Compare the speed of red light and blue light in free space.

In a gas mixture with the same temperature, lighter particles move faster and heavier particles move slower.

If a gas mixture has the same temperature, the lighter particles will move faster and the heavier particles will move slower. This is because the kinetic energy of the gas particles is directly proportional to their mass and temperature, according to the kinetic theory of gases.

Lighter particles have less mass and therefore require less kinetic energy to move at a faster speed compared to heavier particles, which have more mass and require more kinetic energy to move at the same speed. As a result, the lighter particles will move faster and collide more frequently with other particles in the gas mixture, while the heavier particles will move slower and collide less frequently.

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The ball travels a total distance of approximately 89.59 meters before coming to rest.

When the ball is dropped from a height of 12m, it will first travel downwards and then bounce back up to a height of 5/6 x 12m = 10m (assuming no energy is lost during the bounce). The distance traveled during the first part of the motion is simply the distance it fell, which is 12m.

When the ball reaches the top of its first bounce, it will fall back down and then bounce back up again. This process will repeat until the ball comes to rest. The distance traveled during each bounce is twice the height of the bounce (up and down), which is 2 x[tex](5/6)^n[/tex]x 12m, where n is the number of bounces.

The ball will come to rest when it bounces to a height less than the smallest unit of measurement given (in this case, meters). So we can set up an inequality to find the number of bounces:

[tex](5/6)^n[/tex] x 12m < 1m

Taking the logarithm of both sides (with base 5/6), we get:

n > log(1/12)/log(5/6)

n > 5.2

Since n must be a whole number, the ball will bounce 6 times before coming to rest.

The total distance traveled by the ball is the sum of the distances traveled during each bounce, plus the distance traveled during the first part of the motion:

Total distance = 12m + 2 x [tex](5/6)^1[/tex]x 12m + 2 x [tex](5/6)^2[/tex] x 12m + ... + 2 x[tex](5/6)^5[/tex]x 12m

Total distance = 12m x (1 + 2 x (5/6) + 2 x [tex](5/6)^2[/tex] + ... + 2 x [tex](5/6)^5[/tex])

This is a geometric series with first term a = 1 and common ratio r = 5/6. The sum of the first n terms of a geometric series is given by:

S_n = a(1 - [tex]r^n[/tex])/(1 - r)

Substituting the values for a, r, and n, we get:

Total distance = 12m x (1 - [tex](5/6)^6[/tex])/(1 - 5/6)

Total distance = 12m x 7.466 = 89.59m (rounded to two decimal places)

Therefore, the ball travels a total distance of approximately 89.59 meters before coming to rest.

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The change in volume of the piston when the work done is 1000 J and the pressure is a constant 1000 Pa, is 1 m³.

To find the change in volume of the piston you can use the following formula:

Work Done = Pressure × Change in Volume

Here, Work Done = 1000 J, and Pressure = 1000 Pa.

So, the change in volume of the piston is 1 m³ ,when the work done is 100OJ.

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When four lamps are connected in series in a single circuit and one of the lamps burns out, the other lamps will also go out.

This is because, in a series circuit, the current has only one path to flow through, and if one component fails, it interrupts the flow of current, causing the entire circuit to stop functioning.

If one of the lamps in a series circuit burns out, it will interrupt the flow of current through the circuit. When the filament in the lamp burns out, it creates an open circuit, which means that there is a break in the circuit and current cannot flow through it.

Since the current has only one path to flow through in a series circuit, if one component fails, the entire circuit will stop functioning.

When one lamp in a series circuit burns out, it creates an open circuit, which means that there is no path for the current to flow through. As a result, the other lamps in the circuit will also go out because there is no current flowing through the circuit to light them.

This is because the circuit is incomplete without the component that has failed, and the current cannot continue to flow through the remaining components.

In summary, when four lamps are connected in series in a single circuit, if one of the lamps burns out, the other lamps will also go out.

This is because in a series circuit, the current has only one path to flow through, and if one component fails, it interrupts the flow of current, causing the entire circuit to stop functioning.

