Barium-131 is used in the detection of bone tumors. The half-life of barium-131 is approximately 12 days. How long will it take for the radiation level of barium-131 to drop to 1/4 of its original level?.

The distance the 2.0 N object will move, given that 35 J of energy is used to move it is 17.5 m

Work done is defined as the product of force and the distance moved in the direction of the force. Mathematically, it is expressed as:

Work done (Wd) = force (F) × distance (d)

Using the above formula, we can detertmine the distance the object will move as illustrated below:

Work done (Wd) = force (F) × distance (d)

35 = 2 × distance moved

Divide both sides by 2

Distance moved = 35 / 2

Distance moved = 17.5 m

Therefore, we can conclude from the calculation made above that the distance moved is 17.5 m

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Complete question:

You use 35 J of energy to move a 2.0 N object. How far did you move it?

The equivalent capacitance of this system is 12 micro F.

Let

C1 = 4 micro F

C2 = 8 micro F

C_parallel = C1 + C2

= 4 + 8

= 12 micro F

What is capacitance?

Capacitance is the ability of a component or circuit to collect and store energy in the form of electrical charge.

Capacitors are energy storage devices of various sizes and shapes. They consist of two sheets of conductive material (usually thin metals) sandwiched between insulators made of ceramic, foil, glass, or other material, or even air.

Insulators, also called dielectrics, increase the charging capacity of capacitors. Capacitors are sometimes called capacitors in the automotive, marine and aerospace industries.

The inner plate is connected to the two outer terminals. The outer terminal can be long and thin and resemble a small metal antenna or leg. These terminals can be plugged into a circuit.

Therefore, the equivalent capacitance of this system is 12.

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The kinetic energy of the cylinder rolling is 10J

Rolling on a flat surface is a solid cylinder with a mass of 5 kg and a radius of 30 cm. 2 m/s is the rolling speed of the cylinder.

Due to frictional forces, when you slide an object over a surface (like a book over a table), it usually slows down quickly.

The frictional force acting provides the torque necessary for the object to begin rolling by causing it to change its angular momentum.

A moving object or particle has kinetic energy, which depends on both its mass and its rate of motion.

The type of motion could be vibration, rotation about an axis, translation (or motion along a path from one place to another), or any combination of these.

[tex]K.E=mv^2/2[/tex]

=[5 x 2 x 2]/2

=10 J

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The minimum speed must the small sphere have is v = 145.56  m/s

What is law of conservation of energy?

According to the rule of conservation of energy, energy cannot be generated or destroyed; it can only be transformed from one type of energy to another. This indicates that unless energy is added from outside, a system always has the same quantity of energy.

According to the given question,

Let the speed given to small charge q = v

Initially there is only Kinetic Energy present in the system , and potential energy is zero. The initial KE given to q is all transformed to Potential energy  at distance r = 9.00 + 5.00 = 14.00 cm  or 0.14 m from Q where q comes to rest due to the repelling forces.

Therefore, Using Energy Conservation -

PE = (qkQ)/r

KE = 1/2mv^2

PE = KE

1 / 2 * m * [tex]v^2[/tex] = Kq*Q/r

1 / 2 * 6  *  [tex]10^-5[/tex] *  [tex]v^2[/tex] = 8.9 * [tex]10^9[/tex] * 5 * [tex]10^-6[/tex] * 2* [tex]10^-6[/tex]  / 0.14

v = [tex]\sqrt{(0.63571 * 10^5)/3)} m/s[/tex]

v = 145.56 m/s

Minimum speed must the small sphere have, v = 145.56 m/s

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The frequency heard by the observer while the car is approacing 437.3 Hz.

What is doppler effect?

A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift. The change in pitch that happens as an automobile approaches and drives away from a spectator while sounding its horn is a common way to demonstrate doppler shift.

