a mass on a spring bobs up and down over a distance of 17 cm from the top to the bottom of its path once each second. what are its period and amplitude?

Answer:

Scalar quantities are physical quantities which have a magnitude and direction.

e.g. in 5 km, 5 is the magnitude(number) and km is the unit.

some scalar quantities are mass, length, distance, speed, power, energy, temperature etc.

Answer: Values with magnitude but without direction

Explanation:

Majorly there exists two types of quantities, Scalar and Vector.

Vectors: Quantities, with magnitude and direction.

Example: Force, Displacement

Scalars: Quantities, with magnitude but without direction.

Example: Weight, Length, Quantity

we do not need direction to define weight,

it is just 5 kilograms, and NOT 5 kilograms towards east.

The engine in a small airplane is specified to have a torque of 500 N⋅m. This engine drives a 2.3-m-long, 40 kg single-blade propeller.The engine in a small airplane is specified to have a torque of 500 N⋅m. it takes approximately 18.6 seconds for the propeller to reach 2000 rpm.

To determine how long it takes the propeller to reach 2000 rpm, we need to use the torque equation:

T = Iα

where T is the torque, I is the moment of inertia, and α is the angular acceleration.

We can rearrange this equation to solve for α:

α = T/I

where T is the torque and I is the moment of inertia.

The moment of inertia of a thin rod about its center of mass is given by:

I = (1/12)M\(L^2\)

where M is the mass of the rod (propeller) and L is its length.

In this case, M = 40 kg and L = 2.3 m. Therefore:

I = (1/12)(40 kg)(\(2.3 m)^2\)= 44.33 kg⋅\(m^2\)

The torque T is given as 500 N⋅m.

Substituting the values in the equation for α, we get:

α = T/I = (500 N⋅m) / (44.33 kg⋅\(m^2\)) = 11.27 rad/\(s^2\)

We need to find the time it takes for the propeller to reach 2000 rpm, which is equivalent to 209.44 rad/s. We can use the following kinematic equation to find the time t:

ω = ω0 + αt

where ω0 is the initial angular velocity, which is zero in this case.

Substituting the values, we get:

209.44 rad/s = 0 + (11.27 rad/\(s^2\)) t

Solving for t, we get:

t = 18.6 seconds (rounded to one decimal place)

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Answer:

\(A=90^0-B\\B+C=180^0-90^0=90^0\\C=90^0-B\\A=C\)

Explanation:

The temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×10⁴ Pa is approximately 14.3°C.

Using the ideal gas law, we can write: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature. Since the mass of air is not changing, we can write: PV = constant.

Applying this to the situation where the air mass rises to a level where the pressure is 8.70×10⁴ Pa, we get:

Dividing the second equation by the first and using the fact that γ=Cp/Cv=1.40 for air, we get:

Solving for T2, we get:

Thus, the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.70×10⁴ Pa is approximately 14.3°C.

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Answer:

Do you want the independent or dependent? Independent is the Car and the dependent is the meters traveled.

Explanation:

Answer:

sample answer

In this situation, elevation is dependent on time. So, the dependent variable is elevation in feet.

Explanation:

Answer:

hjbyvtf ghbj

Explanation:

uhgbnm,likjh

Answer:

Explanation:

Writing out the Newton's Law pf Cooling:

dT/dt = -k * (T - A),

where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.

If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C,

T = 100

A = 25

dT = 100 - 90 = 10

dt = 1

Putting the figures into the equation:

10/1 = -k * (100 - 25)

k = -10/75°C

After 4 minutes, dT/4 = 10/75 (100 - 25) = 10

dT = 40

Temperature after 4 minutes = 100 - 40 = 60°C

The temperature of a cup of coffee varies according to Newton's Law of Cooling, the temperature of the coffee after 4 minutes is approximately 67°C.

