a water tank in the shape of a hemispherical bowl of radius 5 m5 m is filled with water to a depth of 2 m.2 m. how much work is required to pump all the water over the top of the tank? (the density of water is 1000 kg/m31000⁢ kg/m3 ). (use symbolic notation and fractions where needed.) W

By converting the unit, the gas needed to complete a 142 km trip is 11.15 liters.

We need to know how to convert from mile and gallon to km and liter units to solve this problem. The conversions unit is

1 mile = 1.60934 km

1 gal = 4.54609 liter

From the question above, we know that:

gas mileage = 36 mi / gal

distance = 142 km

Convert the gas mileage to km/l

gas mileage = 36 mi / gal

gas mileage = 36 x  1,60934/4.54609  km/l

gas mileage = 12.74 km/l

Find the required gas

required gas = distance / gas mileage

required gas = 142 / 12.74

required gas = 11.15 liters

Hence, the gas needed to complete a 142 km trip is 11.15 liters.

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Minerals are non–renewable natural resources that are vital for the construction, manufacturing and energy industries. The aim of sustainable mineral development is to ensure mineral use is kept to a minimum amount without having a negative impact on economic growth. This is achieved by efficient use of minerals as well as recycling and the use of alternative materials.

Also, it is important that the natural environment is protected from damage that may be caused by mineral extraction. This will help maintain biodiversity and ensure that contamination is not a problem for future generations. Mineral planning at local, regional, national and EU level ensures the environment is protected and that resources are used sustainably. Recycling, reuse, and conservation of energy and mineral resources are important in achieving these goals.

The student's shoulder supports the weight of the bag.

Free-body diagrams are utilized to display the relative direction and strength of all forces that are being applied to an item in a certain scenario. A unique illustration of the geometric diagrams that were covered in a previous lesson is the free-body diagram. We will make use of these graphics throughout the entire study of physics.

A university student is carrying a backpack. One strap is hanging the rucksack immobile from one shoulder.

The weight of the backpack is balanced by the shoulder of the student.

The free-body diagram is attached below.

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A controlled burn removes dead vegetation that might otherwise help a wildfire start and spread.

The term controlled burn refers to setting up an area in which the fire is controlled in order to avoid wild fires. These are deliberately set up in order to avoid the bush from burning down.

Let us recall that a wild fire is able to blaze across a large causing damage to a buildings as well as life and other properties in the way of the fire and could cause huge looses including loss of habitat.

Thus, the National Park Service sometimes creates controlled burns to mitigate wildfires because  a controlled burn removes dead vegetation that might otherwise help a wildfire start and spread.

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(b) The classical kinetic energy underestimates the experimental value by 1% at speed u = 0.115c.

(c)  The classical kinetic energy underestimates the experimental value by 5% at speed u = 0.257c.

(d) The classical kinetic energy underestimates the experimental value by 50% at speed u = 0.786c.

Kinetic energy, which may be seen in the movement of an object, particle, or group of particles, is the energy of motion.

The classical kinetic energy is given as:

K(c) = (1/2)mu² = (1/2)mc²(u/c)² = (4.5 × 10 ¹⁶) (u/c)²

The actual kinetic energy of the object is given as:

K(r) = [ (1 /(√1-(u/c)²) - 1]mc² = ( 9 × 10⁶)[ (1 /(√1-(u/c)²) - 1]

(b) The speed at which the classical kinetic energy underestimates the experimental value by 1% is:

K(c) = 0.99K(r)

When (1/2) (u/c)² = 0.990 [ (1 /(√1-(u/c)²) - 1]

Solving this we get,

u = 0.115c

(c) Similarly energy underestimates experiment value by 5% :

K(c) = 0.950K(r)

When u = 0.257c

(d) Energy underestimates experiment value by 50% :

Then,

K(c) = 0.500 K(r) when the speed is u = 0.786c

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The instantaneous velocity of the ball is 18ft/s.

The pace at which an object's position changes as perceived from a particular point of view and as measured by a particular unit of time (for example, 60 km/h northbound) is defined as its velocity. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.