By using Doppler's Formula:

fo = v+vo/v+vs x fs

where,

fo = observer frequency of sound

v= speed of sound waves

vo= observer velocity

vs= source velocity

fs= actual frequency of sound waves

It is given that,

fs= 405Hz

vs= 25.5 m/s

v= 345 m/s

fo= 0 m/s

Observer to source = Positive

Source to observer = Negative

fo = v+vo/v+vs x fs  

fo = 345/ 345 - 25.5× 405

fo = 437.3 Hz

Hence, The frequency heard by the observer is 437.3 Hz.

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The frequency heard by the observer while the car is approacing 437.3 Hz.

What is doppler effect?

A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift. The change in pitch that happens as an automobile approaches and drives away from a spectator while sounding its horn is a common way to demonstrate doppler shift.

By using Doppler's Formula:

fo = v+vo/v+vs x fs

where,

fo = observer frequency of sound

v= speed of sound waves

vo= observer velocity

vs= source velocity

fs= actual frequency of sound waves

It is given that,

fs= 405Hz

vs= 25.5 m/s

v= 345 m/s

fo= 0 m/s

Observer to source = Positive

Source to observer = Negative

fo = v+vo/v+vs x fs  

fo = 345/ 345 - 25.5× 405

fo = 437.3 Hz

Hence, The frequency heard by the observer is 437.3 Hz.

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A transistor is used to amplify or switch (rectify) electrical signals or power.

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Cations are always smaller than the parent atom and anions are always larger than the parent atom.

Cations are positively charged ions i.e. one that would be attracted to the cathode in electrolysis while anions are negatively charged ions.

When a balanced atom loses one or more electrons, it will become a positively charged cation but it becomes negatively charged when it accepts one or more electrons.

Cations are always smaller than their parent atoms because they have lesser electrons, while their nuclear charge remains the same. On the other hand, anions are always larger because they have more electrons than their parent atoms.

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The majority of comets and asteroids have not changed much since they were formed in the nebula.

What components make up comets?

The principal components of comets, which resemble dirty snowballs, are ice and freezing carbon dioxide, as well as some sand and biological molecules that were left over from Planetary System's origin. They function as "time capsules," revealing to us the circumstances of our Known Universe 4,5 billion years ago.

Which comet made the largest impact on Earth?

The nucleus of this comet has a diameter of 119 kilometers, according to recent measurements made the with Hubble Space Telescope. making it by far the largest comet ever discovered. Only 5 kilometers broad, the asteroid collision that triggered the last extinction event on Earth about 65 million years ago.

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Momentum is conserved when two moving objects of equal masses collide while traveling in the same direction. The impact between cars 1 and 2 causes car 2 to accelerate.

According to the rule of conservation of momentum, absent an external force, the combined momentum of two or more bodies operating upon one another in an isolated system remains constant. As a result, momentum cannot be gained or lost. Collisions between two objects naturally fall under Newton's third law of motion. When two objects collide, forces of equal magnitude and opposite direction are applied to each object. These forces frequently result in one object gaining momentum and speeding up while the other object slows down.

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Electromagnetic waves for sunlight is  966.48  V/m

a) We know that the intensity of light

                 I = (1/2)ε0cEm2

From the above equation we can write

                Em = √(2I / ε0c)

                      = √2 * 1.24 x 103 / 8.85 x 10-12 * 3 x108

                      = 966.48  V/m

When an electric field and a magnetic field vibrate together, electromagnetic waves, or EM waves, are produced. Thus, magnetic and electric fields oscillate to form electromagnetic waves (EM waves). When an electric field and a magnetic field interact, electromagnetic waves are produced. It follows that they are referred to as "electromagnetic" waves. An electromagnetic wave's electric and magnetic fields are parallel to one another and form a right angle. In addition, they are parallel to the EM wave's direction.

In vacuum, the speed of electromagnetic waves is constant at 3.00 x 108 ms-1. Neither the electric nor magnetic fields can deflect them. On the other hand, they can exhibit diffraction or interference.

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Here, we need to calculate weight.

Weight is given as the product of mass and gravity. This weight over here can also be denoted by force and it is said to be the force exerted by the bodies on the Earth.