To tackle this problem, we can apply Newton's Law of Cooling's differential equation and solve it using variable separation.

dT/dt = -k(T - A)

At t = 0 (initial condition): T = 100°C

At t = 1 minute: T = 90°C

dT/dt = -k(T - A)

At t = 0: dT/dt = -k(100 - 25)

So,

-10 = -k(75)

k = 10/75

Separating variables and integrating, we have:

1/(T - A) dT = -k dt

∫(1/(T - A)) dT = ∫(-k) dt

ln|T - A| = -kt + C

ln|100 - 25| = 0 + C

ln|75| = C

So, the equation will be:

ln|T - A| = -kt + ln|75|

ln|(T - 25)/(75)| = -kt

Now,

ln|((T - 25)/(75))| = -(10/75)(4)

|((T - 25)/(75))| = \(e^{(-40/75)\)

T - 25 = ± 75 *  \(e^{(-40/75)\)

T = 25 ± 75 *  \(e^{(-40/75)\)

T ≈ 25 ± 42.42

Therefore, the temperature of the coffee after 4 minutes is approximately:

T ≈ 25 + 42.42 = 67.42°C

Thus, the temperature of the coffee after 4 minutes is approximately 67°C.

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The planet that has ⅒ of the earth's gravity is the moon.

Gravity is the force exerted by any object with mass on any other object with mass.

Gravity is the force on Earth's surface, of the attraction by the Earth's masses, and the centrifugal pseudo-force caused by the Earth's rotation, resulting from gravitation.

The gravity on the planet Earth is 1 with a acceleration due to gravity of 9.8m/s². One-tenth of this is 0.1 (0.98m/s²).

The planet with the above gravity is the moon with a gravity of 0.166.

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Answer:

Second, fundamental unit of time, now defined in terms of the radiation frequency at which atoms of the element cesium change from one state to another. The second was formerly defined as 1/86,400 of the mean solar day—i.e., the average period of rotation of the Earth on its axis relative to the Sun.

source britannica

Explanation:

This question is incomplete, the complete question is;

Consider a capacitor made of two rectangular metal plates of length L and width W, with a very small gap s between the plates. There is a charge +Q on one plate and a charge −Q on the other. Assume that the electric field is nearly uniform throughout the gap region and negligibly small outside.

Calculate the attractive force that one plate exerts on the other.

Remember that one of the plates doesn't exert a net force on itself. (Enter the magnitude. Use any variable or symbol stated above along with the following as necessary : ε0.)

Answer:

the attractive force F that one plate exerts on the other is Q² / 2ε0⊥ω

Explanation:

Given the information in the questioN;

Electric field by one plate at the pos of other plate is expressed as;

E₊ = r / 2ε0 = Q/2ε0A

SO force on the other plate

F = /QE₊ / = Q² / 2ε0A

F = Q² / 2ε0⊥ω

Therefore the attractive force that one plate exerts on the other is F = Q² / 2ε0⊥ω

The attractive force which one plate exert on the other is

\(F = \frac{Q^2}{2\epsilon LW}\)

From the attached diagram, the charge on the rectangular plates are shown;

since we are told the metal plates is rectangular, the area of the plate is

\(A = L * W\)

The electrical field on one plate at one point against the other will be

\(E_r = \frac{r}{2\epsilon} \\E_r = \frac{Q}{2\epsilon A}\\\)

The force on the other plate can be calculated as

\(F = |QE_r| = \frac{Q^2}{2\epsilon A}\\ F = \frac{Q^2}{2\epsilon LW}\)

The attractive force which one plate exert on the other is

\(F = \frac{Q^2}{2\epsilon LW}\)

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Answer and Explaination:

To solve this problem, we can analyze the forces acting on the mass as it travels up the inclined plane. We'll consider the gravitational force and the force exerted by the spring.

1. Gravitational force:

The force due to gravity can be broken down into two components: one perpendicular to the inclined plane (mg * cosθ) and one parallel to the inclined plane (mg * sinθ), where m is the mass and θ is the angle of the inclined plane.

2. Force exerted by the spring:

The force exerted by the spring can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The force can be written as F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

Given:

Mass (m) = 5.0 kg

Compression of the spring (x) = 20.0 cm = 0.20 m

Angle of the inclined plane (θ) = 30°

First, let's find the force exerted by the spring (F_spring):

F_spring = -kx

To find k, we need the spring constant. Let's assume that the spring is ideal and obeys Hooke's Law linearly.

