - Mg

T = 0

Thus, the reading of the scale due to the given masses is 0.

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The chain supporting the basket is at a 45° angle to the vertical and horizontal component is 1244.6N.

When an object's speed stays the same and neither increases nor decreases, we say it is moving at a constant speed.

Mass of the person is 82kg and mass of the basket is 45 kg.

New total mass, M = 82+45 = 127kg.

Here, Fe is centrifugal force

v is velocity of the person

r is radius of the circle,

r = 7.1m

Now, Tsin 45° = Mg [ here Mg is weight of person and basket]

T = Mg/sin 45° = Mg√2

Now, vertical component of the tension,

Fy = Tsin 45° = Mg = (127×9.8)kg-m/s²

Fy = 1244.6N

Now, horizontal component,

Fx = Tcos 45°

Fx = Mg/Tan 45°

Fx = Mg/1

Fx = 1244.6N

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Diffuse dome lighting method has a light source placed inside the surface of a partially reflective dome, with the camera focused on the object through a hole in the middle.

What is Diffuse dome lighting?

Machine vision dome lights, commonly referred to as "cloudy-day illumination," produce diffuse lighting. Reflected light offers gentle, shadow-free lighting that is non-directional and non-directional. At close working distances, this effect is ideal for scrutinizing highly specular, curving objects.

The CCD stands for a Charge Coupled Device, which is a semiconductor element that converts images into digital signals.

Cameras are used by machine vision to collect visual data from the surroundings. It then prepares the data for usage in various applications by processing the photos using a mix of hardware and software. Specialized optics are frequently used in machine vision technologies to capture pictures.

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A toggle clamp is a tool that you use to firmly secure components or pieces in place, frequently but not always as part of a production process.

A toggle clamp is a device that you employ, often but not exclusively as part of a production process, to firmly place components or parts in place. A toggle clamp's main characteristics are its rapid action and ability to be easily turned on and off by an operator.

Toggle clamps also lock in place firmly. Because of this, toggle clamps are frequently employed in production lines where components need to be held firmly and quickly removed during routine manufacturing procedures.

Toggle clamps come in six primary categories: vertical toggle clamps, horizontal toggle clamps, plunger toggle clamps (also known as push action toggle clamps), hook action toggle clamps, plier action toggle clamps, and cam action toggle clamps.

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The sun rotates in the counterclockwise direction when viewed from above the North Pole of the Sun.

The Sun rotates on its axis approximately once in 27 days. This rotation was first discovered by observing the motion of the Sun. The Sun's axis of rotation is tilted by about 7.25 degrees from the axis of Earth's orbit, so we see most of the Sun's north pole in September and most of its south pole in March each year. The Sun's "surface" that is visible, up to the photosphere. The powerful magnetic fields in the vicinity of sunspots produce active regions on the Sun that often generate disturbances such as solar flares and coronal mass ejections (CMEs). Because they are colder than their surroundings, sunspots seem "black.". The average number of spots on the face of the Sun is not constant, but varies over a multi-year cycle.

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The mohorovicic discontinuity is the Boundary where the crust gives way to the mantle

What is Mohorovicic discontinuity ?

The line separating the Earth's crust and mantle is known as the Moho discontinuity. Because it was found by a Croatian scientist named Andreaja Mohorovicic, it retains that name. Within the (lithospheric) plate, this boundary denotes a change in seismic wave velocity from the crust to the uppermost mantle. The surface that separates the earth's crust from its mantle, located roughly 24 to 30 miles (40 to 50 km) below the continents and 6-7 miles (10 to 12 km) below the ocean floor.

According to the above definition

We get to know that

The mohorovicic discontinuity is the Boundary where the crust gives way to the mantle

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The original mass of the sample was 14.79 grams.

We know that rate of reaction of first order reactions is given by: [tex]kt = 2.303* log(R'/R)[/tex]

where k = rate of reaction = 0.0198

           t = time = 98.3 days

           R = final mass = 2.14 grams

Putting these values in above equation we get R' = 14.79 grams.

i.e. The original mass of the sample was 14.79 grams.

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A one corresponds to the greatest magnitude of acceleration of the particle.

What is acceleration?

Any procedure where the velocity varies is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.