If we take the gravity to be 10 m/s²,

then the weight for each given mass will be,

weight of 0.05 kg = 0.05*10 = 0.5 N

weight of 0.075 kg = 0.075 * 10 = 0.75 N

weight of 0.100 kg = 0.100 * 10 = 1 N

weight of 0.125 kg = 0.125 * 10 = 1.25 N

weight of 0.150 kg =0.150 * 10 = 1.5 N

weight of 0.175 kg = 0.175 * 10 = 1.75 N

weight of 0.200 kg = 0.200 * 10 = 2 N

weight of 0.225 kg = 0.225 * 10 = 2.25 N

weight of 0.250 kg = 0.250 * 10 = 2.5 N

weight of 0.275 kg = 0.275 * 10 = 2.75 N

weight of 0.300 kg = 0.300 * 10 = 3 N

Therefore, through this we got to know that the weight of the body is also the force exerted by the body on the Earth.

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The magnitude of the current required to produce 1.4 kg of sodium metal in one hour is 1398.38 Amps

Weight of Sodium = 1.4 kg = 1400 g

The molar mass of Sodium = 23 u

Moles of Sodium = 1400/23 = 52.174

No. of atoms of copper = 52.174 * 6.023 x[tex]10^{23}[/tex] = 3.14 x [tex]10^{25}[/tex]

Each copper requires a 1e charge,

So total charge = 1.602 x[tex]10^{-19}[/tex] * 3.14 x [tex]10^{25}[/tex]= 5034180.52 C

I = total charge/time

Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The current is frequently represented by the capital letter I. The standard unit is the ampere, represented by the letter A.

So I = 5034180.52/3600 = 1398.38 Amps

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When a diesel cycle and Otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is  Otto cycle because the area shown in the P-V  graph for the same ratio is more than diesel cycle.

In an engine cylinder the ratio of maximum and minimum volume of the combustion chamber and cylinder is termed as compression ratio.

Hence, When a diesel cycle and Otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is  Otto cycle because the area shown in the P-V  graph for the same ratio is more than diesel cycle.

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A lab technician uses laser light with a wavelength of 640 nm to evaluate a diffraction grating, and this particular grating has 195.31 lines per millimeter.

Its wavelength is 640 nm.

L=40.8 cm The distance between the grating and the screen

The first dazzling fringe is six centimeters away from the centre of the order for laser light. According to the deduced results from Young's experiment, which tie the order of bright fringes to the central order,

With the approach of laser light is small-angle approximation, y = m(wavelength)(L)/d and d = m()(L)/y

Using the value d= 1*640*10^-9*0.48/0.06m = 5.120*10^-9 as a starting point

The line density is 1/d = 1/5.120*10^-9, or 195.31 lines per millimeter.

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Latent heat of vaporisation is required for liquidation of bag per 1 kilogram.

The amount of thermal energy produced when a gas condenses into a liquid or the amount needed for a liquid to evaporate into a gas is known as the latent heat of vaporization.

The enthalpy of vaporization is another name for the latent heat of vaporization. Steam burns are extremely harmful because of the high latent heat of vaporization that water has.

The energy required to change the state of 1 kg of a substance without affecting its temperature is known as the specific latent heat of that substance.

We can tell that the substance is being measured per unit mass due to the distinction from latent heat. Additionally, specific latent heat is a dense feature of matter because it is measured per unit mass.

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Both hills' lowest speeds for the sled are the same.

Sleds—also known as sleighs—are wintertime vehicles that are often pulled across ice or snow by either horses or dogs. The travois and the sidecar, which were its predecessors, are said to have been the earliest human-powered vehicles.

An open-topped, often medium- to large-sized sleigh is used to transport people or cargo. Reindeer, dogs, or horses are frequently used as the drivers. While the name "sled" is still used generally in American parlance, it frequently refers to a smaller, frequently recreational, equipment.

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When we increase the distance by two, the moment of inertia increases by a factor of four.

A measure of an object's resistance to changes in its rotating motion, the moment of inertia (commonly abbreviated as "I") is used in physics. It measures the amount of mass disposed about a rotational axis. The equivalent of mass in linear motion is the moment of inertia in rotational motion.