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The Van der Waals equation is [tex]F_{}(r)=- \frac {AR_1R_2}{(R_1+R_2)6r^2}[/tex], The meaning of the letter are,

F(r) = van der wall force,

R₁ = radius of first atom,

R₂ = radius of second atom,

r = distance between two atoms.

Van der Waals forces, which depend on the separation between atoms or molecules, are weak intermolecular forces. These interactions between uncharged atoms and molecules give rise to these forces. the above equation is a van der waals force where each notation has physical meaning

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The total mechanical energy is conserved and is mgh.

At the height h, the energy in the ball is its potential energy and the kinetic energy of the ball at the height is zero.

Potential energy, PE = mgh

Kinetic energy, KE = 0

So, total mechanical energy, TE = KE + PE

TE = mgh

As the ball is moving, the potential energy will be converted to its kinetic energy.

mgh = 1/2mv²

v = √2gh

When it reaches the ground, the energy of the ball is kinetic energy and potential energy is zero.

KE = 1/2 mv² = mgh

PE = 0

TE = mgh

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The electric potential greatest in magnitude is point B. The correct option is B.

The electric potential at a point due to a point charge Q is given by the equation:

V = k * Q / r

where k is the Coulomb constant, Q is the charge, and r is the distance from the point charge.

For the two positive charges in the given scenario, the electric potential at any point is the sum of the electric potentials due to each individual charge:

V = k * q / r1 + k * q / r2

where r1 is the distance from point A to the first charge, r2 is the distance from point A to the second charge, and q is the magnitude of each charge.

Since both charges are positive, the potential at any point will be positive, and the magnitude of the potential will increase as the distance from the charges decreases.

At point A, the distances to both charges are equal to d, so the potential is:

V(A) = 2 * k * q / d

At point B, the distance to one charge is d and the distance to the other charge is sqrt(2) * d (by using the Pythagorean theorem), so the potential is:

V(B) = k * q / d + k * q / (sqrt(2) * d)

Since sqrt(2) > 1, the potential at point B is greater than the potential at point A.

At point C, the distance to one charge is d and the distance to the other charge is 2d, so the potential is:

V(C) = k * q / d + k * q / (2d)

This is less than the potential at point B.

At point D, the distance to one charge is sqrt(2) * d and the distance to the other charge is d, so the potential is:

V(D) = k * q / (sqrt(2) * d) + k * q / d

This is also less than the potential at point B.

At point E, the distance to both charges is sqrt(2) * d, so the potential is:

V(E) = 2 * k * q / (sqrt(2) * d)

This is less than the potential at point B.

Therefore, the correct answer is (B) point B, where the potential is greatest in magnitude.

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The body's initial position was +10m from the origin and its final position was -10m 1 second later. The displacement of the body was  -20 meters.

To find the displacement of the body, you need to subtract the initial position from the final position.

In this case, the initial position was +10m and the final position was -10m, substituting these values

Displacement = Final Position - Initial Position
Displacement = (-10m) - (+10m)
Displacement = -10m-10m

                       = -20m

The body's displacement was -20 meters.

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Satellites in low-Earth orbits are more likely to crash to Earth during the maximum solar periods of the sunspot cycle because, during these periods, there is increased solar activity, such as solar flares and coronal mass ejections.

This heightened activity leads to stronger solar radiation and an expansion of Earth's atmosphere, causing an increased drag on satellites. As a result, the satellites' orbits decay faster, making them more prone to crashing into Earth.

The sunspot cycle is directly relevant to us here on Earth because it can cause coronal mass ejections and other activity that can disrupt radio communications and knock out sensitive electronic equipment. It also plays a significant role in global warming, affects compass needles, affects plant photosynthesis, and strongly influences the earth's weather.

This means that the sunspot cycle can have a significant impact on our technology and communication systems, which are critical to our daily lives. Coronal mass ejections can cause major geomagnetic storms that have the potential to knock out power grids, damage satellites, and disrupt GPS signals. These storms can also create beautiful auroras that are visible in many parts of the world, but they can also have severe consequences for our infrastructure.