In order to be defined, the physical vector quantity known as velocity needs to have both a magnitude and a direction. Speed is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI. Speed is the scalar absolute value (magnitude) of velocity (metric system).

Calculations:

at t=1s, the height is y=50(1)-16(12)=34ft.

at t=1.1s, the height is y=50(1.1)-16(1.12)=35.64ft

Between these two heights, the change in time is 0.1s. The change in height is 35.64ft-34ft=1.64ft.

Therefore [tex]V_{avg}=\frac{del y}{del t} = \frac{1.64ft}{0.1s} =16.4ft/s[/tex]

at t=1.01s, the height is y=50(1.01)-16(1.012)=34.1784ft

between t=1.01s and t=1s the change in time is 0.01s and the change in height is 0.1784ft.[tex]V_{avg}=\frac{0.1784ft}{0.01s} =17.84ft/s[/tex]

at t=1.001, the height is y=50(1.001)-16(1.0012)=34.017984ft

between t=1s and t=1.001s, the change in time is 0.001s and the change in height is 0.017984ft

[tex]V_{avg} =\frac{0.017984ft}{0.001s}=17.984ft/s[/tex]

It appears that as the time interval approaches 0, the average velocity approaches 18ft/s. Therefore it is safe to assume the instantaneous velocity at t=1s is 18ft/s.

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The interference pattern remains the same if the rate of electrons going through the slits is decreased to one electron per hour during a diffraction process.

This is referred to as a condition which occurs when two waves meet and combine while traveling along the same medium such as air, water etc.

The interference pattern is the same if the the rate of electrons going through the slits is decreased to one electron per hour during a diffraction process. The decrease in the rate of electrons doesn't affect the pattern of the waves being a constructive or destructive one.

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The give scenarios illustrates the following laws of motion respectively:

The three laws of motion are stated below as follows:

First law - it states that a body continues in its state of rest or uniform motion in a straight line unless acted upon by an external force. This is also known as the law of inertia.

Second law - it states that the rate of change of the momentum of a body is directly proportional to the applied force and takes place in the direction of the applied force. This law is restated as acceleration is proportional to force and inversely proportional to mass.

Third law - for every force, there is an equal and oppositely directed reaction.

Considering the individual scenarios:

Pushing a baby on a swing is easier than pushing an adult on the same swing - Second law

Water spills from a glass carried by someone who is walking steadily and suddenly stops short - First law

When thrown with the same force, a soccer ball accelerates more than a bowling ball - Second law

A magician pulls a tablecloth out from under a dish on a table without disturbing the dish - Third law

A rocket launches into space, pushing fuel exhaust in one direction and the rocket in the opposite direction - Third law

A book rests on top of a shelf and does not move until a student accidentally knocks it off - First law

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565.2 cm trace of water left on the floor

Given that,

A wet bicycle tire leaves a trace of water on the floor

The tire has a radius of 30 cm. and the bicycle wheel makes 3 full rotations before stopping

The trace of water left on the floor is the circumference of cycle

The circumference of circle is:

r = 30 cm

Therefore,

Given that,

bicycle wheel makes 3 full rotations before stopping

trace of water = 3 x 188.4 = 565.2

Thus, 565.2 cm trace of water left on the floor.

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The Hailey's comet aphelion distance from the sun is 36 A. U.

The Hailey's comet perihelion distance = 0.6 amu

The Hailey's comet orbital period = 76 years

According to Kepler's law,

The time duration is T.

T = 76 years.

The semi-major axis is a.

The semi-major axis of Hailey's comet is,

[tex]T ^{2} =a ^{3} [/tex]

[tex]a = \sqrt[3]{(T) ^{2} }[/tex]

[tex]a = \sqrt[3]{(76) ^{2} }[/tex]

= 18 A. U

The semi-major axis of Hailey's comet is 18 A. U.

The Hailey's comet aphelion distance from the sun is,

= 2 × a

= 2 × 18

= 36 A. U

Therefore, Hailey's comet aphelion distance from the sun is 36 Astronomical Units.