The idea of a moment of inertia is essential to rotational dynamics and is applied in many branches of mechanics, engineering, and physics. It is essential for understanding how spinning things such as wheels, gears, flywheels, and heavenly bodies like planets move.

The moment of inertia is given by:
I = mr²

Here, mass (m) and distance (d).

If we increase the distance from r to 2r. The new moment of inertial is:
I = m(2r)²

I = 4mr²

Hence, when we increase the distance by two, the moment of inertia increases by a factor of four.

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The correct solutions are -

(a) The net energy transferred to the system by heat during one complete cycle is 15 kJ

(b) The net energy input per cycle by heat is -15 kJ

The net energy transferred to the system is equal to work done. The work done will be calculated by the calculating the area enclosed in the figure.

The area = 1/2 × (8 - 2) × 5

Performing multiplication and division on Right Hand Side of the equation

Work done = 1/2 × 6 × 5

Work done = 3 × 5

Work done = 15 kJ

On reversing the cycle, the net energy input per cycle be heat will be -15kJ.

Hence, work done is 15 kj and net energy input is -15kJ.

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The complete question is attached in the figure.

The L operates on [tex]\psi_3^3[/tex] eigenvalue will be equal to [tex]\sqrt{12}.[/tex]

z component of angular momentum is operates on [tex]\psi_3^3[/tex] gives [tex]L_z=3[/tex]

As per the data given in the question,

Quantum numbers of Electron n=4, l=3, and m=3.

Here, we need to find

(a) orbital angular momentum L and

(b) z component of orbital angular momentum [tex]\left(L_z\right)[/tex].

(a)

If orbital angular momentum (L) operates on spherical harmonic wave function of electron it gives an eigenvalue.

Then, we can write it as:

[tex]L^2 \psi_l^m=l(l+1) \hbar^2 \psi_l^m \\\\L \psi_l^m=\sqrt{l(l+1)} \hbar \psi_l^m[/tex]

Where, l is orbital quantum number and [tex]\hbar[/tex] is the reduced plank's constant.

We have l=3 and m=3

So,

[tex]& L \psi_3^3=\sqrt{3(3+1)} \hbar \psi_3^3 \\& L \psi_3^3=\sqrt{3(4)} \hbar \psi_3^3 \\& L \psi_3^3=\sqrt{12} \hbar \psi_3^3 \\& L=\sqrt{12} \hbar[/tex]

Therefore, the L operates on [tex]\psi_3^3[/tex] eigenvalue will be equal to [tex]\sqrt{12}.[/tex]

(b)

If z component of orbital angular momentum is operates on [tex]\psi_1^m[/tex], it give eigenvalue as follows,

[tex]L_z \psi_l^m=m_z \hbar \psi_1^m[/tex]

Here, [tex]m_z[/tex] is the magnetic quantum number.

[tex]L_z \psi_3^3=3 \hbar \psi_3^3 \\L_z=3 \hbar[/tex]

Therefore, if z component of angular momentum is operates on [tex]\psi_3^3[/tex] gives [tex]L_z=3[/tex]

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The numerical value of the orbital angular momentum is 1.8265719672742281e-34 J s, and the numerical value of the z component of the orbital angular momentum is 1.5818577255e-34 J s

The orbital angular momentum of an electron is given by the formula:

L = √l(l + 1) (h/2π)

where l is the orbital quantum number.

In this case, l = 3, so the orbital angular momentum is:

L = √3(3 + 1) (h/2π) = √12 (h/2π) = 1.8265719672742281e-34 J s

The z component of the orbital angular momentum is given by the formula:

Lz = m(h/2π)

where m is the magnetic quantum number.

In this case, m = 3, so the z component of the orbital angular momentum is:

Lz = 3(h/2π) = 1.5818577255e-34 J s

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Answer:

Explanation:

Given:

m₁ = 100 kg

m₂ = 1800 kg

V₂ = 4.8 m/s

____________

V₁ - ?