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The object that has zero angular momentum about that axis is the one that is located exactly on the axis. This is because angular momentum is the product of an object's moment of inertia (which depends on its mass and distribution) and its angular velocity.

Since the axis of rotation is perpendicular to the page, the distance of each object from the axis is the same. Therefore, the only factor that affects angular momentum is the mass and velocity of each object. Since all five objects have the same mass and velocity, the only way to have zero angular momentum is to have one object on the axis, which would have zero distance from the axis.
To determine the object with zero angular momentum, we must consider the relationship between angular momentum (L), mass (m), velocity (v), and distance (r) from the axis of rotation. The formula for angular momentum is:

L = m * v * r

An object has zero angular momentum when L = 0. In this case, one of the factors (m, v, or r) must be zero. Since all five objects have mass m and velocity v, the only factor that can be zero is the distance (r). Therefore, the object with zero angular momentum is the one located at point A, where the distance r from the axis of rotation is zero.

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The radius of the output plunger to the radius of the input piston is roughly 6.43.

What is the plunger radius to piston radius ratio?

We can use the principle of hydraulic systems, which states that the pressure applied to an incompressible fluid in a closed system is transmitted equally throughout the system. Therefore, the pressure applied to the input piston is equal to the pressure applied to the output plunger.

Let's denote the radius of the input piston as r1, and the radius of the output plunger as r2. The force applied to the input piston is F1 = 63.9 N, and the weight of the chair is F2 = 1540 N.

The input piston is under the following pressure:

P1 = F1 / A1

= F1 / (π * r1^2)

where A1 is the area of the input piston.

The pressure applied to the output plunger is:

P2 = F2 / A2

= F2 / (π * r2^2)

A2 denotes the area of the output plunger.

Because the pressure is distributed evenly throughout the system, we have:

P1 = P2

Therefore,

F1 / (π * r1^2) =

F2 / (π * r2^2)

Simplifying this equation, we get:

r2^2 / r1^2 = F2 / F1

Substituting the values, we get:

r2^2 / r1^2 = 1540 N / 63.9 N

r2 / r1 = √(1540 / 63.9)

r2 / r1 = 6.43

As a result, the radius of the output plunger to the radius of the input piston is roughly 6.43.

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Diffraction of light is defined as the phenomenon where the bending of light happens around corners such that it spreads out and illuminates areas where the formation of shadow is expected.

Here diffraction grating, is defined as an optical element that divides the light into various wavelengths.

The formula for diffraction is: dsinФ=nλ

where, d is the distance between the slits, Ф is the diffracting angle, n is the order number and λ is the wavelength.

Given, grating is 2090 grooves per centimeter for n=1,

d=n/λ

Then,

d = 1 × 10⁻² / 1990  = 5.025 × 10⁻⁶ m

sinФ=nλ/d

1 × 640 × 10⁻⁹ /  5.025 × 10⁻⁶  = 0.127

Ф = Sin⁻¹ ( 0.127) = 7.29 degrees

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When we say that the moon is moving eastward among the stars, we are referring to its apparent motion across the night sky relative to the fixed position of the stars.

When we observe the moon in the night sky, we can see that it appears to move across the sky over time. If we were to track its path over several nights, we would notice that it moves in an eastward direction relative to the stars.

This means that the moon appears to be traveling along the same path as the stars, but at a slightly faster pace. This is because the moon is orbiting around the Earth, which is rotating on its axis, causing the stars to appear to move in a circular pattern in the sky.

So when we say that the moon is moving eastward among the stars, we are referring to its apparent motion across the night sky relative to the fixed position of the stars.

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Beats are the result of the alternate cancellation and reinforcement of two sound waves of slightly different frequencies. When two waves with different frequencies interfere with each other, they create a pattern of alternating loud and soft sounds, which is known as beats.

The frequency of the beats is equal to the difference between the frequencies of the two waves. For example, if two waves with frequencies of 500 Hz and 505 Hz interfere with each other, they will produce beats with a frequency of 5 Hz. The amplitude of the beats depends on the amplitude and phase of the two waves, as well as the frequency difference between them.