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The driver observes as the police car approaches [tex]f^{\prime}=3036 \mathrm{~Hz}[/tex]

An observer traveling at speed is a driver [tex]v_O=25.0 \frac{\mathrm{m}}{\mathrm{s}}[/tex] and the source is the swiftly moving police vehicle [tex]v_S=40.0 \frac{\mathrm{m}}{\mathrm{s}}[/tex].The frequency of the sound that the source emits is [tex]f=2500Hz[/tex] The speed of the sound is [tex]v=343 \frac{\mathrm{m}}{\mathrm{s}}[/tex].

(a) The source and the observer approach one another. Then, we apply [tex]13.30[/tex]

substituting numerical numbers for the positive values of [tex]V_O[/tex] and [tex]V_S[/tex]

[tex]\begin{gathered}f^{\prime}=f=2500 \mathrm{~Hz} \times \frac{343 \frac{\mathrm{m}}{\mathrm{s}}+25.0 \frac{\mathrm{m}}{\mathrm{s}}}{343 \frac{\mathrm{m}}{\mathrm{s}}-40.0 \frac{\mathrm{m}}{\mathrm{s}}} \\f^{\prime}=3036 \mathrm{~Hz}\end{gathered}[/tex]

Hence, the driver observes as the police car approaches [tex]3036 Hz[/tex] is the frequency.

When a wave source is moving relative to an observer, the Doppler effect or Doppler shift is a phenomenon that can be seen. A typical physical illustration of the Doppler Effect is when an ambulance crosses you while its siren is on. Let's take a closer look at the Doppler effect's nuances.

The Doppler effect is a significant phenomenon in planetary science and other scientific fields. The frequency of any sound or light wave produced by a moving source with regard to an observer is said to fluctuate as a result of the Doppler effect or Doppler shift.

A source's waves are compressed as they move in the direction of the observer. In contrast, waves from a source that is moving away from the observer become longer.

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As in a series circuit, if you have two parallel wires with current flowing in opposite directions, the magnetic fields of the two wires will be moving in the same direction at the point of intersection and will repel one another.

In a parallel circuit, the branches divide the current so that only a portion of it passes through each branch. In a parallel circuit, each branch has the same voltage or potential difference, but the currents may differ. For instance, in a residential electrical circuit, the same voltage is provided across each lamp and appliance, but depending on their power requirements, each load draws a varied amount of current. A group of comparable batteries connected in parallel can produce more current than a single battery while maintaining the same voltage.

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 The electric field at the center of uniformly charge ring is zero if the charge were placed at a point on the axis of the ring other than the center.

if the charge were placed at a point on the axis of the ring other than the center the electric field then there is no motion.

electric field - It is a force produced by any charge near its surrounding.

If the charge were placed at a point on the axis of the ring other than the center then there is no motion because at the center of the ring E.F ( Electric field is zero.

electric filter the point on the axis of uniformly charged ring depend on the distance of the point from the center of the ring.

.

E.F =  0 because each half cancels each other . the negative charge will be in equilibrium as every part of the ring is uniformly attracted by it.

The electric field at the center of uniformly charge ring is zero if the charge were placed at a point on the axis of the ring other than the center.

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The fundamental frequency will observe  the change by the multiple of [tex]\sqrt{2}[/tex]

The fundamental frequency of a standing wave which has

string of length L

mass per unit meu

has the tension T

is given by f = 1/2L[tex]\sqrt{T/meu}[/tex]

Now we are required to find if the tension is doubled, with all other factors held constant, what will be the effect on the fundamental frequency

According to the formula,

the fundamental frequency f is directly proportional to the factor of square root

Hence, when the tension of the string is doubled while other factors of the system remain constant ,the formula will become

f= 1/2L[tex]\sqrt{2T/meu}[/tex]

Hence the change in the fundamental frequency will be of the factor [tex]\sqrt{2}[/tex]

Therefore, the change will be of [tex]\sqrt{2}[/tex]

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Increasing the coil's number of turns expanding the current. Putting a core made of iron into the solenoid.

