Calculate the wavelengths of the components of the first line of the Lyman series, taking the fine structure of the 2p level into account. (Give your answers to at least four decimal places. Use values hc = 1239.8 eV · nm and E1 = 13.606 eV.)
smaller value: ____ nm
larger value: ____ nm
I already asked this but received an incorrect answer.

The speed and direction of piece b is 11.33m/s positive x direction.

Total momentum = 0 (at rest)

Applying conservation of linear momentum,

Momentum after explosion = momentum before explosion

MaVa + MbVb + McVc = 0

100(-60) + 150Vb + 70(86) = 0

Vb = 11.33m/s

Speed of Vb = 11.33m/s

In Newtonian mechanics, momentum is the result of an object's mass and velocity, more precisely linear momentum or translational momentum. This mechanical quantity is typical. It has. a direction. and a magnitude., making. it a vector. quantity. The momentum of an item is expressed as: [tex]displaystyle mathbf p =m mathbf v.mathbfp = m mathbf v[/tex]  if m is the object's mass and v is its velocity (also a vector quantity).

The kilogram metre per second (kg m/s), which is a unit of measurement for momentum in the International System of Units (SI), is a unit of measurement for a newton-second.

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The mass of the crate when it is directed up the incline will be equal to 5.8 kg that is option C is correct.

This problem can be solved using the concept of Newton's second law of motion. The mathematical expression of this will be

F = ma

where F is the force, m is mass and a is the acceleration.

Now, net force will be expressed as

Fₙ = 40N - mg (sin 30°) = m(2 m/s²)

where 40 N is the force parallel to incline and mg (sin 30°) is the vertical component of force.

From this we solve for m as

m = 40/6.9

m = 5.8 kg

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The unstretched length of the spring is 3.333 m

Calculation :

k = Spring constant = 1.5 N/m

g = Acceleration due to gravity = 9.81 m/s²

l = Unstretched length

Frequency of SHM motion is given by

[tex]f_{s} = \frac{1}{2\pi }\sqrt{\frac{k}{m} }[/tex]

Frequency of pendulum is given by

[tex]f_{p} = \frac{1}{2\pi }\sqrt{\frac{g}{l} }[/tex]

Given in the question

[tex]f_{s} = \frac{1}{2\pi }\sqrt{\frac{k}{m} }[/tex]     =  [tex]f_{s} = \frac{1}{2\pi }\sqrt{\frac{g}{l} }[/tex]

[tex]\frac{1}{2\pi }\sqrt{\frac{k}{m} }= \frac{1}{2}\frac{1}{2\pi }\sqrt{\frac{k}{m} }[/tex]  

l = [tex]\frac{4gm}{k}[/tex]

l = [tex]\frac{4*9.8*\frac{1.2}{9.8} }{1.44}[/tex]

l = 3.333 m

The unstretched length of the spring is 3.333 m

The word "force" has a precise meaning. At this level it is appropriate to describe the force as pushing or pulling. A force does not contain or "have within" an object. A force is applied from one object to another. The concept of force is not limited to living things and inanimate things

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Assumptions scientists make include:

a nature can be understood through systematic study.

All scientists make essential assumptions. One is determinism—the idea that every one events inside the universe, such as conduct, are lawful or orderly. the second one assumption is this lawfulness is discoverable.

Technological know-how operates on the assumptions that herbal reasons give an explanation for herbal phenomena, that evidence from the herbal world can inform us approximately the ones causes, and that these reasons are constant.

A hypothesis is an assumption, an concept this is proposed for the sake of argument so that it may be examined to look if it might be authentic. in the medical technique, the speculation is constructed earlier than any applicable research has been done, other than a fundamental historical past overview.

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The age of the object can be found using the equation   [tex]t=\frac{1}{k}ln\frac{[A_{0} ]}{[A]}[/tex].