The graph given is of Kinetic energy rs position. Kinetic energy [tex]$K \cdot[/tex] [tex]E=\frac{1}{2} m v^2$[/tex]. Since mass ' m ' is Constant we can write K.E [tex]$\propto v^2$[/tex]

So when kinetic energy is maximum, speed is maximum. when kinetic energy is changing/increasing at maximum rate implies speed is also increasing at maximum rate implies acceleration is maximum. So when acceleration of the particle is zero, slope is zero. ie rate of change of kinetic energy is zero. So the answers ave:

1) Acceleration zero: B, D, F & H.

2) A, E, G; out of these 3 points, at[tex]$A^{\prime}$[/tex] the slope is maximum.

[tex]$\Rightarrow$[/tex]At 'A', acceleration is maximum.

3) Maximum[tex]$K \cdot E \Rightarrow$[/tex] highest point : 'B' Corresponds to highest K.E.

4) Lowest speed corresponds to lowest kinetic energy. [tex]$\Rightarrow$[/tex] ' D '

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____________________________________________________

We are given the following:

Given the formula for finding acceleration, we fill in the blanks.

[tex]A=14.35*13.29[/tex]

[tex]A=190.7115=190.7[/tex] ← Acceleration/Final Solution

_____________________________________________________

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The current in the circuit with the coil is greater than the current in the circuit with the uncoiled wire

Electric current is the flow of electric charge in a circuit.

Since a long wire of finite resistance is connected to an ac generator, in this circuit, we know that the length of wire has a resistance and will draw a current from the generator.

Now, the wire is then wound into a coil of many loops and reconnected to the generator, the wire now has an inductance. In this circuit, the inductance of the wire causes it to draw extra current apart from that drawn by the resistance of the wire.

So, since it draws extra current, thus, the current in the circuit increases when the long finite wire is wound into a coil of many loops.

So, the current with the coil is greater than the current in the circuit with the uncoiled wire

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Answer: 80 mph

Explanation:

The speed of visible light waves when travelling through a vacuum is about 3 X 10⁸ m/s.

What is electromagnetic waves?

In terms of science, electromagnetic radiation is made up of electromagnetic field waves that travel over space while carrying radiant electromagnetic energy. It consists of X-rays, gamma rays, microwaves, infrared, light, and radio waves. These waves are all a component of the electromagnetic spectrum.

The speed of electromagnetic waves, which includes visible light, radio light and x-rays is 3 X 10⁸ m/s. This is same as that of the speed of visible light in the presence of air.

The speed of light is depicted using the letter 'c', and it a universal constant value. It is a physical constant and important in many areas of physics.

The speed of light in water is 2.25 X 10⁸ m/s and that in glass is 2 X 10⁸ m/s. The speed varies with respect to the medium.

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The box accelerates down the incline at 2.4m/s^2.

A mass m particle will slide down a smooth inclined plane if it is released onto it with a friction force F=0. We resolve in the direction of motion to determine the particle's acceleration as it slides. F = ma, mg cos(90) = ma, gg cos(90) = a, gg sin() = a.

By using zigmaFx = max, we will determine the acceleration.

However, we must first determine the friction force Ff.

Because cos 30 degree = 0.866 and Fy = ma y = 0 result in FN - 0.87mg = 0, we may calculate FN as (0.87)(20Kg)(9.81 m/s2) = 171N.

From Ff = mue FN = 0.30)(171 N)= 51N, we can now calculate Ff.

We get Ff - 0.50mg = ma x 51N - (0.50)(20)(9.81)N = (20kg)(ax) from the expression zigmaFx = max, where ax = -2.35 m/s2.

At 2.4 m/s2, the box quickens its descent of the hill.

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That seems relatively fast to me. Wave speed is typically between 160 to 320 km/h, so the 4.5 hours it would take for these waves to travel from the buoy to the coastline is in line with the expected wave speed.

What is Wave?
A wave is a spreading dynamic disturbance (transition from equilibrium) with one or even more quantities in physics, mathematics, as well as related fields. When a wave is periodic, its constituent parts repeatedly oscillate around an equilibrium (resting) valuation at a given frequency. A travelling wave is defined as one in which the a whole waveform moves inside one direction; in contrast, a standing wave is defined as a pair of superimposed promotes the flow moving in the opposite directions. In a standing wave, the vibration's amplitude nulls out at certain locations where the wave's amplitude appears smaller and even zero. Wave equations, which are standing wave fields of two opposing waves, or one-way wave equations, which describe the propagation of a single wave in a specific direction, are frequently used to describe waves.