(a) Because Bpropto n states that the magnetic field will grow if the number of turns per unit length is increased.

(b) Once more, B=mu 0(H+M)=mu 0(nI+M) is true, with M being the magnetization of the magnetic material. Therefore, the magnetic field will intensify if we place a magnetic substance within the solenoid.. (correct option)

c) because, according to Bpropto I, the magnetic field will increase if we raise the current.. (correct option)

(d) Because Bpropto frac1 L, if we lengthen it but keeping the total number of turns same , the magnetic field will decrease....(option (d) is incorrect)

(e) If we keep the number of turns per unit length constant , the magnetic field will unchanged ....(option (e) is incorrect )

The way it is wound, or more specifically, the circle, is referred to as the cross section. Circle does not depend on what it has within.

A solenoid is a wire wound in general in a circular shape, even when it is not forced, the cross section refers to the way in which it is wound, in general to the circle and is joined to determine the area A = π r². This circle is the same whether it is in the air, a liquid, or a solid because it is independent of what is inside,

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Mars Retrograde Happens Every Two Years

As seen from the Earth(observer), the planets don't always make steady progress along the ecliptic(Path of the planets). They usually move in the same direction as the Sun (i.e., eastward), but from time to time they seem to slow down, stop, and reverse direction (i.e., move westward). This apparent reversal is called retrograde motion.

Apparent retrograde motion occurs when the observer (Earth) and the retrograding object (e.g., Mars) align with the Sun. Retrograde motion is an illusion  created when we observe other planets from the moving planet Earth.

Example:

A familiar example of retrograde motion occurs when you pass a car on the freeway, the car being passed appears to move backwards relative to you.

For the planet mars, it takes almost two years to observe this kind of motion.

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The net force on the room door to the hallway. the door size is 8 ft by 3 ft due to an exhaust fan keeps a room’s pressure at a vacuum pressure of 10 inch of water is 5.554 Newton approximately.

The pressure(P) on the object is the amount of force applied per unit area.

Mathematically, the force(F) can be written in terms of pressure and area(A) as:

F = PA

Here the given data is:

A = [tex]8\ ft\times 3\ ft[/tex]

   = [tex]2.4384\times 0.9144 \ m^2[/tex]

P = [tex]10\ \text{inch of water}[/tex]

  = [tex]0.254 \times 9.80638 \ Pa[/tex]

Therefore the force can be written as:

F = [tex]0.254 \times 9.80638 \times 2.4384\times 0.9144[/tex]

  [tex]\approx 5.554 \ N[/tex]

Hence, the Net force is 5.554 Newton approximately.

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Both the law and its application make advantage of closed loops and symmetries.

Comparing Ampere's law to Biot-Savart law, the former is simpler to apply. In more complicated situations when symmetry cannot be applied, the Biot-Savart law is used.

Ampere's law is more helpful and simpler to apply if there is symmetry.

Gauss's law is used to compute the electric field, while Ampere's law is used to calculate the magnetic field.

The significance of the Biot-Savart law is as follows:

Both Ampere's law and the Biot-Savart law are applied to determine the magnetic field generated by a conductor that is carrying current. When there is symmetry present, we often employ Ampere's law.  

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The fitness industry that is among the easiest to avoid for people who want to get and stay fit is the industry of losing weight.

This is because fitness training includes anything from cardiovascular exercises, like running, jogging, etc to strength training like bench presses, deadlifts, squats, etc.

However, when it comes to losing weight, this involves a variety of exercises and this can be difficult and takes time, hence, people tend to avoid it.

This refers to the process of working out or engaging in exercises in order to be in a healthy state and well-being.

Hence, we can see that The fitness industry that is among the easiest to avoid for people who want to get and stay fit is the industry of losing weight.

This is because fitness training includes anything from cardiovascular exercises, like running, jogging, etc to strength training like bench presses, deadlifts, squats, etc.

However, when it comes to losing weight, this involves a variety of exercises and this can be difficult and takes time, hence, people tend to avoid it.