The rate of decay:

In contrast to chemical reactions, the decay of a certain nucleus cannot be predicted and is unaffected by physical factors like temperature. There are two factors that affect the rate of isotope decay. The average number of undecayed nuclei in the system must double, as must the rate of decay for undecayed nuclei. the isotope's stability because some decay more quickly than others. The number of nuclei that decay per second is determined by the rate of decay.

The rate of the Decay is given as

                   [tex]\frac{-dA}{dt} =k[A][/tex]

On integrating the above we have

                 [tex]ln\frac{[A_{0} ]}{[A]}=kt[/tex]

                         [tex]t=\frac{1}{k}ln\frac{[A_{0} ]}{[A]}[/tex]

The number of nuclei has no bearing on the likelihood that a fixed nucleus would decay. Each nucleus has a predetermined likelihood of decaying in a certain length of time. The number of decaying nuclei will rise as the number of nuclei increases, but that is actually to be expected.

It's similar to rolling a large number of dice; the proportion of dice showing a particular digit to the total number of dice you roll. Keeping with this scenario, let's say you take away a dice if it displays 1. This is comparable to the disintegration of a nucleus. The number of dice eliminated will initially be large, but as the number of dice decreases, so will the number being removed.

The age of the object can be found using the equation:

                            [tex]\frac{-dA}{dt} =k[A][/tex]

                             [tex]t=\frac{1}{k}ln\frac{[A_{0} ]}{[A]}[/tex]

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The presence of a current in an ammeter depends on the state of an external electrical switch. If the switch is closed, there will be a current in the ammeter; if the switch is opened, there will be no current in the ammeter. The length of time the switch has been in a particular state does not affect the presence of a current in the ammeter.

The presence of a current in an ammeter depends on the state of an external electrical switch. A switch is a device used to break or make an electrical connection, and can be used to control the flow of electricity in a circuit. In the following cases, the presence of a current in the ammeter can be determined:

(1) If the switch has just been closed, there will be a current in the ammeter. When the switch is closed, it creates an electrical connection, allowing electricity to flow through the circuit, and thus a current to be registered on the ammeter.

(2) If the switch has been closed for a long time, there will still be a current in the ammeter. This is because the switch is still in the closed position, allowing electricity to flow through the circuit, and thus a current to be registered on the ammeter.

(3) If the switch has just been opened, there will be no current in the ammeter. When the switch is opened, it breaks the electrical connection, preventing electricity from flowing through the circuit, and thus no current will be registered on the ammeter.

(4) If the switch has been opened for a long time, there will still be no current in the ammeter. This is because the switch is still in the open position, preventing electricity from flowing through the circuit, and thus no current will be registered on the ammeter.

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Force is 436.59 N and the speed is 1.746 kN.

A) Force F = P*A = 0.5*rho*v^2*A = 0.5*1.2*10.5^2*6*1.1 = 436.59 N

B) If v is doubled then F increases by 4 times since F is proportional to the square of the speed.

then F2 = 4*436.59 = 1746.35 N = 1.746 kN

A body can change its condition of rest or motion through the application of force, which is an external agent. It has. both a magnitude. and. a direction. The application of force is the point at which force is applied, and the direction in which the force is applied is referred to as the direction of the force. If motion is conceivable, gravitational forces can separate phases of various densities. One option is widespread melting, but high temperatures are not anticipated for the early Earth (Chapter 2). Sorting as a result of deeply buried ices outgassing is a more likely explanation. Such processes would have altered the moment of inertia, necessitating a modification of angular velocity.