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A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal. Its speed while rolling down is 3.0 m/s.

The mass of the solid cylinder, [tex]m=5.25 kg[/tex]

The inclination of the plane, θ=[tex]18^{0}[/tex]

The speed of a solid cylinder rolling down an inclined surface is calculated using the following formula:

The kinetic energy of the cylinder

[tex]K=3/5 mgh[/tex]

[tex]1/2mv^{2} =3/5 mgh[/tex]

[tex]v=\sqrt{6gh/5}[/tex]

Substituting for the values h as [tex]h=mgcos[/tex]θ

we get the speed as

[tex]v=3.0 m/s[/tex]

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The amount of work that the engine of the spacecraft must do to move above the circular orbit is 1.48 x 10⁻¹⁷ mM (Joules).

The established fact that the gravitational attraction between two objects varies also on square of their distance leads to the geometry of planetary orbits. The attractive product of two items decreases to a fourth of its initial amount when the distance between them is doubled.

W = Fd

where;

F is the spacecraft's gravitational field,

d is the displacement of the spacecraft.

The spacecraft's gravitational pull is specified as;

F = GmM/R²

where;

m is the planet's mass (for the circular orbit)

M is the spacecraft's mass.

R is the spacecraft's displacement.

The tasks that the spacecraft must complete are as follows:

W = FR

W = GmM/R² x R

W = GmM/R

W = (6.67 x 10⁻¹¹ x mM) / (4500000)

W = 1.48 x 10⁻¹⁷ mM (Joules)

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The statement predicts magnetic flux toward being 37.82*10⁻⁷ Wb, 131.73*10⁻⁷ Wb and 131.73*10⁻⁷ Wb

It typically sits between the engine and the ignition module of your car. When the automobile key is turned, solenoids (also known as start solenoids or starter relay) operate by combining big electric pulses from your vehicle's charge with smaller electrical impulses from ignition system.

(a). Flux is given by

Ф= BACosФ

μ₀ηIL² cos0

= 4*π*10⁻⁷*1370*3.11*0.0275²

=  37.82*10⁻⁷ Wb

(b). Here diameter and length are equal

Ф = BACosФ

    = μ₀ηI(π(L/2)²)cos 0

    = 4*π*10⁻⁷*1370*3.11*3.14*(0.028)²

    = 131.73*10⁻⁷ Wb

(c). Here as length is greater than diameter the flux will be same as flux    on solenoid        

Ф = 131.73*10⁻⁷ Wb

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The complete question is-

A single-turn square loop of side L is centered on the axis of a long solenoid. In addition, the plane of the square loop is perpendicular to the axis of the solenoid. The solenoid has 1370 turns per meter and a diameter of 7.70 cm, and carries a current of 5.11 A.

Part A: Find the magnetic flux through the loop when L= 2.75 cm .

Part B: Find the magnetic flux through the loop when L= 5.60 cm .

Part C: Find the magnetic flux through the loop when L= 13.5 cm .

Their speed after collision is 2.5.

What is the reason for this?

An ice skater with a mass of 50 kg is moving at a speed of 6m/s.

The ice skater with 50 kg mass collides with a second stationary skater whose mass is 70 kg.

These skaters cling together after the collision and they also move without friction.

Their speed after the collision would be as follows:

Formula: mv = mv

from above information, we know that

Mass of first skater is m= 50 kg

Speed of first skater v= 6m/s

Mass of second skater is m= 70 kg

Speed after collision v=?

mv = mv

50 x 6 = (50 + 70) v

v = 50 x 6 / 120 = 2.5

So therefore, their speed after collision would be 2.5.

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Hence there exist no solution for such angular position, in other words there is no fourth order maximum fringe.

The distance between the two consecutive peaks or troughs of a wave is known as its wavelength. It is calculated in the wave's direction.

The angular position of the bright fringes in the double slit interference is given by the following relation

[tex]m\lambda=d\sin\funcapply\left(\theta_m\right)[/tex]

Where,

m: Is the dazzling fringe's order, m.