Beats can be heard when two instruments playing slightly out of tune with each other, or when tuning an instrument to a reference tone. They can also be used in music to create interesting and complex rhythms and harmonies.

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The correct option is option (a) 0.16°C.

We can use the equation for potential energy, which is PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the falls. We can assume that all of the potential energy is converted to thermal energy, which is given by Q = mcΔT, where Q is the amount of heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. We can set these two equations equal to each other and solve for ΔT:

mgh = mcΔT

Canceling out the mass of the water and dividing both sides by c, we get:

gh/c = ΔT

Substituting in the given values of g, h, and c, we get:

(9.8 m/s^2)(80 m)/(4,186 J/kg°C) = 0.186°C

Therefore, the increase in water temperature at the bottom of the falls if all the initial potential energy goes into heating the water is approximately 0.186°C, which is closest to answer choice (a) 0.16°C.

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The total distance that the springs in parallel are compressed is 5 cm.

Given information,

mass, m = 5kg,

The total distance that springs compressed, x = 10 cm

where x = x₁ + x₂,

the force exerted by the spring is given as

F = -k.x

The force exerted  by spring at series is,

Fs = - Ks(x₁ + x₂)

and,

F₁ = -K₁x₁

F₂ = -K₂x₂

Fs = F₁ = F₂,

equating values,

- Ks(x₁ + x₂) = -K₁x₁

since, x₁ = x₂ and K₁ = K₂,

Ks = K₁/2

Ks = 0.5K₁

Fs = - 0.5×K(x₁ + x₂)

The force exerted  by spring at parallel is,

Fp = F₁ +  F₂

Fp = -K₁x₁ + (-K₂x₂)

Fp  = -2K₁x₁

Equating,

Fs = Fp

- 0.5×K₁×10 = -2K₁x₁

x₁ = 2.5 cm

The total distance is,

2.5 + 2.5 = 5 cm

Hence, The springs in parallel are compressed by a total distance of 5 cm.

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The reason that one feels colder than the other is because of thermal conductivity and heat transfer mechanisms. Metals generally have high thermal conductivity. when you touch a metal, its heat is rapidly conducted to your skin, making it feel cold. In contast wood has a lower thermal conductivity.

In order to set the configuration of RC circuit to smooth a rectified signal, one needs to choose the right combination of resistor and capacitor values.

The R-value controls the charging and discharging rate of the capacitor, while the C-value determines the amount of charge it can store.

The time constant depends on R and C and determines the capacitor's charging or discharging time.

Longer time constants lead to smoother output signals but cause response delays. Choosing appropriate R and C values requires balancing the desired smoothing effect, input signal characteristics, power dissipation in the resistor, maximum voltage rating of the capacitor, and temperature coefficient.

It is important to make a careful selection to avoid instability or damage to the RC circuit.

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The statement that is not true is: "the intensity of transmitted light is proportional to the sine of the angle between the polarizing sheet and the light." The intensity of transmitted light is actually proportional to the square of the cosine of the angle between the polarizing sheet and the light. This is known as Malus' law.

The correct relationship for the intensity of transmitted light (I_t) through a polarizing sheet is given by Malus' Law: I_t = I_i * cos^2(θ), where I_i is the intensity of incident light and θ is the angle between the polarizing sheet and the light's polarization direction.

So, the intensity is proportional to the square of the cosine of the angle, not the sine of the angle.

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The drift velocity (v) of charge carriers in a conductor is given by the following equation: v = I / (n [tex]\times[/tex] A [tex]\times[/tex] q).

v = I / (n [tex]\times[/tex] A [tex]\times[/tex] q)

where:

v is the drift velocity, measured in meters per second (m/s)

I is the current flowing through the conductor, measured in amperes (A)

n is the number of charge carriers per unit volume of the conductor, measured in per cubic meter ([tex]m^(-3)[/tex])

A is the cross-sectional area of the conductor, measured in square meters (m^2)

q is the charge of a single carrier, such as an electron, measured in coulombs (C)

This equation relates the drift velocity of the charge carriers to the current flowing through the conductor, the number of charge carriers per unit volume, the cross-sectional area of the conductor, and the charge of a single carrier. The drift velocity represents the average velocity of the charge carriers as they move through the conductor in response to an applied electric field.