Next, let's calculate the gravitational force components:

Gravitational force parallel to the inclined plane (F_parallel) = mg * sinθ

Gravitational force perpendicular to the inclined plane (F_perpendicular) = mg * cosθ

Since the inclined plane is frictionless, the force parallel to the inclined plane (F_parallel) will be canceled out by the force exerted by the spring (F_spring) when the mass reaches its highest point.

At the highest point, the gravitational force perpendicular to the inclined plane (F_perpendicular) will be equal to the force exerted by the spring (F_spring).

Therefore, we have:

F_perpendicular = F_spring

mg * cosθ = -kx

Now, let's substitute the known values and solve for k:

(5.0 kg * 9.8 m/s^2) * cos(30°) = -k * 0.20 m

49.0 N * 0.866 = -k * 0.20 m

42.426 N = -0.20 k

k = -42.426 N / (-0.20 m)

k = 212.13 N/m

Now that we know the spring constant, we can calculate the maximum potential energy stored in the spring (PE_spring) when the mass reaches its highest point:

PE_spring = (1/2) * k * x^2

PE_spring = (1/2) * 212.13 N/m * (0.20 m)^2

PE_spring = 4.243 J

The maximum potential energy (PE_spring) is equal to the maximum kinetic energy (KE_max) at the highest point, which is also the energy the mass has gained from the spring.

KE_max = PE_spring = 4.243 J

Next, we can calculate the height (h) the mass reaches on the inclined plane:

KE_max = m * g * h

4.243 J = 5.0 kg * 9.8 m/s^2 * h

h = 4.243 J / (5.0 kg * 9.8 m/s^2)

h = 0.086 m

The height the mass reaches on the inclined plane is 0.086 m.

Now, we can calculate the distance traveled.

A 5.0 kg object compresses a spring by 0.20 m with a spring constant of 25 N/m. It climbs an incline, reaching a maximum height of 0.0102 m before coming back down, traveling a total distance of 0.0428 m.

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Answer:

Explanation:

Area of the room = Length × Width

Given

Length = 12.71m

Width = 5.46m

Area of the room = 12.71m×5.46m

Area of the room = 69.3966m²

To get the area of the error, we will use the relationship;

∆A/A = {∆L/L + ∆W/W}

∆A/A = {0.01/12.71 + 0.01/5.46}

∆A/A = {0.0007868+ 0.001832}

∆A/A = 0.0026182

∆A = 0.0026182A

Since Area A = 69.3966m²

∆A = 0.0026182(69.3966)

∆A ≈ 0.1817m²

Hence error in the area of the room is 0.1817m²

In mathematics, a Euclidean space is a geometric space in which the distance between two points is measured using the Euclidean distance formula. In 4-dimensional Euclidean space, there are 4 mutually perpendicular directions, which are commonly referred to as the x, y, z, and w directions. These directions are perpendicular to each other, meaning that they form right angles with one another.

The concept of 4-dimensional Euclidean space can be difficult to visualize, as it is a concept that exists beyond our everyday three-dimensional world. However, we can think of it as an extension of three-dimensional space, in which there is an additional direction (the w direction) that is perpendicular to the x, y, and z directions. This additional direction allows for the representation of additional information or variables in the space.

For example, in four-dimensional Euclidean space, we could represent the position of a point using four coordinates (x, y, z, w) rather than just three (x, y, z). This additional coordinate could represent a variety of different quantities, such as time, energy, or some other physical property.

Answer:

2 J

Explanation:

Work = change in energy

W = ΔKE

W = ½ mv²

W = ½ (100 kg) (0.2 m/s)²

W = 2 J

Answer:

4Nm

Explanation:

Work done is force times distance.

The force is given as mass x (speed )^2 / raduis . Expressed mathematically we have ;

Mv^2/r

Then for the slightest measurable distance r we have: the work done as;

Mv^2/r × r

= Mv^2

= 100 × 0.2 × 0.2= 4Nm

Answer:

Explanation:

Sure, I'd be happy to help you with the question!