According to the condition of the problem, the  momentum  are equal:

m₁·V₁ = m₂·V₂

Speed:

V₁ = m₂·V₂ / m₁ = 1800·4.8 / 100 ≈ 86 m/s

The method would astronomers use to find the distance to a galaxy so far away that individual stars are impossible to make out (resolve) is finding the redshift .

A manifestation of the Doppler Effect is redshift. The sound or light waves that are released by an object as it moves away from us are stretched out, which lowers their pitch and causes them to migrate towards the red end of the electromagnetic spectrum, where light has a longer wavelength.

An important topic for astronomers is "red shift." The term can be taken literally; when the light's wavelength is stretched, the light is perceived as having "shifted" toward the red portion of the spectrum. When a source of sound moves in relation to an observer, sound waves experience a similar phenomenon.

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Total energy in compressing a spring is [tex]kx^{2}/2[/tex].

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The minimum value of M1 to keep a board from falling off the platform is 90 kg.

The mass (M1) placed on the left side edge of the board

the mass of the board = 60 kg

the length of the board = 6 m

If the mass on the right side = 30 kg, and the length of the board L1 = 2m

Then, the length L2 which extend over the edge = 4m

Consider the center of gravity in the board that lies at the length of the board midpoint.

Then, the distance (D) of the gravity center from the platform end = 3 - 2

= 1

The moment when the platform end, the mass (M1) placed on the left side edge of the board can be computed as:

M1= 60kg+120kg/2

M1=180kg/2

M1=90kg

Therefore, The minimum value M1 needed to keep the board from falling off the platform is 90 kg.

Mass is a quantitative measure of inertia, a fundamental property of matter.

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hope this helps solve your question

In this problem we have spherical symmetry, so we can apply Gauss theorem to find the magnitude of the electric field:

∫ E(r) . dr = q / ε₀

where the term on the left is the flux of the electric field through the gaussian surface, and q is the charge contained in the surface.

Here we are analyzing the field at a distance , so outside the solid ball. If we take a gaussian sphere with radius r, we can rewrite the equation above as:

E(r) . 4πr² = q/ε₀  (1)

where 4πr² is the surface of the sphere.

The charge contained in the sphere, q, is equal to the charge density  times the volume of the solid ball, 4/3πr³ₐ:

q = ρ (4/3πr³ₐ)  (2)

Combining (1) and (2), we find

E(r) . 4πr² = (4/3ρπr³ₐ) / (3ε₀)

E(r) = ρπr³ₐ / 3ε₀r²

And we see that the electric field strength is inversely proportional to the square of the distance, r.

B) Now we are inside the solid ball: . By taking a gaussian sphere with radius r, the Gauss theorem becomes

E(r) . 4πr² = q / ε₀ (1)

But this time, the charge q is only the charge inside the gaussian sphere of radius r, so

q = ρ(4/3πr³) (2)

Combining (1) and (2), we find

E(r) . 4πr² = 4ρπr³ / 3ε₀

E(r) = ρr / 3ε₀

And we see that this time the electric field strength is proportional to r.

C) E(0)=0.

limr→∞E(r)=0.

The maximum electric field occurs when r=rb.

From part A) and B), we observed that

ρr / 3ε₀ (1)

so it increases linearly with r

E(r) = ρrₐ³ / 3ε₀r²  (2)

so it decreases quadratically with r

--> This implies that:

1) At r=0, the electric field is 0, because if we substitute r=0 inside eq.(1), we find E(0)=0

2) For r→∞, the electric field tends to zero as well, because according to eq.(2), the electric field strength decreases with the distance r

3) The maximum electric field occur for , i.e. on the surface of the solid ball: in fact, for  the electric field increases with distance, while for  the field decreases with distance, so the maximum value of the field is for .

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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: A solid ball of radius rb has a uniform charge density ρ.

Part A What is the magnitude of the electric field E(r) at a distance r>rb from the center of the ball? Express your answer in terms of ρ, rb, r, and ϵ0.