[tex]\lambda :[/tex]580-nm (Is the wavelength of the incident light on the double slit.)

d: 0.100mm (Is the distance between the centers of the two slits.)

[tex]\theta_m:[/tex] is the angle at which the mth fringe is located.

[tex]\begin{aligned}\theta_4 & =\sin ^{-1}\left(\frac{4 \lambda}{d}\right) \\& =\sin ^{-1}\left(\frac{4 \times 580 \times 10^{-9}}{1.00 \times 10^{-4}}\right)\end{aligned}[/tex]

    [tex]=\sin ^{-1}(0.02)\\=1.14[/tex]

Where, the sine function can never have a value greater than 1 , hence there exist no solution for such angular position

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The force of gravity acting on the column of water is 1,02,900 N.

Given that, height of the liquid column is 7

Area = 1.5 m²

We know that, volume of water = 1.5* 7 = 10.5 m³

10.5 m³ when converted into litres can be written as 10,500 litres

Water mass = 10,500 litres * (1kg/litre) = 10,500 kg

Force of gravity on water is nothing but weight of the water

⇒ 10,500* 9.8 = 1,02,900 N

Pressure on the bottom of the tank = 1,02,900/1.5 = 68,600 N/m² = 68,600 pascal

Thus, the force of gravity acting on the column of water is calculated to be 1,02,900 N.

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The ball was moving at 11.1 m/s in the horizontal direction just before it hit the ground.

What is horizontal direction?
Horizontal direction is a term used to describe a direction parallel to the horizon. It is an important concept in navigation and surveying, since it helps to determine a person's geographic location. Horizontal direction is usually expressed as an angle, measured clockwise from the direction of true north. It is important to remember that the angle for horizontal direction increases as the person turns clockwise from true north. For example, if a person were facing north, their horizontal direction would be 0°. If they were facing northeast, their horizontal direction would be 45°. In addition to its use in navigation, horizontal direction is also used in architecture and engineering. For example, when designing a building, architects use horizontal direction to determine which way the building should face in order to maximize the amount of natural light that enters the building.

We can use the equation vf^2=vi^2 + 2ad, where vf is the final velocity, vi is the initial velocity, a is the acceleration due to gravity (9.8 m/s^2) and d is the displacement.
In this case, vf = 0 m/s (since the ball has stopped moving at the end of its fall), vi = unknown, a = 9.8 m/s^2, and d = 3.32 m.
We can rearrange this equation to solve for vi: vi = sqrt(vf^2 - 2ad)
vi = sqrt(0^2 - 2(9.8)(9.47)) = -11.1 m/s
Since the velocity is negative, it is moving in the opposite direction of the displacement. Therefore, the ball was moving at 11.1 m/s in the horizontal direction just before it hit the ground.

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a) Displacement current density  for the capacitor is  113.4 A/m²

b) Rate of change of the electric field is   1.48157826 V/m.s

c) Magnetic field between plates at r of 1.93 cm  is  5.563×10⁻6 Tesla

d) Magnetic field between plates at r of 1.10 cm is  7.833 x 10-7 Tesla

Since we are given the radius of a parallel-plate capacitor which is 4.00 cm( 0.04 m) and the Conduction current = Ic =  0.570 A .we know  the  formula for the Displacement current density is

JD = Id/A, where  Id is the conduction current and A is the area of the capacitor, and A= πr² = π(0.04)²= 0.005024 m². As we know  conduction current has equal displacement between the capacitor plates so  Id = Ic

JD = 0.570/0.005024  = 113.4 A/m²

For the second case, we know the  rate of change of the electric field is:

dE/dt = JD/ε₀ , where JD is the displacement current density and ε₀ is the permittivity of free space (  8.854×10⁻¹² C²/N.m²)

so, dE/dt = 113.4/8.854×10⁻¹² =1.48157826 V/m.s

for the third case, the formula for The induced magnetic field between the plates  will be :

B = (μ₀/2)*JD*r, μ₀ is the permeability of free space(4π×10⁻⁷ T.m/A)and r is the distance from the axis.