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|E| = 16.67 N/C and the direction of this Electric field is in the downward direction.

We have a Charge particle present inside a Electric field.

We have to determine the magnitude (in n/c) and direction of an electric field that exerts a 2 x [tex]10^{-5}[/tex] Newton.

The electric field intensity at a point R meters away from a charge Q is the amount of force experienced by the test charge ([tex]$q_{o}[/tex]) of unit magnitude at a distance R meters away the Charge Q. Mathematically -

E = [tex]$\frac{F}{q}[/tex]

According to the question, we have -

F = 2 x [tex]10^{-5}[/tex] Newton

|Q| = - 1.2 [tex]\mu[/tex]C = - 1.2 x [tex]10^{-6}[/tex]  [tex]\mu[/tex]C = 1.2 x [tex]10^{-6}[/tex] [tex]\mu[/tex]C

Therefore -

E = [tex]$\frac{2\times 10^{-5} }{1.2\times 10^{-6} }= \frac{100}{6} = 16.67\;N/C[/tex]

Therefore -

|E| = 16.67 N/C and the direction of this Electric field is in the downward direction.

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The interference pattern remains unchanged when  the diffraction of electrons passing through two closely spaced slits if the rate of electrons going through the slits is decreased to one electron per hour.

Interference pattern is the overall pattern that results when two or more waves cancel each other, generally showing areas of constructive and destructive interference

When one electron interferes with itself, it creates an interference pattern. According to the quantum mechanical theory, the electron simultaneously occupies two different states and simultaneously passes through two different slits at the same time which causes interference. Therefore, the interference pattern is going to be same, even if the rate of electrons  going through the slits is decreased.

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The force the earth exerts on a person that is 1 kg is 9.8 N.

The force the person exert on earth is 9.8 N.

If our planet were twice as far from the Sun as it is now, the Sun’s force on the Earth will be quarter the initial value.

The force the earth exerts on you is calculated as follows;

F = mg

where;

F = 1 kg x 9.8 m/s²

F = 9.8 N

Thus, the force the earth exerts on an object that is 1 kg is 9.8 N.

Also, based on Newton's third law of motion, the force the exerts on you is equal to the force you exert on Earth.

F = GmM/R²

where;

F = (6.67 x 10⁻¹¹ x 5.97 x 10²⁴ x 1.98 x 10³⁰) / (150.23 x 10⁹)²

F = 3.5 x 10²² N

F = GmM/(2R)²

F = GmM/(4R²)

F = ¹/₄GmM/R²

Thus, if our planet were twice as far from the Sun as it is now, the Sun’s force on the Earth will be quarter the initial value.

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The force between the charges will be 10.9 N.

The electrostatic attraction particles that make up the electrostatic force behave as both an attracting and a repulsive force. The force is inversely proportional to the square of the distance between them.

F ∝ 1 / r²

F = k / r²

Fr² = k

When two tiny charged objects are 0.11 of a distance apart, they repel one another with a force of 2.53. If the distance between the two particles is cut to 0.053 and the charge on each item is decreased to 67.9% of its initial amount. Then the force will be

F₁r₁² = F₂r₂²

2.53 × (0.11)² = F × (0.053)²

F = 10.9 N

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According to the thrust force, the acceleration is 0.001 m/s².

We need to know about force to solve this problem. According to second Newton's Law, the force applied to an object will be proportional to mass and acceleration. Hence, it can be written as

F = m . a

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

From the question above, we know that

F = 1 N

m = 1000 kg

By substituting the given parameters, we can calculate the acceleration

F = m . a

1 = 1000 . a

a = 1/1000 m/s²

a = 0.001 m/s²

Hence, the acceleration is 0.001 m/s².

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The value of electric flux for mentioned plane will be 657N⋅m²/C at 40° with the x axis.

For a uniform electric field passing through a plane surface,

electric flux(ϕ)=EAcosθ

where,

θ is the angle between the electric field and the normal to the surface,

E is the electric field

A is surface area

(a) The electric field is perpendicular to the surface so θ=0

​

=(3,50×10³ N/C)[(0.350m)(0.700m)]cos0

=858N⋅m²/C

(b)

The electric field is parallel to the surface θ=90

, so cosθ=0

therefore,

the flux is zero.

