if the 2 currents are same direction and forces are attractive, what is the direction of force wire 1 on wire 2

a.  the depth of cut  is 0.625 inches.

b. the material removal rate is 0.003125 cubic inches per minute.

c. the time required to complete the cutting pass is 20 minutes.

a) The required depth of cut can be determined by :

DOC = (4 in - 2.75 in)/2 = 0.625 in

Therefore, the depth of cut is  0.625 inches.

b) The material removal rate can be found by applying:

MRR = DOC x Width of cut x Feed rate

assuming we are using a standard carbide insert tool with a width of cut of 0.5 inches.

MRR = 0.625 in x 0.5 in x 0.010 in/rev = 0.003125 cubic inches per minute

c) The time required to complete the cutting pass is determined by:

Time = Length of cut / (Cutting speed x Width of cut x Feed rate)

Time = 48 in / (400 ft/min x (0.5 in) x (0.010 in/rev) x (1/12 ft/in)) = 20 minutes

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The formula C=4R, where is the permittivity of open space, may be used to determine the capacitance of a merged mercury drop, assuming it is an isolated sphere. The capacitance is around 1.68 pF with R = 5.61 mm.

The formula C=4R, where R is the drop's radius and is the permittivity of free space, may be used to determine the capacitance of a merged mercury drop. As the capacitance of an isolated sphere is exactly proportional to its radius, the capacitance produced by the merger of two drops with similar radii is equal to the total of the capacitances of the individual drops. Given that the radius of the combined drop in this instance is R = 5.61 mm, the capacitance can be estimated using the formula C = 4(8.85 x 10-12 F/m) (5.61 x 10-3 m)2, yielding a capacitance of around 1.68 pF.

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If a tsunami warning is issued for the island, they will have approximately 11.7 hours before the waves arrive.

What is Magnitude?

Magnitude is a measure of the strength or intensity of a physical quantity or phenomenon, such as an earthquake or a sound wave. It is often expressed using a numerical scale, with higher values indicating greater strength or intensity. In the case of earthquakes, magnitude is typically measured using the Richter scale or the moment magnitude scale, which take into account the amplitude of seismic waves and the energy released by the earthquake.

To calculate the time it takes for a tsunami to travel from Japan to the island, we can use the following formula:

t = (2 * pi * d) / g * ln(1 + sqrt(h/d))

where t is the time it takes for the tsunami to travel, d is the average water depth, h is the wave height, and g is the acceleration due to gravity (9.8 m/s^2).

Magnitude of the earthquake: 8.5

Wavelength of the tsunami: 200 km = 200,000 m

Average water depth: 4,900 m

To calculate the wave height, we can use the following formula:

h = (M / 5) * (D / 10)^1/2

where M is the magnitude of the earthquake and D is the distance between the earthquake epicenter and the observation point (in this case, the island). Note that this formula is an approximation and may not be accurate for all cases.

Using the given values, we get:

D = 8,000 km = 8,000,000 m

h = (8.5 / 5) * ((8,000,000 / 10)^1/2) = 2,738.6 m

Substituting these values into the formula for t, we get:

t = (2 * pi * 4,900) / 9.8 * ln(1 + sqrt(2,738.6/4,900)) = 11.7 hours

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The marble that rolled down an inclined ramp with an acceleration of 0.500 m/s for 7.00 seconds will travel 12.3 meters from the point where it was released. Thus, the correct option is A.

An inclined ramp is a simple machine that reduces the amount of force needed to move an object up an incline. The force that makes the marble move is gravity. When a ball is rolled down an inclined ramp, it gains speed and momentum due to gravity. The formula for the distance travelled by a ball is given by:

d = (1/2) × a × t²

where, a is the acceleration of the ball, t is the time for which the ball is rolled down the ramp, d is the distance travelled by the ball.

Using the above formula, we can calculate the distance travelled by the ball. So, substituting the given values in the formula:

d = (1/2) × 0.500 m/s² × (7.00 s)²

d = (1/2) × 0.500 m/s² × 49.00 s²

d = 12.3 meters

Therefore, the correct option is A.

