how to find the moment of inertia about an axis of several particles given the positions and masses of the particles

Answer:

d

Explanation:

Density, temperature, and pressure increase as you move inward in the interior of the Sun. This means that the weight of the star pushing inward at a given radius _________ as you move inward toward the core.

a. increases

b. decreases

c. stays the same

d. There is not enough

The Magnitude of current is 0.087A.

Given- length of line = 40 cm = 0.4 m

Livery magnetic field = 0.04 Tesla

magnetic force = 0.0140 N

Direction of inflow of current is unknown.

To cipher the magnitude of current we can employ following equation-

Force = LBi

where this force is called Lorentz force.

This is net magnitude of force to offset the magnetic effect as per faraday.

L, B, i represents length of the line, magnetic field and current factor.

Just substituting the values.

= 0.400 *0.4 * i

i = 0.087 A

Therefore, the current produced by the force is 0.087A

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It can be said that the speed is v=3.9.0m/s

given data use for calculation:-

Generally the equation for the kinetic energy  is mathematically given as

K.E. = 1/2 m v2

K.E.=1/2*.008*(400*400)

K.E.= 640J

therefore velocity:-

[tex]V^{2}[/tex]= 2*KE/m

V= 3.9 m/s.

The energy an object has as a result of motion is referred to as kinetic energy. If we want to accelerate an object, we must exert force. To apply a force, we must work hard. When the work is done, energy will have been transferred to the item, causing it to move at a new, constant speed.

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A light-rail system's dc power line, which carries 1000 A at an angle of 30.0° to the Earth's 5.0*10^5T field, exerts 2.5N of force on a 100-m portion of this line.

A force in physics is an effect that has the power to alter an object's motion. A force can cause an object with mass to change its velocity, or accelerate (for example, moving from a condition of rest). Intuitively, a push or a pull can also be used to describe force. Being a vector quantity, a force has both magnitude and direction. The SI unit of newton is used to measure it (N). A combination of tram and metro components define the passenger urban rail transit system known as "light rail transit" (LRT).

F = BIlsin(tetha)

F = 5*10^-5*(10^3)(10^2)*sin(pi/6)

F = 5*1/2

F = 2.5N

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The relationship between image distances and object distances for a lens is given by the lens formula: 1/I = 1/f - 1/u, where I is the image distance, f is the focal length of the lens, and u is the object distance.

In the given scenario, the object is kept at the same distance from both lenses A and B, which is between F and 2F of each lens. The image distances I1 and I2 will be different for the two lenses because the focal lengths of the lenses are different, as represented by the different powers P1 and P2.

We can use the lens formula to find the relationship between the image distances of the two lenses.

For lens A: 1/I1 = 1/f1 - 1/u

For lens B: 1/I2 = 1/f2 - 1/u

Where f1 and f2 are the focal length of lenses A and B respectively.

As we know that the object distance is same for both lenses, we can subtract these two equations to get the relationship between I1 and I2.

1/I1 - 1/I2 = 1/f1 - 1/f2

This equation shows that the relationship between the image distances of the two lenses is determined by the difference between the focal lengths of the lenses. If the focal lengths of the lenses are equal, the image distances will also be equal. But if the focal lengths are different, the image distances will also be different.

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The height of the bungee jumper from the earth, given that it has a mass of 78 Kg is 134.17 m

From the question given above, the following data were obtained:

Considering the above data, we can determine the height of the bungee jumper as follow:

PE = mgh

102562 = 78 × 9.8 × h

102562 = 764.4 × h

Divide both sides by 764.4

h = 102562 / 764.4

h = 134.17 m

Thus, we can conclude that the height is 134.17 m

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On dropping the sandbag the amplitude of vibrations will decrease.

when compared to its equilibrium position, the displacements or distance traveled by a spot on a vibrating body or wave.

The cart-spring mechanism loses energy when the sandbag is dropped. Because of this, the amplitude cannot be constant.

The system would only be able to gain energy if the amplitude increased. The sandbag is dropped, yet there is no gain in energy.

