in the context of spearman's two-factor theory of intelligence, an intermediate class of factors common to a group of activities but not to all is called .

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

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

Fc = m v² / r

Fg = G M m / r²

Fc = Fg

m v² / r = G M m / r²

v² = G M / r

M = r v² / G

g = Acceleration due to gravity

G = Gravitational constant

M = Mass of star

r = Distance between both bodies

G = 6.67 * 10⁻¹¹ N m² / kg²

r = 8.6 * 10¹¹ m

T = 402 days = 3.47 * 10⁷ s

v = 2 π r / T

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

v = 15.56 * 10⁴ m / s

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

Ms = 20.1 * 10²⁶ kg

F = G M m / r²

F = m g

Equating,

m g = G M m / r²

Mp = g r² / G

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

Mp = 8.58 * 10²⁵ kg

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

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

(a). Flux is given by

Ф= BACosФ

μ₀ηIL² cos0

= 4*π*10⁻⁷*1370*3.11*0.0275²

=  37.82*10⁻⁷ Wb

(b). Here diameter and length are equal

Ф = BACosФ

    = μ₀ηI(π(L/2)²)cos 0

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

    = 131.73*10⁻⁷ Wb

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

Ф = 131.73*10⁻⁷ Wb

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The complete question is-

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

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

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

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

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

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

According to the given information

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

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

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

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

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

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

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The original mass of the sample was 14.79 grams.

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

where k = rate of reaction = 0.0198

           t = time = 98.3 days

           R = final mass = 2.14 grams

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

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

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

What is an example of frequency?

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

What does frequency serve to accomplish?

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

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The time it takes for it to travel through the air is 5m / 343 m/s = 14.57 msec.

We know that it travels faster through the metal, so if the difference is 11, then tm = 11–14.57 ms

which means the speed through the metal is 5/0.00066 = 7575 m/s

But this is not a good answer, as the speed of sound in the air can vary over a large range. And the difference between 11 and 11.66 ms is small.

For example, the 343 number is at 20ºC. At 25ºC it is 346 m/s, which has a travel time of 11.55 ms, and when you subtract, you get 0.55 ms, or a speed of 7330 m/s. So it depends on the exact temperature, which you did not define.

Temperature is a measure of hot or cold expressed on one of several scales including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy spontaneously flows. Temperature is a measure of how hot or cold something is Specifically.

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

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

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

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

Where,

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

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

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

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

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

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

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

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The screwdriver being described above has a mechanical advantage of 65 N. Accordingly, this straightforward device would exert 65N of force on the can's lid for every 20N of force applied to the screwdriver.

A screwdriver's handle can have its torque increased by increasing the diameter of the handle. The force exerted by a person's hand on the handle must be farther away from the screwdriver's shaft in order to increase the torque that is applied to the screw by the tool.

The mechanical advantage and force that a screw can exert for a given applied force increase as the distance between its threads decreases. However, since most real screws have high levels of friction, the mechanical advantage they provide is less than that predicted by the previous equation.

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The percentage decrease in the tension of the dulcimer string vibration is 99.09%.

Current vibration = 247 Hz

Required vibration = 260 Hz

We know that'

= V = vμ

= √ (T/μ)

Combining the two equations of two different vibrations'

= (T₁ / T₂) = (v₁/v₂)²

The percentage decrease is =

= [ 1 - (T₁ / T₂) ] X 100%

= [ 1 -  (v₁/v₂)² ] X 100%

= [ 1 -  (247/260)² ] X 100%

= [ 1 - 0.009025] X 100 %

= 99.09 %

The string with is supposed to vibrate at 260 Hz is vibrating at 247 Hz, thus the percentage decrease required to reduce the tension so that it vibrates at correct frequency is 99.09%.

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The molar mass of the gas is

43.008 g/mol

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

1 mol = 22.4 liters

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

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

The molar mass = mass of gas / number of moles

molar mass = 1.92 g / 0.0446 mol

molar mass = 43.008 g/mol

Hence, molar mass of the gas is

43.008 g/mol

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

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

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

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

Here, Fe is centrifugal force

v is velocity of the person

r is radius of the circle,

r = 7.1m

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

T = Mg/sin 45° = Mg√2

Now, vertical component of the tension,

Fy = Tsin 45° = Mg = (127×9.8)kg-m/s²

Fy = 1244.6N

Now, horizontal component,

Fx = Tcos 45°

Fx = Mg/Tan 45°

Fx = Mg/1

Fx = 1244.6N

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The force with which the man presses the knife against the stone is 2.96 N.

Given that,

Diameter of the stone d = 45 cm = 0.45 m

Radius r = 45/2 cm = 22.5 cm = 0.225 m

Initial angular velocity ω₀ = 200 rpm = 200* 2π/6 rad/s = 20.94 rad/s

Final angular velocity ωf = (1 - 0.1)* 200 rpm = 180 rpm = 180* 2π/6 rad/s = 18.85 rad/s

Mass of the stone m = 25 kg

Coefficient of kinetic friction μ*k = 0.2

Time t = 10 s

Part a:

By using the equation of motion with uniform angular acceleration we will find out the angular acceleration of grindstone:

ω* f = ω₀ + α*t

⇒ α = ( ω* f - ω₀) / t = (18.85 rad/s - 20.94 rad/s)/ (10s) = -0.21 rad/s²

Negative sign shows that the wheel is decelerating.