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(a)The angular velocity v(d)' is 0.936 m/s

(b)The velocity of the sphere is 3 rad/s

Let us assume that

angular velocity of member ABC is v(d)'

velocity of the sphere = ω'

Write the moment of inertia of the member ABC

I(G) = 1/12 ML²

I(G) = 1/12*(2.4)(0.75m)²

I(G) = 0.112 kgm²

After the impact

ω = ω'(ccw)

ν'(G) = (L/4)ω' (upwards)

ν'(A) = (L/4) ω' (downwards)

Take the moments about B

m(d)v(d)(L/4) + 0 = m(d)v'(d)(L/4) + I(G)ω' + Mv'(G)(L/4)

m(d)v(d)(L/4) = m(d)v'(d)(L/4) + I(G)ω' + M(L/4)²ω'

m(d)v(d)(L/4) = m(d)v'(d)(L/4) + ] I(G) + M(L/4)² ]ω'

(0.8)(3)(0.75/4) = (0.8)v'(d)(0.75/4) + [ 0.112 + (2.4)(0.75/4)²

0.45 = 0.15v(d)' + 0.1963ω' -------------------- (eq1)

From the coefficient of restitution,

v(d)' - v(A)' = -e [ v(d) - v(A) ]

v(d)' - (L/4)ω' = -(0.5) [3-0]

v(d)' - (0.75/4)ω' = - 1.5

v(d)' - 0.1875ω' = - 1.5 ---------------------- (eq 2)

From eq 1 and eq 2

v(d)' = 0.936 m/s

ω' = 3 rad/s

Therefore, the angular velocity is 0.936 m/s and the velocity of the sphere is 3 rad/s.

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Answer:

50

Explanation:

100×50÷1000= 50

this is easy question

To measure the distance to nearby stars, astronomers use the effects of stellar parallax or by determination of distance by observing parallax works mostly for nearby stars (1).

Parallax is a method used by looking at the shift of two fixed points relative to one another seen from the observer's point of view. The parallax of a star is expressed in units of arc seconds, so this parallax is an angle, while the distance is expressed in units of parsecs with 1 parsec = 3.26 light years. The trigonometry parallax method can only be used to get the distance to the nearest stars, which is up to 100 parsecs.

To measure the distance of a star, astronomers do not use distance units such as meters or kilometers, but the Astronomical Unit, which is equivalent to the average distance between the Earth and the Sun, about 150 million kilometers.

The question is incomplete, it should be:

Based on what you know about measuring the distance to stars, select all of the correct statements from the following list?

1) Determination of distance by observing parallax works mostly for nearby stars.

2) For the distance to far stars, it is necessary to use spectroscopic parallax.

3) To determine the luminosity of a star, you must first know the distance.

4) There are no other stars within a parsec of the sun.

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Evaporation is a cooling process and condensation is a warming process.

Condensation is the transition of a region of matter from a gaseous state to a liquid state and the opposite of vaporization. This word most often refers to the water cycle. Condensation is the process by which water vapor becomes a liquid. This is the opposite of evaporation, which turns liquid water into vapor. Condensation occurs in one of two ways. When the air cools to its dew point or becomes saturated with water vapor, it can no longer hold water.

Evaporation is always a cooling process. For evaporation to occur, energy is needed by the liquid molecules that are changing phase into gas. This energy is taken from the surroundings in the form of heat energy. So when evaporation occurs, the temperature of the surroundings will decrease, making evaporation a cooling process.

Condensation occurs when warmer, moist air comes into contact with cooler surfaces such as frames, windows, and other superstructures, or cooler areas inside an insulating shell (where moisture has penetrated the vapor barrier).

Therefore, evaporation is a cooling process and condensation is a warming process.

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Answer:

Check explaination

Explanation:

A - Transformer is the right option 100%

The laser beam emits 1.939 x 10¹⁷ photons after being activated for 0.050 seconds.

A laser emits an extremely focused beam of energy that may be used in a variety of equipment and technologies. Laser Amplification by Stimulation of Radiation Emission is what the letters in the term laser stand for. Light Amplifier by Stimulated Radiation Emission is what the elements in the term laser stand for.

As we are aware,

This pace of energy is equivalent to power in numbers.