The sandbag possesses kinetic energy at equilibrium, which escapes the system containing the sandbag. Since the amplitude and system energy are inversely proportional (E=1/2(k)A2), a decrease in system energy must result in a decrease in the motion's amplitude.

Thus, the amplitude is reduced.

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6 N is the frictional force between the block and surface.

In physics, a force is a power that can change the motion of an item. A force can purpose an object with mass to alternate its pace. Pressure also can be described intuitively as a push or a pull. A force has both value and path, making it a vector quantity.

A pressure is a push or a pull and it affects our each day lives because without force, people might not be capable of open and near stuff or lift up our arms or legs .

Variety of Forces :

* Muscular Forces, muscular tissues features to produce a ensuing force which is referred to as 'muscular force'.

* Frictional Forces, while an item modifications its nation motion, 'frictional pressure' acts upon.

* Carried out pressure.

* Tension force.

* Spring force.

* Gravitational pressure.

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A node is a position of a) minimum amplitude.

In the field of physics, the position where there is the lowest amplitude present in a particular wave is referred to as a node.

In a wave, the nodes can be produced as the regions of destructive interference where the amplitude is minimum.

For example, consider a guitar that has its strings vibrating. In such a case, the place where there will be minimum amplitude will be the ends of each string. Hence, we will refer to the ends of each string as the nodes of the guitar.

On the other hand, anti-nodes are the positions on a wave where the amplitude is the highest.

Although a part of your question is missing, you might be referring to this question:

A node is a position of

a) minimum amplitude

b) maximum amplitude

c) maximum resonance

d) minimum resonance

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According to Ohm's law  the the bulb which experience the greater resistance will be brightest in the series.

Ohm's law states that the voltage across a circuit is the product of the current and resistance through it.

Thus, V = IR.

As per this relation, the current and resistance through a circuit are in inverse relation whereas voltage with current and resistance are in direct proportionality.

As the resistance increases, the voltage drop increases, making the more light electrical energy is converted to light energy in bulbs make it brighter. Therefore, the bulb with higher resistance i. e 22 ohms would be the brightest.

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Average velocity depends on the molar mass of the molecule, and it is highest for [tex]H_{2}[/tex]. Average kinetic energy is the same for all molecules, at a constant temperature, because it does not depend on molar mass.

An object's kinetic energy is the energy it has as a result of motion. It is described as the effort required to move a mass-based body from rest to the indicated velocity.

The sum of all the atoms' individual masses in grams that make up a mole of a specific molecule is known as the molar mass, sometimes referred to as molecular weight. Grams per mole is the unit of measurement.

Hence, average velocity depends on the molar mass of the molecule, and it is highest for [tex]H_{2}[/tex].

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The cart's increased speed is the same as when it first took off.

Rate is the speed from which an object travels along a path over time, whereas velocity is the speed and orientation of an item's motion.

We're informed that;

At first, the cart is at rest. So, u = 0 m/s.

A brief period of time is spent with a constant force applied.

The final speed that the force gives the cart is what we'll call v.

Newton's first equation of motion yields the following results:

v = u + at

Where;

The ultimate speed is v.

The starting speed is u.

Acceleration is a.

t is time.

u = 0 m/s, therefore we now have;

v = 0 + at

v = at

Let's now use Newton's second rule of motion to construct a formula to introduce force;

F = ma

Where;

Force is f.

mass is m.

Acceleration is a.

So, a = F/m.

F/m for an in and v = at to obtain;

v = (F/m)t

The final speed, v, is evidently exactly related to the force. So, if the force is constant, the end speed will also stay constant.

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The complete question is -

A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. Suppose we repeat the experiment but, instead of starting from rest, the cart is already moving with constant speed in the direction of the force at the moment we begin to apply the force.

After we exert the same constant force for the same short time interval, the increase in the cart's speed:

A. is equal to two times its initial speed.

B. is equal to the square of its initial speed.

C. is equal to four times its initial speed.

D. is the same as when it started from rest.

E. cannot be determined from the information provided.

The angular speed of the wheel in radians per second is 1.17 radians/s.