Let's denote the input as x. According to the function machine, the input is multiplied by 6 and then 80 is subtracted from the result to obtain the output.

So, the function can be written as:

Output = (6 * x) - 80

Now, the problem states that the input is the same as the output. Therefore, we can set up the equation:

x = (6 * x) - 80

Let's solve this equation to find the value of x:

x = 6x - 80

Subtracting 6x from both sides, we get:

x - 6x = -80

Combining like terms, we have:

-5x = -80

Dividing both sides by -5, we find:

x = (-80) / (-5)

Simplifying the expression, we have:

x = 16

Therefore, the input (x) that results in the input being the same as the output is 16.

To work out these types of questions, it's important to carefully read the instructions and understand the operations being performed in the function machine. Then, you can set up an equation with the input and output, and solve for the unknown value. Always double-check your solution to ensure it satisfies the given conditions of the problem.

Answer:

16

Explanation:

(x*6) - 80 = x

Multiply the parentheses

6x - 80 = x
Add 80 to each side to get
6x = x + 80
Subtract x from both sides to get
5x = 80
Divide both sides by 5
x = 16

Answer:

85

Explanation:

soln

given that;

frequency=17Hz

wavelength=5m

speed?

formula for wavelength is;

wavelength= speed/frequency

then ; making v the subject formula

we have that v=wavelength*frequency

v=17*5=>85ms

Answer:Magnetic fields from two sources add up as vectors at each point, so the strength of the field is not necessarily the sum of the strengths1. Magnetic fields are vectors, which means they have direction as well as size. Therefore, the sum of two magnetic fields is not simply the sum of their magnitudes2.

Explanation:

The object's speed shortly before it lands on the earth is 40 m/s.

The speed at which something moves in a specific direction is known as its velocity. as the speed of a car driving north on a highway or the pace at which a rocket takes off. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed.

The parameters are as follows: the pebble's time, t = 4 s; the object's velocity right before impact;

The kinematic equation is as follows;

v = in which

v = 0+10 (4)

The object's speed right before impact with the earth is v = 40 m/s2, where g is the acceleration caused by gravity and an is a constant of 10 m/s2. As a result,

the object's final velocity before impact is 40 m/s.

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The physics behind the movement of electric charges between parallel plates is based on the principles of electrostatics. Electric charges are either positive or negative, and they are affected by electric fields.

Electric fields are created by a difference in electric potential, which is measured in volts. When a voltage is applied to a set of parallel plates, the charges within the plates will be affected by the electric field, and will move in response to it.

When a voltage is applied to a set of parallel plates, the positive charges in the plate connected to the positive voltage will be attracted to the negative voltage, while the negative charges in the plate connected to the negative voltage will be attracted to the positive voltage.

The movement of charges between the plates is also affected by the presence of any obstacles or resistances in the electric field, such as resistance in the wire. This can slow down the movement of charges and result in a decrease in the current flowing through the circuit.

In all, the movement of charges between electric parallel plates is the result of the electric field created by a difference in electric potential, and the movement of charges is called drift velocity. The movement is also affected by the presence of resistance.

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The "ln A" column was completed by calculating the natural logarithm of the disintegrations per minute (A) for each time (t) value. Plotting A vs. t shows the exponential decrease in radioactive activity over time.

To complete the column labeled "ln A" and create a graph of A vs. t, we need to calculate the natural logarithm of the disintegrations per minute (A) for each corresponding time (t) value. The natural logarithm (ln) of a number can be calculated using a calculator or software. Let's calculate and complete the table:

Time (hours) (t) Disintegrations per minute (min⁻¹¹) (A) ln A

0 363 ln(363) ≈ 5.894

6 184 ln(184) ≈ 5.214

12 93.2 ln(93.2) ≈ 4.535

18 47.3 ln(47.3) ≈ 3.857

24 24.0 ln(24.0) ≈ 3.178

Now, we have completed the "ln A" column.