As things evolve throughout time,

using mathematics,

power : P = E /t

Total Energy : E = P t

= (1.5)(0.050)

= 0.075 J

The laser beam's wavelength is = λ = 514 nm

One photon's energy is given by E ' = h c /λ

= (6.626068 × 10⁻³⁴ )(3 x 10⁸)/(514 x10⁻⁹)

= 0.03867 x 10⁻¹⁷ J

The amount of photons the laser beam emits:

= (total energy) / (energy per photon)

= 0.075 J / 0.03867 x 10⁻¹⁷ J

= 1.939 x10¹⁷ photons

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The force that the table exerts on the box1 is 65.2N

As given in the question we are assuming box 2 and 3 aren't touching.

The forces on box 2 are:

gravitational force

Force of tension

Normal force

The box isn't accelerating so

T + N2 - Fg2 = 0

The forces acting  on the box 3 are:

gravitational force

Tension

Since box 3 isn't accelerating

T - Fg3 = 0

The tension force will be same in both cases so:

Fg3 + N2 - Fg2 = 0

So

N2 = Fg2 -Fg3

N2 = Fg2 - Fg3

= 39-25.3 = 13.7 N

Remember forces are equal and opposite.

Now,

write the equation for the forces which are acting on Block 1

There is the force of gravity

normal force acting from the table and

A force which is equal and is opposite to the normal force on block 2

N1 - F(g1) - N2 = 0

N1 = Fg1 +N2

N1 = 51.5 + 13.7 = 65.2 N

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The cord's tension remains constant during the movement at 28.0 N. 94.08 J is the change in the cart's kinetic energy during motion.

the force exerted on the cart is the tension T in the chord itself. so,

F=T

Calculate the displacement of the cart.

d=[tex]\sqrt{x_{1}^{2}+h^{2} } -\sqrt{x_{2}^{2}+h^{2} }[/tex]

subsitute 5.0m for x₁,1.0m for x₂,and 1.60m for h.

d=[tex]\sqrt{5.0^{2}+1.60^{2} } -\sqrt{1.0^{2}+1.60^{2} }[/tex]

d=3.36m

calculate the change in kinetic energy of the cart.

ΔK=Fd

substitute 28.0N for F and 3.36m for d.

ΔK=28.0×3.36

ΔK=94.08 J

Tension is a force that runs the length of a medium, particularly one that is conveyed by a flexible medium like a rope or cable.

An action-reaction pair of forces acting at either end of the aforementioned elements is what is referred to as tension. Consider a rope; aside from the endpoints, every section of the rope experiences tension force in both directions. The ends feel strained on one side and the force of the attached weight. The tension fluctuates in several places along the string.

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(a) The maximum height to which Superman can lift the water is 10.32874 m

(b) On the Moon there is no atmosphere so no atmospheric pressure which means when the straw is placed in water water will not rise in the tube.

Pₐ = Atmospheric pressure = 101325 Pa

g = Acceleration due to gravity = 9.81 m/s²

h = Height of water

ρ = Density of water = 1000 kg/m³

If the walls of the tube do not collapse that means that maximum pressure inside will be the atmospheric pressure

Atmospheric pressure is given by

Pₐ = ρgh

height = Pₐ /ρg

h = 101325 / 1000 * 9.81

h = 10.328 m

The maximum height is 10.32874 m.

(b) On the Moon there is no atmosphere so no atmospheric pressure which means when the straw is placed in water water will not rise in the tube.

Therefore, the maximum height to which Superman can lift the water is 10.32874 m.

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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: Superman attempts to drink water through a very long vertical straw. With his great strength, he achieves maximum possible suction. The walls of the tubular straw don't collapse.

(a) Find the maximum height through which he can lift the water.

(b) Still thirsty, the Man of Steel repeats his attempt on the Moon, which has no atmosphere. Find the difference between the water levels inside and outside the straw.]

Newton's Law of acceleration best describes why this occurs.