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In addition to hundreds of smaller objects they have been discovering in the Kuiper Belt recently, astronomers were surprised to find dwarf planet Eris.

The first object that was bigger than Pluto was Eris. The initial estimate of Eris' size was 1,240 miles (2,000 kilometers) in diameter. It was later discovered to be a bit smaller, with a diameter of 1,163 miles (1,864 kilometers). Its moon, Dysnomia, was also discovered.Eris' orbit is far more eccentric than Pluto's, ranging from 38 to 97 astronomical units (AU) from the Sun.

Eris takes 557 Earth years to orbit the Sun. Despite the fact that Pluto's path also varies in shape, it is always closer to the Sun than Eris. Pluto and Eris were both discovered in the early 21st century, in 1930 and 2005, respectively. Because it was the largest known body in the Kuiper Belt, Pluto was formerly classified as the Solar System's ninth planet. Following the discovery of Eris and other trans-Neptunian objects, Pluto was reclassified as a dwarf planet.

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The kinetic energy of the trunk increases by ½ mvf² = ½ m(10.65 m/s)²= 71.44 J during the displacement.

Net work = ΔK

W = Fd cosθ

W1 = F1d cosθ = (5.86 N)(3.010 m) cos(67.8°) = 6.99 J

W2 = F2d cosθ = (9.180 N)(3.010 m) cos(67.8°) = 10.97 J

W3 = F3d cosθ = (3.850 N)(3.010 m) cos(67.8°) = 4.58 J

Net work = W1 + W2 + W3 = 6.99 J + 10.97 J + 4.58 J = 22.54 J

Therefore, the net work done on the trunk by the three forces is 22.54 J.

ΔK = ½ mvf² - ½ mvi²

Since the trunk moves a distance of 3.010 m and is initially at rest, we can use the equation:

vf² = 2ad

where a is the acceleration of the trunk, which is given by:

a = ΣF / m

where ΣF is the net force on the trunk, which we can find using:

ΣF = F1 + F2 + F3

ΣF = (5.86 N + 9.180 N + 3.850 N) = 18.89 N

Therefore, the acceleration of the trunk is:

a = ΣF / m = 18.89 N / m

Since the trunk moves leftward, the acceleration is also leftward, so we can use a negative value for a.

Substituting the values for a and d, we get:

vf² = -2(-18.89 N / m)(3.010 m) = 113.51 (m/s)²

Taking the square root, we get:

vf = 10.65 m/s

Therefore, the change in kinetic energy of the trunk is:

ΔK = ½ mvf² - ½ mvi² = ½ m(10.65 m/s)²- 0 = ½ mvf²

Kinetic energy is a type of energy that an object possesses by virtue of its motion. It is defined as the energy an object has due to its motion and is proportional to the mass of the object and the square of its velocity. The formula for kinetic energy is KE = 1/2mv^2, where m is the mass of the object and v is its velocity.

Kinetic energy is a scalar quantity and has units of joules in the International System of Units (SI). It is a fundamental concept in physics and is used to describe many physical phenomena, including the motion of particles, the behavior of gases, and the motion of waves. In many cases, kinetic energy can be transformed into other forms of energy. For example, when a ball is thrown upwards, its kinetic energy is gradually converted into gravitational potential energy as it moves higher and higher.

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The researcher's observation that more auxin collects in the sides of stems and roots that are not exposed to light is likely due to the phenomenon of phototropism.

In the process of phototropism, light influences the direction and rate of growth of plant cells. In particular, light induces the cells on one side of a stem or root to create less auxin than the cells on the shaded side. Less auxin is produced on the lighted side and more auxin is produced on the shaded side as a result. The hormone auxin is essential for controlling the growth and development of plants. Auxin generally promotes cell growth and elongation at greater concentrations while inhibiting cell elongation at lower concentrations. Since the cells on the lighted side of the stem or root will contain less auxin when there is light.