Part B What is the magnitude of the electric field E(r) at a distance r Express your answer in terms of ρ, r, rb, and ϵ0.

Part CLet E(r) represent the electric field due to the charged ball throughout all of space. Which of the following statements about the electric field are true?

Check all that apply.

E(0)=0.

E(rb)=0.

limr→∞E(r)=0.

The maximum electric field occurs when r=0.

The maximum electric field occurs when r=rb.

The maximum electric field occurs as r→∞.]

The position of the object thrown upward with an initial velocity of 64 feet per second at an initial height of 80 feet from the ground after 10 seconds from the ground is 709.38 m

According to equation of motion,

s = u t + 1 / 2 a t²

s = Displacement

u = Initial velocity

t = Time

a = Acceleration

u = 64 ft / s

u = 19.5 m / s

t = 10 s

s = ( 19.5 * 10 ) + ( 1 / 2 * 9.8 * 10² )

s = 195 + 490

s = 685 m

Total distance from the ground,

d = h + s

h = 80 ft = 24.38 m

d = 24.38 + 685

d = 709.38 m

The final position of the object from the ground is 709.38 m

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The Mechanical energy is equal to the Initial gravitational energy as mechanical energy is stored in the object as gravitational potential energy.

Energy cannot be created or destroyed, according to the rule of conservation of energy. However, it is capable of change from one form to another.

An isolated system's total energy is constant regardless of the types of energy present. The law of energy conservation is adhered to by all energy forms. The law of conservation of energy essentially says that:

The total energy of the system is conserved in a closed system, also known as an isolated system.

Therefore, in a closed system like the universe, if energy is lost in one area, energy must be gained in a different area of the system by an equal amount. There is no known instance of the conservation of energy being broken, despite the fact that it cannot be proven.

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We can conclude that total mass of protons and electrons in  is  9.07043 u.

What is Atomic mass ?

Atomic mass means the sum of total number of protons and neutrons present in an atom.

When an atom is neutral then number of protons equal the number of electrons.

Mass of a proton equals to 1.007276 u, mass of neutron equals to 1.008664 u.

For example, in a  atom there are total 9 protons and number of neutrons is 19 - 9 = 10.

Since, it is a neutral atom so number of electrons will also be 9.

So, total mass will be calculated as follows.

                 Total mass = 9 (mass of electron + mass of proton)

                                     = 9 (1.007825 u)

                                     = 9.07043 u

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a) the magnitude of the force on particle is 9.7 x 10⁻¹² N and direction is 45° counter clockwise.

b) if spheres are in outer space of 0.0150, then velocity will be 3 x 10⁻⁵ km/s

We know

Force = G (m₁m₂/d²)

(a) F(net) = F₁ + F₂ + F₃

         G (mm(p)/d²) + G (mm(p)/d²) + 2G (mm(p)/2d²)

|F(net)| = G[ mm(p) / d² ](√2 + 1)

          = [6.67 x 10⁻¹¹ x 1 x (0.015) / (0.5)² ] (√2 + 1) = 9.7 x 10⁻¹² N

The magnitude of the force is 9.7 x 10⁻¹² N.

Direction 45° counter clockwise

(b) Initial velocity U(p) = √2Gm(2+√2/d - 2/150)

      = √2 x 6.67 x 10⁻¹¹(2 + √2 / 0.5 - 2/150)

      = 3 x 10⁻⁵ m/s

Therefore, the velocity at which it moves is 3 x 10⁻⁵ km/s.

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The 520 nm wavelength is the longest at which a metal will emit an electron.

The wavelength, which is also the distance between two wave crests and troughs, is the measurement of wave length. In cycles per second (Hz), the term "frequency" refers to the number of vibrations that cross a specific area in a second (Hertz). This article talks about the relationship between wavelength and frequency.

The length of a waveform signal that is propagating in space or over a wire is measured by the separation between identical points (adjacent crests) in the adjacent cycles. This length is often stated in meters (m), centimeters (cm), or millimeters (mm) in wireless systems (mm).

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