The number of charge carriers per unit volume (n) depends on the material of the conductor and the temperature. In metals, the charge carriers are typically electrons, and the number density is on the order of 10^28 to 10^29 electrons per cubic meter.

The cross-sectional area (A) of the conductor is the area of the cross-section of the conductor perpendicular to the direction of the current flow, and is a measure of the amount of material available for the charge carriers to move through.

The charge of a single carrier (q) is typically the charge of an electron, which is approximately 1.6 x [tex]10^{-19[/tex] coulombs.

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The Ideal Gas Law assumes gas molecules have zero volume and do not interact with each other, while the Van der Waals equation accounts for their finite volume and intermolecular forces. The Van der Waals equation is more accurate at high pressures and low temperatures, while the Ideal Gas Law is more accurate at low pressures and high temperatures.

The Van der Waals equation of state and the Ideal Gas Law are two different equations used to describe the behavior of gases.

The Ideal Gas Law is based on the assumption that gas molecules have zero volume and do not interact with each other, except during elastic collisions. It is represented by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature.

The Van der Waals equation of state, on the other hand, accounts for the fact that gas molecules do have finite volumes and that they interact with each other through intermolecular forces. It is represented by the equation: (P + a(n/V)²)(V-nb) = nRT, where a and b are empirical constants that take into account the attractive and repulsive forces between gas molecules, respectively.

In summary, the Ideal Gas Law assumes that gas molecules have zero volume and do not interact with each other, while the Van der Waals equation accounts for the finite volume and intermolecular forces between gas molecules. The Van der Waals equation is more accurate at high pressures and low temperatures, while the Ideal Gas Law is more accurate at low pressures and high temperatures.

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If the mass is now replaced with one that has a value of 4M and the spring is again pulled back a distance X, force of the spring is four times.

Simple harmonic motion is a specific kind of periodic motion of a body that arises from a dynamic equilibrium between an inertial force that is proportional to the body's acceleration away from the static equilibrium position and a restoring force on the moving object that is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position. Oscillating spring perform SHM.

Force applied on the spring is spring constant times distance.

For system 1,

m = m

x = x

F = mx

for system 2,

m = 4m

x=x

F' = 4mx

looking at both the systems,

F' = 4F

Hence force of the spring will be 4 times.

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The heat source will be concentrated at a point 6 feet deep in the center of the mirror.

The mirror equation is a fundamental equation in optics that relates the distance of an object from a curved mirror to the distance of its image from the mirror. It is also known as the mirror formula.

To find the focal point of a parabolic mirror, we need to use the mirror equation:

[tex]1/f = 1/p + 1/q[/tex]

where f is the focal length, [tex]p[/tex] is the distance between the mirror and the object, and q is the distance between the mirror and the image.

For a parabolic mirror, we can assume that the object is at infinity, so [tex]p[/tex] is essentially infinite. Therefore, the equation simplifies to:

[tex]1/f = 1/q[/tex]

We also know that the diameter of the mirror is [tex]20[/tex] feet, which means the radius is 10 feet. Using the equation for a parabola:

[tex]y^2 = 4px[/tex]

where y is the distance from the vertex of the parabola to a point on the curve, and x is the horizontal distance from the vertex. At the opening of the mirror, [tex]y = 0[/tex] and [tex]x = 10[/tex], so we can solve for [tex]p[/tex]:

[tex]0^2 = 4p(10)[/tex]

[tex]p = 0[/tex]

This means the mirror's focus is located at its vertex, which is [tex]6 feet[/tex] deep. Therefore, the heat source will be concentrated at a point [tex]6 feet[/tex] deep in the center of the mirror.

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The force between the Earth and the moon is determined by the gravitational attraction between the two objects, which is given by the equation F = G(m1m2)/r^2, where F is the force, G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.