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Answer:

Yo dude, if you had a beaker of liquid in outer space, it wouldn't push down on the bottom or the sides of the beaker like it would on Earth. In space, there's no gravity to make the liquid settle down, so it forms a round shape because of surface tension. So basically, the liquid would just float around in a ball inside the beaker. If you moved the beaker around, the liquid would just roll around with it like a bouncy ball.

The charge is shared equally between the two spheres because metals are good conductors of electricity.

When two metal spheres are connected by a metal wire, the charge is distributed equally between the two spheres. This occurs because metals are good conductors of electricity, which allows electrons to flow freely between them.

The electrons will move from one sphere to the other, redistributing the charge until their charges are equal. This is because of the principle of electric charge distribution, which states that a conductor will always redistribute electric charge until it reaches equilibrium.

The process of connecting two metal spheres with a wire and allowing the electrons to flow between them is an example of electrical conduction.

This is a fundamental process in electrical circuits and is the basis for many important technologies, including electronics, power generation, and transmission.

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"The colours on an oil slick are caused by reflection and interference." Correct option is B.

Different bands of the oil slick create different colours as the oil film progressively thins from the centre to the edges.

Interference is what gives an oil slick drifting on water or a soap bubble in the sun their vibrant colours. The colours that interact most positively are the ones that are most vibrant. Thin film interference is the name given to the phenomenon because it occurs when light reflected from various thin film surfaces interferes with one another.

The most crucial interfering principle is the superposition principle.

This hair colour procedure primarily uses jewel tones and rainbow colours, including burgundy, royal blue, deep purple, green, and deep red. Alternating the colours that give your hair an oil spill appearance is the best method to make your skin tone and hair look good together. Best choice is B.

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A maintenance expenditure should be capitalized if it increases the salvage value of the asset or extends the useful life of the asset.

An expenditure is a payment made in return for a product or service. Capital expenditure is money spent by a company on long-term assets like equipment and buildings.

Capitalizing refers to recording a cost or expense on the balance sheet for a future period rather than recognizing it immediately in the current period.

Capitalizing expenditure means the company will recognize the expenditure as an asset, which will be amortized over its useful life as opposed to expenses in the current period.

Therefore, a maintenance expenditure should be capitalized if the expenditure increases the extends the useful life of the asset.

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Answer:

Approximately [tex]28.6\; {\rm m}[/tex].

Explanation:

Let [tex]u[/tex] denote the initial velocity of the vehicle, and let [tex]v[/tex] denote the velocity of the vehicle after skidding. It is given that the initial velocity was [tex]u = 22.4\; {\rm m\cdot s^{-1}}[/tex]. Since the vehicle skidded to a stop, [tex]v = 0\; {\rm m\cdot s^{-1}}[/tex].

Let [tex]t[/tex] denote the duration of the skid. It is given that [tex]t = 2.55\; {\rm s}[/tex].

Under the assumption that acceleration is constant, SUVAT equations will apply.

Specifically, the SUVAT equation [tex]x &= (1/2)\, (u + v)\, t[/tex] will be satisfied. In this equation, the displacement of the vehicle is equal to average velocity times duration. This equation allows the displacement [tex]x[/tex] to be found from [tex]u[/tex], [tex]v[/tex], and [tex]t[/tex] without knowing the exact value of acceleration:

[tex]\begin{aligned}x &= \left(\frac{u + v}{2}\right)\, t \\ &= \left(\frac{22.4 + 0}{2}\; {\rm m\cdot s^{-1}}\right)\; (2.55\; {\rm s}) \\ &\approx 28.6\; {\rm m}\end{aligned}[/tex].

The speed of the electron when it strikes the anode is vfinal = 2.6x107 m/s.

Vacuum tubes were often utilized in radios and other devices before the development of solid-state electronics. A diode is a straightforward sort of vacuum tube that simply consists of two electrodes enclosed in a highly evacuated space.

The cathode, one electrode, emits electrons from its surface while being kept at a high temperature.