Newton's second law - the law of acceleration (acceleration = pressure/mass). Newton's 2d regulation states that the acceleration of an item is without delay related to the net pressure and inversely associated with its mass. Acceleration of an object relies upon on  things, force and mass.

The legal guidelines are: (1) each item movements in a straight line except acted upon by way of a pressure. (2) The acceleration of an item is without delay proportional to the internet pressure exerted and inversely proportional to the object's mass. (3) For every motion, there may be an same and opposite reaction.

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a. the force that the mountain climber must exert with her feet in N) on the vertical rock face to remain stationary is 273 N.

b. the minimum coefficient of friction between her shoes and the cliff is 0.268.

What is the term of friction?

The force that prohibits one solid object from traveling across another is known as friction. Static friction, sliding friction, rolling friction, and fluid friction are the four main categories of friction.

a).

Balancing the forces in x-direction,

F cos(15) = T sin(31)

F = T sin(31)/cos(15)     ...... (1)

balancing the forces in y-direction,

T cos(31) + F sin(15) = 52 x 9.8 = 509.6

T cos(31) + (T sin(31)/cos(15)) sin(15) = 509.6

T = (509.6 cos(15))/(cos(31) cos(15) + sin(31) sin(15))

T = 512 N

Force, F = 512 sin(31)/cos(15)

= 273 N

b)

Coefficient of friction,

u = sin(15)/cos(15)

= 0.268

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After 2seconds of sending sonar, a ship hears an echo. The depth of the sea is 1500 meters if the sound wave speed in water is 1500 m/s.

Let sea depth equal d.

Considering that the sound wave's water speed (v) is 1500 m/s

The sound must travel to the ocean's bottom before being reflected back to the ship, resulting in a total distance of two dimensions for the sound.

Time (t) = 2s for receiving the echo

Total distance traveled times the speed of sound

1500 m/s is equal to 2d/2s = 1500 m.

Consequently, the water is 1500 meters deep.

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If the block's mass is m, block's initial velocity is v and the spring constant is k, the maximum compression in the spring is  sqrt(mv² /k)

Applying the law of conservation of energy, since it is a frictionless surface, all the kinetic energy of the block will be converted to the potential energy of the spring.

The kinetic energy of the block:

Ek = 1/2 . mv²

Where:

m = mass of block

v = block's initial velocity

The potential energy of the spring:

Ep = 1/2 . kx²

Where:

k = spring constant

x = maximum compression in the spring

It holds:

Ek = Ep

1/2 . mv² =  1/2 . kx²

x = sqrt(mv² /k)

Hence, the maximum compression in the spring is sqrt(mv² /k)

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The electric field at the center of the metal ball due only to the charges on the surrounding of the metal ball is 0 N/C.

The electric field is defined as the force acting on a positive test charge, per unit charge. units are thus N/C for the electric field. It is similar to the gravitational field on the surface of the Earth for a test mass mo

The electric field is a vector field. It has a magnitude and a direction. Another example is vector field is the wind distribution. Temperature distribution is an example of a scalar field.

Lines indicate the direction of F if a test charge is placed there, Field lines point away from positive charge, and toward negative charge, density of lines indicates the strength of the field.

Field lines cannot cross. If they did, there would be more than one possible direction for a particle to travel at a given point. The lines themselves have no meaning the field is present everywhere.

Since metal ball is considered as a solid sphere So the electric field inside metal ball is given by E=(p/3Eo)г

Where r is the distance from center and rho is charge density. Hence at the centre r=0

Then electric field =(p/3Eo)* 0 = 0 N/C

Hence electric field at the centre of the metal ball due to it's own charge only is 0  N/C.

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The time of the travel with 20m/s is 17.5 seconds. Thus, the final velocity of the car will be 63 m/s.

Velocity of an object is the measure of the distance travelled per unit time. The rate of change in velocity is called the acceleration.