To plot a graph of A vs. t, we can use these values. A represents the disintegrations per minute (activity), and t represents time in hours. The graph will show how the activity decreases over time due to radioactive decay. The x-axis will represent time (t), and the y-axis will represent the natural logarithm of activity (ln A).

Plotting ln A against t should result in a decreasing exponential curve, which is typical for radioactive decay processes.

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The magnitude of the damping coefficient is = 0.277 Ns/m

We can use the formula for the damped harmonic motion of a spring-mass system:

At t=0, the displacement of the egg is x = 0.300 m, and at t=5.00 s, the displacement has decreased to x = 0.100 m.

The angular frequency of the motion is:

w = sqrt(k/m) = sqrt(25.0 N/m / 0.0500 kg) = 10.0 rad/s

The equation for the amplitude of the motion at time t is:

A = x / cos(wt + delta) * e^(bt/2m)

At t=0, we have:

A = 0.300 m / cos(0 + delta) * e^(b0/20.0500 kg) = 0.300 m / cos(delta)

At t=5.00 s, we have:

A = 0.100 m / cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg)

Dividing these two equations, we get:

0.300 m / cos(delta) / (0.100 m / cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg)) = e^(b5.00 s/20.0500 kg)

Simplifying, we get:

cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg) / cos(delta) = 3.00

Taking the natural logarithm of both sides, we get:

ln(cos(10.0 rad/s * 5.00 s + delta) * e^(b5.00 s/20.0500 kg) / cos(delta)) = ln(3.00)

Using the properties of logarithms, we can simplify this to:

ln(cos(10.0 rad/s * 5.00 s + delta)) + b*5.00 s / 0.0500 kg / 2 - ln(cos(delta)) = ln(3.00)

We can rearrange this equation to solve for b:

b = (2/5.00 kg) * (ln(3.00) - ln(cos(10.0 rad/s * 5.00 s + delta)) + ln(cos(delta)))

The phase angle delta is unknown, but it cancels out when we take the difference between the two equations for A. Therefore, we can choose any value of delta and still get the correct value of b.

Let's choose delta = 0 for simplicity. Plugging in the values, we get:

b = (2/0.0500 kg) * (ln(3.00) - ln(cos(10.0 rad/s * 5.00 s)) + ln(cos(0)))

b = 0.277 Ns/m

Therefore, the magnitude of the damping coefficient is = 0.277 Ns/m

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A 50.0-g hard-boiled egg moves on the end of a spring with force constant k=25.0N/m. It is released with an amplitude 0.300 m. A damping force Fx=−bv acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient b.

Answer:

A light-year is the distance light travels in one year.

Answer:

Explanation:

a unit of astronomical distance equivalent to the distance that light travels in one year, which is 9.4607 × 1012 km (nearly 6 million million miles).

In the figure below, the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm is 63 m/s.

Periodic or oscillatory motion is defined as a motion that repeats itself. Due to a restoring force or torque, an object in such motion oscillates around an equilibrium position.

Energy is conserved in oscillation.

So, the maximum loss in Potential Energy = Maximum gain in Kinetic energy

5 J - 1 J = Maximum gain in Kinetic energy

Maximum gain in Kinetic energy = 4 J

\(0.5 \times m \times vmax^2 = 4\\0.5 \times 2.0 \times 10^-3\; Kg \times vmax^2 = 4 J\\vmax^2 = 4 \times 10^3 m^2/s^2\\vmax = 63.2 m/s\)

Therefore, the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm is 63 m/s.

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In this scenario, the cat sliding down the rubber rod and falling into metal pail "a" caused the transfer of charge to pail "a". This transfer of charge caused pail "a" to become charged and the metal pails "b" and "c" that were in contact with it, were also charged by induction.

When the shelf broke, the metal pails fell separated to the non-conducting floor, resulting in the charge being separated and no longer being able to move from one metal pail to another.

After the cat ran away, the charged metal pails likely remained charged, as there was no conductor available for the charge to flow through and neutralize.