The cathode and the opposite electrode, known as the anode, are kept at a potential difference of a few hundred volts, with the anode being at a greater potential.

An electron leaves the

cathode of a diode with a radius of 6.200x10⁻²cm and

an anode with a radius of 0.5580 cm, and

with a potential difference of 320 V.

The initial speed of the electron is 0 m/s.

The speed (vfinal) when it strikes the anode can be calculated using the equation vfinal = (2 × e × V)1/2,

where e is the electron charge (1.6x10⁻¹⁹C).

Therefore, the speed of the electron when it strikes the anode is

vfinal = (2 × 1.6x10⁻¹⁹ × 320)1/2 = 2.6x107 m/s.

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If the masses of two planets in space that gravitationally attract each other are doubled and the distance between them is also doubled, then the force between them remains the same.

To determine the force between two planets, we use the formula:

F = Gm1m2/r^2

where F is the force of gravitational attraction between the two planets, G is the gravitational constant, m1 and m2 are the masses of the planets, and r is the distance between them.

If both masses are doubled and the distance between them is also doubled, the new force between them can be calculated as follows:

F' = G(2m1)(2m2)/(2r)^2

Simplifying this expression, we get:

F' = Gm1m2/r^2

which is the same as the original force between the planets.

Therefore, if the masses of two planets are doubled and the distance between them is also doubled, the force between them remains the same.

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Given equal-sized samples (volumes) of galena and quartz, the Galena sample will feel heavier because of its higher specific gravity. Thus, the correct option is A.

Specific gravity is the ratio of the density of a substance to the density of a standard substance in physics. It's typically applied to liquids and solids, but it may also be applied to gases. The most often utilized standard material for liquids and solids is water at 4°C. A substance's specific gravity is dimensionless and is often represented by the Greek symbol ρ.

Relative Density of the given substances:

Galena's specific gravity is 7.5, Quartz's specific gravity is 2.65, and Liquid mercury's specific gravity is 13.6. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water. The specific gravity of water is 1.0. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water.

We can conclude from the values above that liquid mercury is heavier than galena, which is in turn heavier than quartz. Therefore, since both quartz and galena are being measured with equal sizes or volumes, galena will feel heavier than quartz.

Therefore, the correct option is A.

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When a current travels through a conductor in a circular motion, a magnetic field with growing concentric circles is created.

Electromagnetism is established when an electrical current flows through a simple conductor, such as a length of wire or cable.

As magnetic fields produced by moving charges are proportional to the current, a conductor carrying current creates a magnetic field around it. Generally speaking, the sub-atomic particles in the conductor, such as the moving electrons in the atomic orbitals, are responsible for this magnetic field.

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A change in velocity in short period of time means the acceleration is large, hence the net force must be proportionately large as well.

A force is a physical quantity that induces a body to undergo an alteration in speed, direction of motion, or shape. A force can be classified as a push or a pull. When forces are equal, the forces are balanced and the object is not moving. Otherwise, if the forces are not equal, making it unbalanced will not give the object any movement.

The force that induces the change in the speed or direction of an object is referred to as a net force. The net force is equal to the product of the mass of the object and its acceleration. Newton (N) is the unit of measurement for force.

When a ball bounces against a wall, there will be a large change in velocity in a short period of time. This means the acceleration is large, hence the net force must be proportionately large as well.

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Answer:

The weight of the 225-kg space probe on the moon is 364.5 N (newtons).

Explanation:

To calculate the weight of the space probe on the moon, we can use the formula:

weight = mass x acceleration due to gravity

where mass is given as 225 kg and acceleration due to gravity on the moon is 1.62 m/s^2.

weight = 225 kg x 1.62 m/s^2

weight = 364.5 N

Therefore, the weight of the 225-kg space probe on the moon is 364.5 N (newtons).

The spiral galaxies are characterized by the arms winding out from a central nucleus while the elliptical galaxies are characterized by their lack of structure or a central bulge.