Given that, initial velocity u = 20 m/s

distance = 350 meters.

time of travel = distance/ velocity

 = 350 m/20 m/s = 17.5 s.

Acceleration = 2.5 m/s²

the final velocity v = u + at.

v = 20 + (2.5 × 17.5 ) = 63 m/s.

Therefore, the final velocity of the car is 63 m/s.

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A pristine nickel surface with a work function of 5.1 eV is exposed to 206 nm light. The photoelectrons released from this surface have a maximum speed of 521.8 x 10^3 m/s.

An electron of the metal can receive photon energy from incident light, which is equal to the planck's constant times the light's frequency.

f = c/∧

assuming that all of the photon energy has been utilized

First in removing electrons from metals (work function)

Second, the leftover is used to furnish the photoelectron with kinetic energy:

V(m) = √2/M(hc/∧)-5.1eV.

where: M = 9.11 x10^3 kg; is the mass of nickel

h = 6.63 x 10 -34 Js; is plancks constant

c = 3 x 10^8 m/s; is the speed of light

∧ = wavelength of light = 206 nm = 206x10-9m

v(m) = (2 x 6.63 x 10-34 x 3 x10^8)/206 x 10-9 x 9.11x10^3 - 5.1 eV

v(m) =  521.8 x 10^3 m/s.

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A decrease in porosity occurs when rocks form joints or faults.

Option B is correct

Porosity is the entire available area for groundwater to live in. A rock's or sediment's porosity impacts how much water it can hold. The porosity of sediments and sedimentary rocks is influenced by the size, shape, and degree of sorting of the grains as well as the degree of cementation.

A good permeability must coexist with good porosity for groundwater to enter a rock. The pore gaps between the rock grains must be linked for a rock to be permeable and allow water to pass through it.

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The nebular theory proposes the sun and planets formed from a rotating cloud of interstellar gases and dust called a Solar nebula

What is nebular theory?

The creation of solar systems is explained by the nebular theory. According to the explanation, stars are produced from clouds of interstellar gas and dust, and the term "nebula" is Latin for "cloud." It takes around 100 million years for an undifferentiated cloud to develop into a star system with planets and moons.

The nebular theory proposes the sun and planets formed from a rotating cloud of interstellar gases and dust called a solar nebula

According to the nebular theory, the Sun and all of the plants in the solar system descended from the solar nebula, an interstellar cloud of gases and dust. The term "nebula" itself is a Latin word for cloud. The nebula began to collapse over time, and the centre of the collapse (the central mass) eventually turned into a protostar.

It should be noted that this protostar was distinct from our current star in that it lacked the continuous nuclear fusion process that our stars do now. When nuclear fusion begins in the centre of a protostar, it transforms into a star.

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The ratio that measures the reasonableness of accounts receivable outstanding, and can be used to estimate the average collection period of accounts receivable is the accounts receivable turnover ratio.

The amount owed to a business for goods or services that have been delivered or utilized, but for which consumers have not yet made payment is known as accounts receivable, or AR. A current asset is defined as accounts receivable on the balance sheet. Any sum that clients owe for purchases they made with credit is considered AR. Account receivable is the term used to describe any unpaid invoices or cash that a business is owed by customers. Accounts that a company is entitled to get as a result of delivering a good or service are referred to by the phrase. Receivables, also known as accounts receivable, are a type of line of credit that a business extends to customers. Typically, the terms of receivables stipulate that payments must be made within a reasonable amount of time.

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a) D = -4273(x)-2327(y)

b) average speed v = 23.33m/s

c) average velocity V = -13.51m/s  south of west.