Find the circumference of the wheel.

Angular speed is the rate at which an object rotates or revolves around an axis or center. It is usually measured in radians per second or revolutions per minute (rpm).

Circumference = 2πr

r = 20 cm

Circumference = 2π (20 cm) = 40π cm

Find the linear speed.

Linear speed = 47 cm/s

Find the angular speed.

Angular speed = Linear speed/Circumference

Angular speed = 47 cm/s/40π cm

Angular speed = (47/40π) radians/s

Angular speed = 1.17 radians/s

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The thrust for each of four engines is3.42 m/s^2.

Calculation:

F = 4 *  5999N = 23,996 N.

  F = ma =23,996 ,

6999*a = 23,996 ,

 a =23,996 / 6999 = 3.42 m/s^2.

Acceleration (a) is defined as the product of the change in velocity (v) and the change in time (t) in the equation a = v/t (t). You can use this to get the change in velocity in m/s2 (meters per second squared).

The rate at which velocity changes is known as average acceleration: Where an is the average acceleration, v is the velocity, and t is the time, we have -a=vt=vfv0tft0. (Average acceleration is indicated by the bar ).

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The magnetic flux through this surface is 7.5 × [tex]10^{-5}[/tex] Wb, for the solenoid with the given radius and length carrying a current of 3 Amperes.

The surface integral of the normal component of the magnetic field B over a surface is known as the magnetic flux through that surface. The standard notation is Φ or ΦB. The weber is the SI unit for magnetic flux, and the maxwell is the CGS unit.

Calculation:

It is given that,

Radius of the solenoid, r = 5 cm = 0.05 m

Length of the solenoid, L = 5 m

No of turns, N = 8000

Current, I = 3 A

The radius of the circular plane surface, r' = 2 cm = 0.02

Area of the circular surface,

A = π × r² =  π × (0.02)²= 0.00125 m²

The magnetic flux through this surface is given by :

∅ = B × A

B is the magnetic field of the solenoid,

∅  = μ₀ × N/L × I × A

∅  = 4π × [tex]10^{-7}[/tex] × 8000/5 × 3 × 0.00125 m²

∅  =  7.5 × [tex]10^{-5}[/tex] Wb.

Hence, the magnetic flux through this surface is 7.5 × [tex]10^{-5}[/tex] Wb, for the solenoid with the given radius and length carrying a current of 3 Amperes.

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Answer:

takes a long time to come, so you get to observe theirs as a science experiment.

Explanation:

The simple machines that are used in the tool or device include all of the following:

In Science, a simple machine can be defined as a type of machine that is designed and developed with no moving parts, but can be used to perform a specific work.

Additionally, there are six (6) simple machines and these include the following;

Generally speaking, a simple machine allows for the transformation of energy into work.

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The law of conservation of energy states that energy is neither created nor destroyed; it is transformed and transferred (option B).

The law of conservation of energy is a principle stating that energy may not be created or destroyed but can only be transformed i.e. converted from one form to another.

This means that a system always has the same amount of energy, unless it's added from the outside.

The law states that the total energy of an isolated system remains constant; it is said to be conserved over time.

Therefore, according to this question, the law of conservation of energy is described correctly by option B.

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The change in entropy of a system will be 6.25 kJ/K. For further explanation you can read below.

The change in entropy of a system is given by the equation ΔS = Q/T, where Q is the heat transferred and T is the temperature at which the transfer occurs. In this case, the temperature of the hot water is initially 1.00×102 ∘C and it cools to room temperature, which is 20.0 ∘C. Note that entropy is a measure of the disorder or randomness of a system, and that this calculation assumes that the heat from the hot water is completely transferred to the room, increasing its disorder. It also assumes that the specific heat of the cup and any change in temperature of the room are negligible, which is generally a good approximation for a small cup of hot water in a large room.