Star formation refers to the process by which dense areas within molecular clouds in interstellar space, typically lasting tens of millions of years, form newborn stars. It takes a long time for stars to form, and this process is not well understood.

In comparison to spiral galaxies, elliptical galaxies have low star formation.

Furthermore, elliptical galaxies are made up of stars with a wide range of ages, indicating that the star formation process was rapid and early on in their history.

Spiral galaxies have more gas and dust in their disks than elliptical galaxies, and these are the sites of intense star formation.

The arms are believed to be regions of higher density of stars and interstellar material, as well as more significant gravitational interactions among stars, gas, and dust than in the rest of the disk.

Thus, spiral galaxies are sites of ongoing star formation while elliptical galaxies are mainly populated by old and evolved stars that no longer form. Therefore, spiral galaxies have a higher rate of star formation than elliptical galaxies.

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The two planets that are coming together are Saturn and Jupiter. On December 21st, 2020, the two planets will be at their closest point, an event known as the Great Conjunction.

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The distance did the arrow travel over if it were in the air for 2.4 seconds is  100.8 meters.

An arrow leaves a bow with a speed of 42 m/s. Its velocity is reduced to 34 m/s by the time it hits its target. And the arrow traveled in the air for 2.4 seconds.

To find the distance traveled by the arrow, we can use the following formula:

S = v₀t + 1/2at²

where, S = distance traveled v₀ = initial velocity = 42 m/s, t = time taken = 2.4 s, a = acceleration = ? u = final velocity = 34 m/s.

As per the question, the arrow is traveling through the air, so the acceleration is due to gravity, which is equal to 9.8 m/s².So, a = 9.8 m/s². Now, we can substitute the given values in the above formula:

S = 42 m/s × 2.4 s + 1/2 × 9.8 m/s² × (2.4 s)²

S = 100.8 m.

The arrow traveled approximately 100.8 meters in the air.

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The sailplane which is going from Earth to Mars is accelerating at 0.033 m/s² in the direction of solar radiation force.

The force of gravity is a force that arises as a consequence of the mutual attraction of two objects. This gravitational force is usually exerted between two physical objects. Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is proportional to the product of their masses.

Acceleration is the rate at which an object changes its speed or direction. Acceleration is a vector quantity that can be positive or negative. If the acceleration is negative, the object slows down. If the acceleration is positive, the object speeds up.

The acceleration on the sailplane can be determined using the following formula:

[tex]F_{net} = ma[/tex]

Where Fnet is the net force acting on the sailplane, m is the mass of the sailplane a is the acceleration on the sailplane.[tex]F_{net} = ma[/tex]

The net force acting on the sailplane can be calculated as:

[tex]F_{net} = F_{rad} - F_{gravitySun} - F_{gravityEarth}[/tex]

Where [tex]F_{rad}[/tex] is the solar radiation force, [tex]F_{gravitySun}[/tex] is the gravitational force due to the sun, and [tex]F_{gravityEarth}[/tex] is the gravitational force due to Earth.

Putting the given values in the above formula:

[tex]F_{net} = 7.70 \times 10^2 N - 173 N - 1.00 \times 10^2 N = 497 N[/tex]

The acceleration on the sailplane is given as:

[tex]a = F_{net} / ma = (497\  N) / 14,900 \ kg = 0.033 \ m/s^2[/tex]

The magnitude of the acceleration on the sailplane is 0.033 m/s² (rounded to three significant figures).

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The electric field at a point "+P" on the y-axis 0. 800 m from the origin is  53.3 N/C.  The net force on "p" (magnitude and direction) is 5.33 x 10^-5 N.

To find the electric field at point "p" on the y-axis, we can use Coulomb's law and the principle of superposition.