In order to find the displacement we have to divide the motion on its X and Y components:

dx1 = 25*2*60min = 3000

dx2 = 30*1*60s/min(cos45) = 1273 m

The total X displacement is the algebraic sum of the movement:

dx = -3000 - 1273 = -4273

We have to do the same on Y:

dy1 = 20*3*60 = 3600

dy2 = 30*1*60(sin45) = 1273

dy = -3600 + 1273 =-2327m

D=-4273(x)-2327(y)

The angle is given by:

α = arctg(dy/dx)

α = 28.57 degrees

That is 28.57 degrees south of west.

the total displacement magnitude is given by:

D = √{(4273) - (2327)}

D= 4865

The average speed is given by:

v = (20*3)+(25*2)(1*60)/6*60

v =23.33 m/s

and the Average velocity is given by:

|v| = 4865/6*60

|v| =13.51 m/s

Therefore, the average velocity is V = -1351 m/s with an angle of 28.57 degrees south of west.

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a) D = -4273(x)-2327(y)

b) average speed v = 23.33m/s

c) average velocity V = -13.51m/s  south of west.

In order to find the displacement we have to divide the motion on its X and Y components:

dx1 = 25*2*60min = 3000

dx2 = 30*1*60s/min(cos45) = 1273 m

The total X displacement is the algebraic sum of the movement:

dx = -3000 - 1273 = -4273

We have to do the same on Y:

dy1 = 20*3*60 = 3600

dy2 = 30*1*60(sin45) = 1273

dy = -3600 + 1273 =-2327m

D=-4273(x)-2327(y)

The angle is given by:

α = arctg(dy/dx)

α = 28.57 degrees

That is 28.57 degrees south of west.

the total displacement magnitude is given by:

D = √{(4273) - (2327)}

D= 4865

The average speed is given by:

v = (20*3)+(25*2)(1*60)/6*60

v =23.33 m/s

and the Average velocity is given by:

|v| = 4865/6*60

|v| =13.51 m/s

Therefore, the average velocity is V = -1351 m/s with an angle of 28.57 degrees south of west.

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the speed of the upper end of the pole just before it hits the groundv  is = 7.27 m / s

Explanation:

At both the greatest and lowest points, we shall practise energy conservation.

first. The highest point

Em₀ = U

Em₀ = m g y

final. smallest point

At this point, we adjust the reference system so that the potential energy is 0

= K

= ½ m v²

how to conserve energy

Em₀ =

mg y = ½ m v²

v = √2 gy

v = √ (2 9.8 2.7) (2 9.8 2.7)

v = 7.27 m / s

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If the coefficient of kinetic friction on the plane is 0.4, the acceleration of the block is 0.3 m/s² and tension is T = 1.82N.

A property of a body that is a measure of inertia is usually viewed as a measure of the amount of matter contained in the body that causes it to have weight in a gravitational field. Mass is a dimensionless quantity that describes the amount of matter in a particle or object.

Calculation:-

Tension force = I/R² × a

= 0.5 × 3.564

T = 1.782 N.

acceleration = 1.782/3

= 0.3 m/s²

The mass of an object is a measure of its inertial properties or the amount of matter it contains. The weight of an object is a measure of the force exerted on it by gravity, or the force required to support it. Mass can best be understood as the amount of matter present in an object or body. Everything around us has mass.

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Mass of the brown. dwarf., M₂ = 4.132 * 10²⁷ kg

Let M₁ = Mass of the main-sequence star

M₂ = Mass of the brown dwarf

v₁ = speed of the main-sequence star

v₂ = speed of the brown dwarf

The system's average distance apart r₁ = r₂ = 1 AU

The brown dwarf's orbital speed is 22 times that of a star in the main sequence.

Consequently, v2 = 22 v1.

Considering that the Sun is a main-sequence star

2 * 1030 kg is the main-sequence star's mass.

Centripetal force: F = Mv2/r

M1v12 = M2v22 M2/M1 = v12/v22 M2/M1 = (1/22) M1v12 = M2v22/r2 M2v22/r2

2 M2/M1 = 0.002066 M2 = 0.002066M1 M2 = 0.002066*2*1030 M2 = 4.132*1027 kg

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