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Answer:

yes the answer is D as the two people if we calculate

Answer:

A

Explanation:

correct on A P E X

\( \huge\boxed{♧ \: \mathfrak{ \underline{Answer} \: ♧}}\)

we know,

\( \boxed{kinetic \: \: energy = \frac{1}{2} m {v}^{2} }\)

So,

\(\longmapsto \dfrac{1}{2} \times 10 \times 0.2 \times 0.2\)

\(\longmapsto0.2 \: joules\)

Answer:

False, it is a fuse.

Explanation:

In electronics and electrical engineering, a fuse is an electrical safety device that operates to provide overcurrent protection of an electrical circuit. Its essential component is a metal wire or strip that melts when too much current flows through it, thereby stopping or interrupting the current. It is a sacrificial device; once a fuse has operated it is an open circuit, and must be replaced or rewired, depending on its type.

Fuses have been used as essential safety devices from the early days of electrical engineering. Today there are thousands of different fuse designs which have specific current and voltage ratings, breaking capacity and response times, depending on the application. The time and current operating characteristics of fuses are chosen to provide adequate protection without needless interruption. Wiring regulations usually define a maximum fuse current rating for particular circuits. Short circuits, overloading, mismatched loads, or device failure are the prime or some of the reasons for fuse operation.

A fuse is an automatic means of removing power from a faulty system; often abbreviated to ADS (Automatic Disconnection of Supply). Circuit breakers can be used as an alternative to fuses, but have significantly different characteristics.

Source: https://en.wikipedia.org/wiki/Fuse_(electrical)

A fuse is a small glass or plastic tube that contains a piece of wire. That wire is carefully calibrated so that it will only allow a certain level of current to pass through it. Any more, and the wire will melt from the heat, breaking the circuit. This means that if a power surge comes into your home, a circuit will be broken before it causes damage to your appliances.

A circuit breaker achieves the same thing, but by a different method. A circuit breaker also disconnects the circuits in your home if the current gets too large but does it using electromagnets. If the current gets high enough, then the electromagnet will become powerful enough to attract a contact and break the circuit that way.

Both circuit breakers and fuses can be used to help with another situation. If you have an appliance with a metal case and that appliance comes in contact with a live wire, it can cause you to electrocute yourself. But if that metal case is connected to a ground wire (the third pin in some plugs), then the electricity will flow through the ground wire, through the circuit breaker or fuse box, and break the circuit, stopping you from potentially getting electrocuted.

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Answer:

The correct answer is Dean has a period greater than San

Explanation:

Kepler's third law is an application of Newton's second law where the force is the universal force of attraction for circular orbits, where it is obtained.

                T² = (4π² / G M)  r³

When applying this equation to our case, the planet with a greater orbit must have a greater period.

Consequently Dean must have a period greater than San which has the smallest orbit

The correct answer is Dean has a period greater than San

Answer:

According to the law of universal gravitation, any two objects are attracted to each other. The strength of the gravitational force depends on the masses of the objects and their distance from each other.

Many stars have planets around them. If there were no gravity attracting a planet to its star, the planet's motion would carry it away from the star. However, when this motion is balanced by the gravitational attraction to the star, the planet orbits the star.

Two solar systems each have a planet the same distance from the star. The planets have the same mass, but Planet A orbits a more massive star than Planet B.

Which of the following statements is true about the planets?

 A.

Planet B will keep orbiting its star longer than Planet A.

 B.

Planet A has a longer year than Planet B.

 C.

Planet A orbits its star faster than Planet B.

 D.

Planet B is more attracted to its star than Planet A.

Explanation:

Answer:

the answer the correct one is c

Explanation:

Electric charges of different signs attract and those of the same sign repel. In addition, there are two types of insulating bodies, where the loads are fixed (immobile) and metallic (with mobile loads.

Let's analyze the situation presented

* A rod with positive approaches and the sphere is attracted, so the charge on the sphere is negative

* A rod with a negative charge approaches and the sphere is attracted, therefore the charge of the sphere must be positive.

For this to happen, the sphere must be unloaded and the charge that creates the phenomenon are induced charges because the mobile charges of the same sign as the sphere are repelled.

when checking the answer the correct one is c