Two spherically symmetric planets with no atmosphere have the same average density, but planet B has twice the radius of planet A. A small satellite of mass mA has period TA when it orbits planet A in a circular orbit that is just above the surface of the planet. A small satellite of mass mB has period TB when it orbits planet B in a circular orbit that is just above the surface of the planet.

Answers

Answer 1

A period of a satellite is the time taken by the satellite to travel round a

body.

The comparison between the periods  [tex]T_B[/tex], and [tex]T_A[/tex] is [tex]\underline {T_B = \dfrac{\sqrt{2} }{4 } \cdot T_A}[/tex]

Reason:

The period, T, of a satellite is given as follows;

[tex]T = 2 \cdot \pi \cdot \sqrt{\dfrac{r^3}{G \cdot M} }[/tex]

Volume of the planet A = [tex]\dfrac{4}{3} \cdot \pi \cdot r^3[/tex]

Mass of planet A, [tex]m_A[/tex] = [tex]\dfrac{4}{3} \cdot \pi \cdot r^3 \times \rho[/tex]

Volume of the planet B = [tex]\dfrac{4}{3} \cdot \pi \cdot (2 \cdot r)^3 = \dfrac{32}{3} \cdot \pi \cdot r^3[/tex]

Mass of planet B, [tex]m_B[/tex] = [tex]\dfrac{32}{3} \cdot \pi \cdot r^3 \times \rho[/tex]

Period of the satellite on planet A, [tex]T_A[/tex], is given as follows;

[tex]T_A = 2 \cdot \pi \cdot \sqrt{\dfrac{r^3}{G \times \dfrac{4}{3} \cdot \pi \cdot r^3 \times \rho} } = 2 \cdot \pi \cdot \sqrt{\dfrac{1}{G \times \dfrac{4}{3} \cdot \pi \times \rho} }[/tex]

Period of the satellite on planet B, [tex]T_B[/tex], is given as follows;

[tex]T_B = 2 \cdot \pi \cdot \sqrt{\dfrac{r^3}{G \times \dfrac{32}{3} \cdot \pi \cdot r^3 \times \rho} } = 2 \cdot \pi \cdot \sqrt{\dfrac{1}{G \times \dfrac{32}{3} \cdot \pi \times \rho} }[/tex]

Therefore, get;

[tex]\dfrac{T_A}{T_B} = \dfrac{ 2 \cdot \pi \cdot \sqrt{\dfrac{3}{G \times 4 \cdot \pi \times \rho} }}{ 2 \cdot \pi \cdot \sqrt{\dfrac{3}{G \times 32 \cdot \pi \times \rho} }} = \sqrt{\dfrac{32}{4} } = \sqrt{8} = 2 \cdot \sqrt{2}[/tex]

Therefore, [tex]T_A[/tex] = (2·√2)·[tex]T_B[/tex]

[tex]T_B = \dfrac{T_A}{2 \cdot \sqrt{2} } = \dfrac{\sqrt{2} \cdot T_A}{4 }[/tex]

The comparison between [tex]T_A[/tex] and  [tex]T_B[/tex] is therefore;

[tex]\underline {T_B = \dfrac{\sqrt{2} }{4 } \cdot T_A}[/tex]

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Related Questions

Pls help thx need asap!!

Answers

Answer:

10N right

Explanation:

First, we need to find the base of the triangle to find the force acting on the right of the object.

We have been given the hypotenuse and we need to find the adjacent, so we are using cosSOH, CAH, TOAcos(θ) = adjacent ÷ hypotenuse

Next, sub in the values (we don't know the adjacent so i've called it x):

cos(60) = x ÷ 60

To find x, we need to multiply both sides by 60

60 × cos(60) = xx = 30 N

Now we know all the forces, we can work out the net force:

Both of the 40N cancel out because they are opposite forcesThe force on the right of the object is 10N stronger than the force on the left (30N - 20N), so the object would move to the right

The term that is used to quantity the amount of heat in the evaporator is

Answers

Answer:

Enthalpy

The quantity of heat contained in a material as measured from a particular base or point.

The Canadian bobsled team hit the brakes on the sled they are traveling East in so that it decelerates at a rate of 0.43
m/s^2.
a) How long does it take to stop if it travels 85 m before coming to rest?
b) Draw the velocity vector.
c) Draw the acceleration vector.

Answers

Answer:

Explanation:

85 = ½(0.43)t²

t = √(2(85)/0.43)

t = 19.883380...

t = 20 s

v→ 8.55 m/s initial, 0 m/s final

a← 0.43 m/s²

dsfhfdskjhfdkshjkfdhskjdfhkjshjkfhsdkjf

Answers

Answer:

Abcdfeghijklmnopqrstuvwxyz

Explanation:

They are in order

helphelphelp due in 5 minutes answer the question below

Answers

The correct answer is B

A box is 30 cm wide, 40 cm long and 25 cm high. Calculate the volume of the box in cubic centimeter.