B = (4π×10⁻⁷/2)*113.4 *0.01953

B = 5.563× 10⁻⁶ Tesla ,and for the last case, for the radius of 1.10  cm (0.011 m)

B = (μ₀/2)*JD*r

B = (4π×10⁻⁷/2)*113.4 *0.011

B = 7.833 x 10⁻⁷ Tesla

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1.22 m below the surface of a swimming pool's bottom lies a little light fixture. The circumference of this circle is 2.27 m.

One of the fundamental and common symbols is light. It is the holy and the spiritual; it is wisdom and insight. Light is the wellspring of kindness and the true truth; according to Buddhist belief, it also follows transcendence into Nirvana.

The critical angle is found by imagining the refracted ray just grazing the surface (θ₂ = 90°). The index of refraction of water is n₁ = 1.333, and n₂ =1.00

for air, so n₁ sin∅​c = n₂ sin90° gives ∅c =sin⁻¹ (1/1.333)= sin⁻¹ (0.750)=48.6°

The radius then satisfies

tan∅c = r/1.00m

​So the diameter is

d=2[(1.00m)tan∅c]

d=(2.00m)tan48.6° = 2.27m

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​

The wavelength of the light is 6.21 × 10⁻⁷ m.

Single-slit diffraction has an equation

d sin θ = m λ

where

For a small angle, sin θ = tan θ.

θ is the angle where the opposite of the angle is the width apart near the center of the pattern (x) and the adjacent is the distance between the screen from the slits (L). So [tex]tan \: \theta = \frac{x}{L}[/tex]

d sin θ = m λ

d tan θ = m λ

[tex]d \: \frac{x}{L} \:=\: 1 \times \lambda[/tex]

[tex]\lambda \:=\: 4.4 \times 10^{- 5} \times \frac{8.9 \times 10^{- 2}}{6.3}[/tex]

λ = 4.4 × 10⁻⁵ × 1.41 × 10⁻²

λ = 6.21 × 10⁻⁷ m

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The mass of the star of the distant solar system is 82 * 10²² kg and the mass of the planet of the distant solar system is 8.58 * 10²⁵ kg

The planet stays in its orbit and moves in a centripetal motion due to the gravitational force of attraction between the planet and the star.

Fc = m v² / r

Fg = G M m / r²

Fc = Fg

m v² / r = G M m / r²

v² = G M / r

M = r v² / G

g = Acceleration due to gravity

G = Gravitational constant

M = Mass of star

r = Distance between both bodies

G = 6.67 * 10⁻¹¹ N m² / kg²

r = 8.6 * 10¹¹ m

T = 402 days = 3.47 * 10⁷ s

v = 2 π r / T

v = 2 * 3.14 * 8.6 * 10¹¹ / 3.47 * 10⁷

v = 15.56 * 10⁴ m / s

Ms = 8.6 * 10¹¹ * 15.56 * 10⁴ / ( 6.67 * 10⁻¹¹ )

Ms = 20.1 * 10²⁶ kg

F = G M m / r²

F = m g

Equating,

m g = G M m / r²

Mp = g r² / G

Mp = 63.6 * ( 1.8 * 10⁷ / 2 )² / 6.67 * 10⁻¹¹

Mp = 8.58 * 10²⁵ kg

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In surface waves, circular motion refers to particle motion. The particles that make up the majority of the medium are present in both transverse and longitudinal waves.

And travel both perpendicularly to the direction of the transported energy and parallel to it. Surface waves have particle motion that is neither longitudinal wave nor transverse waves. Motion is the phenomenon whereby an item shifts in relation to time. Motion is quantitatively characterized in terms of the body's change in position with respect to the observer's frame of reference as well as the velocity, acceleration, and speed of the body. Each material particle vibrates in a longitudinal wave about its usual rest position.

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The precept of the conservation of momentum dictates that because the stone enters the water and pushes a number of the water downwards, the stone is compelled upwards.

There are 3 unique axes in any delivery, known as longitudinal, transverse, and vertical axes. The movements around them are called the roll, pitch, and yaw respectively.in order for the boat to move, the force of the wind pushes at the sail and reasons the boat to move.

Start something shifting, deliver impetus to something, as in A press convention set the brand new assignment in motion. it is also put as set the wheels in motion, as in permit's set the wheels in motion for the brand new library wing. This idiom dates from approximately 1800.

The answer is C, the force is a result of the interaction between the oars and the water the boat is visiting. that is the force that actions the boat forward.

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