Part b:

Consider the rim of grindstone as a solid disk, therefore the moment of inertia

I = 0.5*m*r² = 0.5*25* (0.225)²

We know that, Torque = Force* perpendicular distance

τ = (μ*k*F)*r ----(1)

Also:

τ = I* α = 0.5*25* 0.225²* 0.21 = 0.133 N-m

F = 0.133/(0.2*0.225) = 2.96 N

Thus, the force with which the man presses the knife against the stone is 2.96N.

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____________________________________________________

We are given the following:

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

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

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

_____________________________________________________

Hope this helps!

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

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

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

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

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

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

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

What is Mohorovicic discontinuity ?

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

According to the above definition

We get to know that

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

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The Total work done lifting the bucket to the top of the building is 405 kg m

What is work?
Work in physics is the energy that is transmitted to or from a object when a force is applied along a displacement. In its simplest form, it equals the goods of the force's magnitude and the distance travelled for a constant force directed in the same direction as the motion. When a force is applied, it is said to have a component that points inside the direction of a displacement of the application point.

The work done lifting the bucket to the top of the building can be calculated by multiplying the force of the weight of the bucket by the distance it is moved. In this case, the force is equal to the mass of the bucket and sand, which is 30 kg, and the distance is 15 m. So, the work done is:
Work = Force x Distance

    = 30 kg x 15 m

    = 450 kg m
However, as the bucket is leaking sand, the mass of the bucket and sand is decreasing as it is being lifted. The mass of the bucket and sand at the top of the building will be less than 30 kg and the amount of work done will be less than 450 kg m.

To calculate the work done lifting the bucket to the top of the building, we need to calculate the mass of the bucket and sand at the top of the building. We can do this by subtracting the amount of sand lost from the initial mass of the bucket and sand. As the bucket leaks 0.1 kg of sand each meter it is lifted, the mass of the bucket and sand at the top of the building can be calculated as:
Mass at top of building = 30 kg - 0.1 kg x 15 m
                       = 27 kg

Now, we can calculate the work done lifting the bucket to the top of the building by multiplying the force of the weight of the bucket and sand at the top of the building by the distance it is moved. In this case, the force is equal to the mass of the bucket and sand at the top of the building, which is 27 kg, and the distance is 15 m. So, the work done is:
Work = Force x Distance

    = 27 kg x 15 m

    = 405 kg m

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

Single-slit diffraction has an equation

d sin θ = m λ

where

For a small angle, sin θ = tan θ.

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

d sin θ = m λ

d tan θ = m λ

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

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

λ = 4.4 × 10⁻⁵ × 1.41 × 10⁻²

λ = 6.21 × 10⁻⁷ m

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

What is Diffuse dome lighting?

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

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

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

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

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

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

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

The radius then satisfies

tan∅c = r/1.00m

​So the diameter is

d=2[(1.00m)tan∅c]

d=(2.00m)tan48.6° = 2.27m

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​

Answer:

A carton of mass 50-kg slides across an icy surface at a speed of 4 m/s. Conclusion : The momentum of a carton of given mass moving with a particular velocity is 200 kg−m/s .

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

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

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

However, we must first determine the friction force Ff.

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

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

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

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

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

Given that, height of the liquid column is 7

Area = 1.5 m²

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

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

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

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

⇒ 10,500* 9.8 = 1,02,900 N

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

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

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

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

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

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

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

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

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Their speed after collision is 2.5.

What is the reason for this?

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

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

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

Their speed after the collision would be as follows:

Formula: mv = mv

from above information, we know that

Mass of first skater is m= 50 kg

Speed of first skater v= 6m/s

Mass of second skater is m= 70 kg

Speed after collision v=?

mv = mv

50 x 6 = (50 + 70) v

v = 50 x 6 / 120 = 2.5

So therefore, their speed after collision would be 2.5.

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

What is acceleration?

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

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

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

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

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

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

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

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

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

What is electromagnetic waves?

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

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

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

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

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

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

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

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

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A: The  momentum of the first player be 450  kg.m/s.

The  momentum of the second player be 800 kg.m/s.

B:  The total momentum of the football players be 1250  kg.m/s.

C: The velocity of the football players after the collision be 7.14 m/s.

The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.

Given that:

One has a mass of 75 kg and is moving at 6 m/s.

The second has a mass of 100 kg and is moving at 8 m/s

So, momentum of the first player = mass * velocity

= 75×6 kg.m/s

= 450  kg.m/s.

The momentum of the second player = mass * velocity

= 100×8  kg.m/s

= 800 kg.m/s.

If the two football players collide, the total momentum of the football players be =  450  kg.m/s + 800 kg.m/s = 1250  kg.m/s.

The velocity of the football players after the collision be = total momentum/total mass =  1250  kg.m/s./(75+100)kg = 7.14 m/s.

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Answer:

Electric field on the surface of the ball 28 kV/m

Explanation:

Given:

R = 15 cm = 0.15 m

q = 7.0·10⁻⁸ C

________________

E - ?

Electric field on the surface of the ball:

E = k·q / R²

E = 9·10⁹·7.0·10⁻⁸ / (0.15)² ≈ 28 000 V/m    or   E = 28 kV/m