First, let's find the electric field contribution at point "p" due to the charge q1 at the origin. We can use Coulomb's law for point charges to find the electric field contribution:

E = k * q / r²

where k is Coulomb's constant, q is the charge, and r is the distance from q to point "p". In this case, r is simply the distance from the origin to point "p", which is 0.8 m. Plugging in the values:

E1 = (9.0 x 10⁹ N*m²/C²) * (+4.00 x 10-⁶ C) / (0.8 m)²

E1 = 18.0 N/C (upwards on the y-axis)

Similarly, the electric field contribution at point "p" due to the charge q2 on the x-axis and at a distance r2 can be calculated Using the Pythagorean theorem, we can find this distance:

r2 = √[(0.3 m)² + (0.8 m)²] = 0.854 m

Plugging in the values:

E2 = (9.0 x 10⁹ N*m²/C²) * (-6.00 x 10-⁶ C) / (0.854 m)²

E2 = 50.6 N/C (at an angle of arctan(0.8/0.3) = 69.4 degrees below the negative x-axis)

To find the total electric field at point "p", we add the contributions from q1 and q2 using vector addition:

Etotal = E1 + E2

Using the component method, we can find the magnitude and direction of the total electric field:

|Etotal| = √[(E_total,x)² + (E_total,y)²]

= √[(-18.0 N/C)² + (50.6 N/C)²]

= 53.3 N/C

θ = arctan[(E_total,y) / (E_total,x)]

= arctan[(50.6 N/C) / (-18.0 N/C)]

= -69.2 degrees

Therefore, the magnitude of the net force on a +1.00 C test charge placed at point "p" is,

Fnet = qtest * |E_total| = (+1.00 x 10^-6 C) * (53.3 N/C) = 5.33 x 10^-5 N

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The additive inverse of each given vector in the appropriate vector space are

(a) The additive inverse of [2, 3] in [tex]R_2[/tex] is [-2, -3].

(b) The additive inverse of [tex]-1 + 3x - 8x^2[/tex] in P2 is [tex]1 - 3x + 8x^2[/tex].

(c) The additive inverse of [1, 2; - 2, 0] in [tex]M_{2\times2[/tex] is [-1, -2; 2, 0].

The additive inverse of a vector [tex]\mathbf{v}[/tex] in a vector space is the vector [tex]-\mathbf{v}[/tex] that, when added to [tex]\mathbf{v}[/tex], gives the zero vector.

(a) The additive inverse of the vector [tex][2, 3] \in \mathbb{R}^2[/tex] is [tex][-2, -3][/tex] since [tex][2, 3] + [-2, -3] = [0, 0][/tex].

(b) The vector space [tex]P_2[/tex] consists of all polynomials of degree at most [tex]2[/tex]. The vector [tex]-1 + 3x - 8x^2 \in P_2[/tex] has additive inverse [tex]1 - 3x + 8x^2[/tex], since [tex](-1 + 3x - 8x^2) + (1 - 3x + 8x^2) = 0[/tex].

(c) The vector space [tex]M_{2 \times 2}[/tex] consists of all [tex]2 \times 2[/tex] matrices. The matrix [tex][1, 2; -2, 0] \in M_{2 \times 2}[/tex] has additive inverse [tex]$[-1, -2; 2, 0]$[/tex], since [tex]\begin{bmatrix} 1 & 2 \ -2 & 0 \end{bmatrix} + \begin{bmatrix} -1 & -2 \ 2 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}[/tex].

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A net torque of [tex]6.0×10^−3 N⋅m[/tex] is sufficient to produce the desired angular acceleration of [tex]150 rad/s^2[/tex].

The net torque required to produce an angular acceleration in a rotating object can be calculated using the formula: net torque = moment of inertia × angular acceleration In this case, the moment of inertia of the grinding wheel is given as 4.0×10^−5 kg⋅m^2 and the angular acceleration required is 150 rad/s^2.

Therefore, the net torque required can be calculated as: net torque = [tex](4.0×10^−5 kg⋅m^2) × (150 rad/s^2) = 6.0×10^−3 N⋅m[/tex]To explain this result, we need to understand the relationship between torque and angular acceleration. Torque is the rotational equivalent of force and it is defined as the product of force and the perpendicular distance between the line of action of the force and the axis of rotation.

When a torque is applied to a rotating object, it produces an angular acceleration in the object, which is a measure of how quickly the object's rotational speed changes.