We can therefore calculate the change in entropy of the room as follows:

ΔS = Q/T = (125 g * 1.00×102 ∘C - 125 g * 20.0 ∘C) / (20.0 ∘C)

      = 6.25 kJ/K

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Heat transfer (in j) occurs from a system Q = - 156 J.

We use thermodynamics principles in this situation. There are already obtained relationships for intense properties like internal energy (U), heat transfer (Q), and work (W) that were based on differential equations. The formula is

ΔU = Q + W

But since these factors depend on their signs, we must remember to take them into account. Van Ness, Smith, and Abbott assert that declining has a negative sign convention. If work is being done ON the system, the sign is positive; however, if work is being done BY the system, the sign is negative. in this instance,

ΔU = - 200 J\sW = - 44 J

In that case, Q can be found.

-200 J = Q - 44 J

heat transfer (in j) occurs from a system Q = - 156 J.

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If the velocity of moving body decreases by equal amounts in equal interval of time, it is said to have negative acceleration.

What is velocity?

The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity. The standard unit of velocity magnitude is the meter per second (m/s).

What is acceleration?

Acceleration is the rate at which an object's velocity with respect to time changes. Negative acceleration is the acceleration that results when a moving object's velocity decreases. When a body's velocity is decreasing, it typically experiences negative acceleration. Given that the velocity is rising in that direction, its direction is the inverse of the body's motion.

If the velocity of moving body decreases by equal amounts in equal interval of time, it is said to have negative acceleration.

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The binding energy per nucleon = 1.368*10^-12

What is energy?

Energy, which is observable in the performance of work as well as in the form of heat and light, is the quantitative property that is transferred to a body or to a physical system in physics. It is a mechanically accepted quantity.

The mass of a proton is 1.00728 amu

The mass of a neutron is 1.00867 amu

The mass of a cobalt-60 nucleus is59.9338 amu

Step 2: Calculate binding energy

The mass defect = the difference between the mass of a nucleus and the total mass of its constituent particles.

Cobalt60 has 27 protons and 33 neutrons.

The mass of 27 protons = 27*1.00728 u = 27.19656 u

The mass of 33 neutrons = 33*1.00867 u = 33.28611 u

Total mass of protons + neutrons = 27.19656 u + 33.28611 u = 60.48267 u

Mass of a cobalt60 nucleus = 59.9338 amu

Mass defect = Δm = 0.54887 u

ΔE =c²*Δm

ΔE = (3.00 *10^8 m/s)² *(0.54887 amu))*(1.00 g/ 6.02 *10^23 amu)*(1kg/1000g)

Step 3: Calculate binding energy per nucleon

ΔE = 8.21 * 10^-11 J

8.21* 10^-11 J / 59.9338 = 1.368 *10^-12

Complete Quetion:-The mass of a proton is 1.00728 amu andthat of a neutron is 1.00867 amu. What is the binding energy pernucleon (in J) of a Co nucleus? (The mass of a cobalt-60 nucleus is59.9338 amu.) a. 3.039× 10^-12 b. 2.487 × 10^-12 c. 7.009 × 10^-14 d. 1.368 × 10^-12 e. 9.432 × 10^-13

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That amounts battery to 220 volts divided by 6.8 times 10 and three less meters between them. That is 6.8 millimeters electric 3.2 times 10 to the four Newtons per Coulomb gives us 32,352 Newtons per Coulomb.

A battery is a device that converts chemical energy into electrical energy by storing it. During chemical reactions in batteries, electrons flow from one material (electrode) to another through an external circuit. The movement of electrons results in an effective electric current.

Electric field due to battery = potential/separation = 220v / 6.8mm = 220v / 0.0068m = 32,352 volts per meter, according to the question.

If there is a battery, two parallel plates spaced 6.8 mm apart will create an electric field.

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Answer:

trust the process

Explanation:

quadratic formula, use synthetic division also use the p-q method for the roots and factoring.