A) 3,000
B) 30,000
C) 15,000
D) 1,200

Answers

Answer:

The correct answer would be A: 3,000.

Explanation:

To find the volume of a box, you have to do l * w * h. You multiply 30, 40, and 25 which gives you an answer of 3,000 cubic centimeters.

What is 1/3 a millisecond in seconds (decimal form)? (0._ s)​

Answers

Answer:

I don't know

Explanation:

plz

plz mark me as brainlist

A 220g mass is on a frictionless horizontal surface at the end of a spring that has a force constant of 7.0N/m The mass is displaced 5 2m from its equilibrium position and then released to undergo simple harmonic motion.
At what displacement from the equilibrium position is the potential energy equal to kinetic energy?​

Answers

Answer:

Explanation:

Your numbers seem wonky, so I'll just assume that the initial displacement is a distance A (Amplitude) from the equilibrium position. Spring constant = k

Initial potential energy is

PE = ½kA²

As potential energy and kinetic energy are constantly exchanging in SHM,

the position x where half of the original spring potential exists is found where

½kx² = ½(½kA²)

    x² = ½A²

    x = (√0.5)A

    x ≈ 0.707A

just plug in your actual starting position A

With A = 5.2 cm

x = 3.67695... 3.7 cm

four particles connected by rigid rods of negligible mass where y1 = 5.70 m. the origin is at the center of the rectangle. The system rotates in the xy plane about the z axis with and angular speed of 5.60 rad/s. a) calculate the moment of inertia of the system about the z axis. b) Calculate the rotational kinetic energy

Answers

The definition of moment of inertia and kinetic energy we can find the results for the questions are:  

          a) The moment of inertia is: I = 32.49 kg m²

          b) The kinetic energy is: K = 509.4 J

a) The moment of inertia is a scalar quantity that has the same function as mass, it is given by

             I = m r²

       

They indicate that the length of the bar is y₁ = 5.70 m, if the two rigid bars form the square that supports the masses, the distance from the center to the end where each mass is:  

            r = y₁ / 2

             r = 5.70 / 2 = 2.85 m

The moment of inertia of the system is.

         I = 4 m r²

Let's calculate.

        I =4 m 2.85²

        I = 32.49m kg m²

If we assume that the mass of each point particle is:

        m = 1 kg

   

         I = 32.49 kg m²

b) They ask for the rotational kinetic energy, if the angular velocity is.

           w = 5.60 rad / s

The kinetic energy for rotational motion is.

         K = ½ I w²

Let's calculate.

          K = ½ 32.49 5.60²

          K = 509.4 J

In conclusion with the definition of moment of inertia and kinetic energy we can find the results for the questions are:

          a) The moment of inertia is: I = 32.49 kg m²

          b) The kinetic energy is: K = 509.4 J

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a matter can be separated into which of the following choices​

Answers

A matter can be separated into three states.

SolidLiquidGasIn solid state the bonding between atoms is maximum.In liquid state the bonding between atoms is less than solid.In gaseous state the bonding between atoms is minimum
1. solid
2. liquid
3. gas

I need HELP! IMMEDIATELY!!!

Answers

Answer:

Option A

Explanation:

N is Chloroplast, P is a large centralized vacuole and R is the cell wall which are found only in plant cells. Hence, the given cell is a plant cell.

S = Rough Endoplasmic Reticulum

P = Vacuole

O = Nucleus

T = Smooth Endoplasmic Reticulum

U = Golgi Apparatus

N = Chloroplast

U = Cell Membrane

M = Mitochondria

R = Cell wall

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

Given below are the names of some objects and materials: Water, basket ball, orange, sugar, globe, apple and earthen pitcher Group them as Eatables and Non eatables.​

Answers

« eatables »

waterorangesugarApple

« non eatables »

basket ballglobe earthen pitcher

hope it helps

You start your bicycle ride at the top of a hill moving East. You coast down the hill at a
constant acceleration of 2 m/s^2. When you get to the bottom of the hill you are moving at
18 m/s, and from there you pedal to maintain that velocity for one minute.

Answers

Answer:

198 meters

Explanation:

I'm not sure but hope it helps

when air gets hot, it rises and forms…

Answers

Answer:

Gas

Explanation:

Hot air rises because gases expand as they heat up. When air heats up and expands, its density also decreases.

Câu 1. Trường hợp nào dưới đây không phải là vật sáng?

A. Chiếc bút chì đặt trên bàn giữa ban ngày.

B. Chiếc bật lửa rơi giữa sân trường lúc trời nắng.

C. Mặt Trời.

Answers

Answer:

A

Explanation:

A. The pencil is on the table in broad daylight

David drives and slows to a stop when he sees a stop sign. A graph of his velocity over time is shown below.
Velocity
20-
P6
15+
As:
10+
MY
5+
Time (s)
Col
t
5
10
15
20
MY
Pro
What is his average acceleration from 10 to 20 seconds?
Pro

Answers

Answer:

-2.0

Explanation:

4. A gas's solubility is best in a liquid solvent when the solution is under high or low pressure

Answers

Answer:

low pressure

Explanation:

the hanging
mass would need to be

Answers

Answer:

what do you need help with I can try to help you

Heat rash is caused by chemical exposure Truth or false

Answers

Answer:

This is false.