The moment of inertia of an object is a measure of its resistance to changes in its rotational motion. It depends on the object's mass distribution and the distance of each element of mass from the axis of rotation. Objects with larger moments of inertia require more torque to produce a given angular acceleration than objects with smaller moments of inertia.

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The answer is C.  Sphere A is repelled from sphere B

Step by step explanation:

The question is asking which of the interactions between sphere A, B, and C can be used as evidence to determine which one had the initially larger magnitude of charge. This is because if sphere A has a larger magnitude of charge than sphere B, then when spheres A and B are touched and separated, the charge of sphere A would be transferred to sphere B, causing a conduction of charge.

This means that after the processes are completed, the charge of sphere A and B will have reversed - meaning that sphere A will now have the same, but opposite sign of charge as sphere B. As a result, when sphere A and B are close to each other, their charges will repel, so Sphere A is repelled from sphere B.

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The ratio of the orbital period of planet B to that of planet A is T_B/T_A = Squareroot 8.

A planet is an astronomical object that orbits a star and does not produce its own light. The vast majority of the thousands of objects we call planets orbit a star in our Solar System. This specific system includes the sun and the eight planets that orbit around it.

Two planets A and B, where B has twice the mass of A, orbit the Sun in circular orbits. The radius of the circular orbit of planet B is two times the radius of the circular orbit of planet A. The formula for calculating the time period of a circular orbit is:

T = (2πr) / v

where, r = radius, v = velocity

For circular orbits, T ∝ (r³/²)

Therefore, T_B/T_A = (r_B³/²) / (r_A³/²)T_B/T_A = (2³/²) / 1³/2T_B/T_A = (square root 8)/1T_B/T_A = Squareroot 8.

Therefore, the ratio of the orbital period of planet B to that of planet A is T_B/T_A = Squareroot 8.

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A) The capacitance of the spherical capacitor is 1.45 pF (picofarads), B) The radius of the inner sphere is 3.60 cm. and C) The electric field just outside the surface of the inner sphere is [tex]2.36 * 10^6 V/m[/tex] (volts per meter).

To calculate the capacitance, we can use the formula C = Q/V, where Q is the charge and V is the potential difference. Plugging in the values, we get [tex]C = (3.20 * 10^{-9} C)/(250 V) = 1.28 * 10^{-11} F[/tex].

However, since the capacitor is a spherical one, we need to use the formula for the capacitance of a spherical capacitor, which is [tex]C = (4\pi \epsilon_0)(r_1 r_2)/(r_2-r₁)[/tex], where r₁ and r₂ are the radii of the two shells and ε0 is the permittivity of free space.

Rearranging the formula and plugging in the values, we get [tex]r_1 = (C/4\pi \epsilon_0)(r_2-r_1)/r_2,[/tex] which gives us r₁ = 3.60 cm.

To calculate the electric field just outside the surface of the inner sphere, we can use the formula

E = [tex]\frac{Q}{4\pi\epsilon_0 r^2}[/tex], where r is the radius of the inner sphere.

Plugging in the values, we get [tex]E = (3.20 * 10^{-9} C)/(4\pi\epsilon_0(0.0460 m)^2) = 2.36 * 10^6 V/m.[/tex]

This electric field arises due to the charge on the inner sphere and induces an opposite charge on the outer shell of the capacitor.

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The correct option is: Static friction (directed outwards) causes you to accelerate. (Option C)

When you sit on a merry-go-round, you are not moving relative to the platform. Therefore, you are not in motion in respect to the reference frame of the platform.

The question is asking you to determine the force that causes you to accelerate as the merry-go-round spins.

Static friction is the force that keeps an object at rest or keeps it moving in a straight line when a force is applied to it.

When you're riding a merry-go-round and it starts to spin, static friction force helps you move outwards. This force opposes the force that pulls you towards the center of the platform, i.e., centripetal force.

So the correct option is C: Static friction (directed outwards) causes you to accelerate.

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