A long, straight wire's magnetic field strength is  1.5 x 10^-8 Tesla

E = 4.5 V/m

Relation between electric field and magnetic field in electromagnetic wave are given by:-

c = E / B

Where, c= velocity of light in vacuum,

e = electric field and ,

B= magnetic field.

B = E / c

B = 4.5 / ( 3 x 10^8)

B = 1.5 x 10^-8 Tesla

With increasing distance and vice versa, the strength of the magnetic field created by an electric current diminishes. Magnetic field lines form concentric circles, and as one moves away from a conductor, the radius of these circles grows, demonstrating a decreasing magnetic field.

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The heat is convicted through the soup. The soup heats up as the spoon is in the soup making the spoon hot. its like saying pouring hot water into a cup and its hot on your hand its convecting through the glass and heating up

The best tool to add waves to straight hair is a curling iron or curling wand. You have total control over the size and positioning thanks to them.

These instruments can assist you in achieving your ideal appearance, but they can also cause heat damage to your hair. According to Phys.org, studies have shown that flat irons and curling irons can char 85% of the keratin proteins in your hair, making it dry and brittle.

Daily bicep curling will enhance exposure to factors that encourage muscle growth. Because the biceps are a smaller muscular group, they recover more quickly between sessions, allowing for a higher overall volume over the course of a given week.

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The velocity of the block after it is hit by the bullet is 1.307 m/s.

Velocity is the rate of change of displacement.

To calculate the velocity of the block after it is hit by the bullet, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the velocity of the block is 1.307 m/s.

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Note that this is a trick question. It is true that the mass of a star affects its life cycle but all stars must go through the stages listed below. Note that the larger the solar mass of a star, the shorter its life cycle. Hence, in each of the stages given here is what will occur:

Prenatal Stage

Birth Stage

Adolescence/Adulthood

Middle age

Old age

Death

The solar mass is a unit of mass used to measure the masses of objects in the solar system, including stars. It is defined as the mass of the Sun, which is approximately 1.989 x 10³⁰ kilograms, or about 333,000 times the mass of the Earth.

Hence, since the earth's sun is 1.989 x 1010³⁰ kilograms, a star described as having 1 solar mass is simply a star equivalent of the Earth's sun.

Note however that the solar mass is often used as a standard unit of mass for comparing the masses of objects in the universe, such as planets, asteroids, and stars.

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Full Question:

Compare the following stages in the lives of a human being and a star: prenatal, birth, adolescence/ adulthood, middle age, old age, and death. What does a star with a solar mass of 1 solar mass do in each of these stages?

a)The  the repulsive force between the 2 protons that are 2 fm apart is 30.6N.

b)The attractive gravitational force between the to protons that are 2 fm apart is [tex]2.27*10^{-35}N[/tex]

c)Because both charges are of the same type, gravitational force is much smaller than repulsive force. The same charges repel one another.

Given,

Distance between the protons ,d = 2 fm = [tex]2*10^{-15} m[/tex]

Charge of proton = [tex]1.67*10^{-19}C = 1.67*10^{-27} kg[/tex]

a)

The repulsive force between the two protons can be calculate by formula,

[tex]F=k\frac{q_1q_2}{d^2}[/tex]

Where, _1 and q_2 are charge of protons and d is distance between them.

k=[tex]8.988*10^9 N.m^2/C^2[/tex]

[tex]F=8.988*10^9(\frac{1.67*10^{-19}}{2*10^{-15}})^2=30.6N[/tex]

b)

The attractive gravitational force between the protons can be calculated by formula,

[tex]F=G\frac{m_1m_2}{d^2}[/tex]

Where, G=gravitational force = [tex]6.67*10^{-11}Nm^2/kg^2[/tex]

[tex]F=6.67*10^{-11}(\frac{1.167*10^{-27}}{2*10^{-15}})^2=2.27233903428*10^{-35}[/tex]

The gravitational force between the protons is [tex]2.27*10^{-35} N.[/tex]

c)

The gravitational force is very much smaller compared to repulsive force because both the charges are of same type. and same charges repel each other.

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