Using the given values, we can calculate the force between the Earth and the moon as follows:

F = G(m1m2)/r^2
F = (6.67 x 10^-11 N*m^2/kg^2) * (5.98 x 10^24 kg) * (7.35 x 10^22 kg) / (3.85 x 10^8 m)^2
F = 1.98 x 10^20 N

Therefore, the force between the Earth and the moon is approximately 1.98 x 10^20 Newtons. This force is what keeps the moon in orbit around the Earth.

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The substances listed in order of increasing boiling point (lowest first) are C2H6, CH3CHO, C2H5OH, and CH3COOH.

C2H6 is a non-polar molecule, meaning it has no permanent dipole moment. The intermolecular forces holding the molecules together are van der Waals' forces, which are weak and require the least amount of energy to overcome.

CH3CHO is a polar molecule due to the carbonyl group, which creates a permanent dipole moment. The intermolecular forces holding the molecules together are dipole-dipole forces, which are stronger than van der Waals' forces.

C2H5OH and CH3COOH are both polar molecules due to the presence of the hydroxyl group (-OH) and the carboxyl group (-COOH), respectively. The intermolecular forces holding the molecules together are hydrogen bonds, which are much stronger than dipole-dipole or van der Waals' forces.

The order of boiling points can be explained by the strength of the intermolecular forces. C2H6 has the weakest intermolecular forces, so it requires the least amount of energy to overcome them and boil. CH3CHO has stronger dipole-dipole forces than C2H6, so it requires more energy to boil. C2H5OH and CH3COOH both have hydrogen bonds, which are the strongest intermolecular forces, so they require the most energy to overcome and boil.

In summary, the boiling point depends on the intermolecular forces present, which are determined by the polarity of the molecule and its molecular mass. Polar molecules with hydrogen bonding have stronger intermolecular forces and higher boiling points.

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The distance between the two charges is approximately 0.0107 meters, or 10.7 millimeters.

Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, can be used to compute the attractive force between two point charges.

Coulomb's Law is formulated as follows:

F = k × |q₁ × q₂| / r²

where:

F = force between the charges (in newtons, N)

k = Coulomb's constant, which is approximately 8.99 x 10⁻⁹Nm²/C²

q₁ and  q₂ = charges of the two point charges (in coulombs, C)

r = distance between the charges (in meters, m)

Given:

q₁ = +90.0 μC = 90.0 x 10⁻⁶C

q₂ = -40.0 μC = -40.0 x 10⁻⁶ C

F = 293 N

k = 8.99 x 10⁹ Nm²/C²

Plugging these values into the formula, we can solve for r:

293 = 8.99 x 10⁹ x |90.0 x 10⁻⁶ x -40.0 x 10⁻⁶| / r²

To simplify the calculation, we can take the absolute value of the product of the charges, since distance is always positive:

293 =  8.99 x 10⁹ x 90.0 x 10⁻⁶ x -40.0 x 10⁻⁶ / r²

Now we can solve for r:

r² = 8.99 x 10⁹ x90.0 x 10⁻⁶ x -40.0 x 10⁻⁶/ 293

r² = 0.000011456

r =  √(0.000011456)

r ≈ 0.0107 m

So, the distance between the two charges would be approximately 0.0107 meters, or 10.7 millimeters.

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The statement "The mass of a body has a bigger effect on the moment of inertia than the location of the center of mass of that body" is generally true.

The moment of inertia (I) is a measure of an object's resistance to rotational motion about an axis. It depends on both the mass of the object and its distribution relative to the axis of rotation. The formula for the moment of inertia is given by:
I = Σ mi * ri^2

where mi is the mass of each particle in the object and ri is the distance of each particle from the axis of rotation.

From this formula, we can see that the mass of the body (mi) has a direct influence on the moment of inertia. The greater the mass, the greater the moment of inertia.

On the other hand, the center of mass is the point at which an object's mass can be considered to be concentrated. The location of the center of mass does not directly affect the moment of inertia; rather, it is the distribution of the mass around the axis of rotation that matters. Therefore, changing the location of the center of mass without changing the mass distribution would not have a significant impact on the moment of inertia.

In conclusion, the mass of a body generally has a bigger effect on the moment of inertia than the location of the center of mass of that body, as the mass directly contributes to the moment of inertia while the center of mass location does not.

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