(c) For the mentioned plane,

electric flux(ϕ)=(3.50×10³N/C)[(0.350m)(0.700m)]cos40.0

=657N⋅m²/C

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1. The horizontal component of the velocity is 1.73×10³ m/s

2. The vertical component of the velocity is 1×10³ m/s

3. The range of the shell is 3.53×10⁵ m

4. The maximum height reached is 1.53×10⁵ m

1. How to determine the horizontal component of the velocity

Horizontal velocity = u × Cosθ

Horizontal velocity = 2×10³ × Cos30

Horizontal velocity = 1.73×10³ m/s

2. How to determine the vertical component of the velocity

Vertical velocity = u × Cosθ

Vertical velocity = 2×10³ × Sin30

Vertical velocity = 1×10³ m/s

3. How to determin the range

R = u²Sine(2θ) / g

R = (2×10³)² × Sine (2×30) / 9.8

R = 3.53×10⁵ m

4. How to determine the maximum height

H = u²Sine²θ / 2g

H = [(2×10³)² × (Sine 30)²] / (2 × 9.8)

H = 1.53×10⁵ m

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The current in the coil that will enable the sphere to rest in equilibrium on the inclined plane is 0.7A.

According to classical physics, a particle is in mechanical equilibrium if there is no net force acting on it. By extension, if there is no net force acting on any of a physical system's component pieces, it is said to be in mechanical equilibrium.

In addition to the definition of mechanical equilibrium in terms of force, there are numerous other formulations that are all mathematically equal. When all of the components' velocities are constant, a system is said to be in equilibrium in terms of momentum. The system is in equilibrium in terms of velocity if velocity is constant. The object's angular momentum is conserved and there is no net torque in a rotational mechanical equilibrium.

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The centripetal force exerted on the earth by the sun is 3.56775 × 10²² N.

Mass of the Earth, m = 6 × 10²⁴ kg

The average distance between the Sun and the Earth is, r = 1.5 × 10⁸ km                                                                                                           .                                                                                                                   r = 1.5 × 10¹¹ m

The path of the Earth around the Sun is circular, with a circumference:

c = 2πr

 c = 2 × 3.1416 ×  1.5 × 10¹¹ m

 c = 9.42478 × 10¹¹ m

The Earth takes time of T = 365.25 days to complete one revolution around the Sun, that is to travel the distance of c.

T = (365.25 days) × (24hr/1day) × (60min/1hr) × (60s/1min)

T = 3.15576 × 10 ⁷s.

Thus the velocity of the Earth is,

v = c/T

v = (9.42478 × 10¹¹ m) / (3.15576 × 10 ⁷s)

v = 2.98653 × 10⁴ m/s

The centripetal force exerted on the Earth by the Sun is given by,

F = 2mv/r

F = 2× (6 × 10²⁴ kg) × (2.98653 × 10⁴ m/s ) /(1.5 × 10¹¹ m)

F = 3.56775 × 10²² N

Therefore, the centripetal force exerted on the earth by the sun is 3.56775 × 10²² N

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The force experienced by the charges when they are placed 2 m apart will be 0.25 N.

The force between two charges is given by Coulomb’s Law.

According to this law, the force between two charges varies inversely as the square of the distance between the charges and is directly proportional to the product of the magnitude of the two charges.

The above statement is represented by the following equation,

F= K Q1 x Q2/r^2

Here, F = Force between the two charges

K = Constant

Q1 and Q2 =  Magnitude of the two charges

r = Separation between the two charges

According to this equation, the force is inversely proportional to the square of the distance between two charges.

Initially, when the two charges are 1 m apart, the force is 1 N.

When the distance between the two charges is doubled,

then according to Coulomb’s Law, the force should decrease by 4 times.

Hence, if the charges are placed 2 meters apart,  the force becomes 1/4= 0.25 N.

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