Explanation:

Heat rash develops when some of your sweat ducts clog. Instead of evaporating, perspiration gets trapped beneath the skin, causing inflammation and rash. Heat rash is usually self-limited, meaning it resolves on its own without treatment. Over-the-counter treatments such as calamine, hydrocortisone cream, itch preparations (such as Benadryl spray), or sunburn lotions can be used as skincare to treat the itching and burning symptoms. Heat rash usually goes away on its own within three or four days so long as you don't irritate the site further. Heat rash happens when the sweat glands get blocked. The trapped sweat irritates the skin and leads to small bumps.

Answer:

FALSE

Explanation:

Heat rash develops when blocked pores or sweat ducts trap perspiration under your skin. Symptoms range from superficial blisters to deep, red lumps. Some forms of heat rash feel tingly  or intensely itchy.

what is the minimum mass in Mol. of plutonium 234 needed to reach a critical mass nuclear reaction?​

Answers

Answer:

vddvdvvdvffdfvd

Explanation:

Tell me any 5 importance of medicinal plants​

Answers

Answer:

Aloe, Tulsi, Neem, Turmeric, and Ginger are medicinal plants that can help with a variety of diseases. Ginger, green tea, walnuts, aloe, pepper, and turmeric are just a few of these plants. Some plants and their derivatives are key sources of active compounds used in aspirin and toothpaste, among other things.

Explanation:

Plant name:                                    Uses:

1. Marshmallow:      ////  Relief from aching muscles and pain in muscle, Heals insect bite.             ////

2.California poppy ////  Relieves tension, Removes nervous system

3. Tulsi                ////   Cures sore throat, Cures fever and asthma

4. Neem               ////       Cures skin diseases, Cures diabetics

5. Aloevera      ////             Heals burns, Relieves constipation

(Hope this helps can I pls have brainlist (crown)☺️)

what is deviation of light by prism​

Answers

Answer:

When a ray of light passes from one medium to another it changes its path, this phenomenon of light is called the deviation of light. When a ray of light passes through a prism it suffers refraction twice. Once while it enters the prism and again while it emerges from it.

If the law allows abortion based on sex, should we also allow abortion based on race, ethnicity, or skin color? Briefly explain why you believe this is right or wrong.

Answers

Answer:

No because you don't have to be black or white you don't have to be a pacific race to just get it like lets say for example a asian person come in and they want to get a abortion but the doctor say no then that person can end up killing her self or when the baby is born she could end you know doing something bad. But no you do not have to be a pacific person to just get it

Explanation:

--[50 POINTS]--
1)A block of mass 25 kg is placed on flat ground. The coefficient of static friction and kinetic friction are 0.73 and 0.16
a.If a person pushes the block and the block is moving, what will be the acceleration of the block?


2) A block has a mass of 79 kg. The coefficient of static and kinetic friction between the sled and the ground is 0.87 and 0.37. Person A tries to pull the block with 210N, but fails.
a) Person B successfully pulls the sled with 909N. What is the acceleration of the sled?

Answers

Newton's second law allows us to find the results for the acceleration of the blocks are:

1) The acceleration is a = 559 m / s²

2) The acceleration is a = 7.88 m / s²

Newton's second law states that the net force is equal to the product of the mass and the acceleration of the body.

       ∑ F = m a

Where the bold letters indicate vectors, F is the force, m the mass and the acceleration of the body.

The reference system is a coordinate system with respect to which the decomposition of the forces is carried out, in the attached we have a free body diagram of the system.

1) They indicate that the body mass is 25 kg.

y-axis

       N - W = 0

       N = W = m g

x-axis

        F -fr = ma

The friction force is a macroscopic force that results from the sum of all the microscopic interactions between the two surfaces, it has the formula

        fr = μ N

Where fr is the friction force, N the normal and very the friction coefficient.

This friction coefficient has two values:

Static. For when with there is not relative motion between the two surfaces. Dynamic. When there is relative motion between the two surfaces.

We substitute.

         F - μ m g = m a

a) The system moves which is the acceleration.

Suppose that the force that star to move the system keeps constant, just before the system begins to move the coefficient of friction is static, let's find the applied force.

         F = μ m g

         F = 0.73 25 9.8

         F = 178.85 N

The block begins to move and the friction coefficient decreases to the dynamic value, we look for the acceleration.

         a = [tex]\frac{F - \mu \ m g}{m}[/tex]  

         a = [tex]\frac{178.85 - 0.16 \ 25 \ 9.8 }{25}[/tex]  

         a = 5.59 m / s²

2) In this case the mass of the block is 79 kg and the applied force is

        F = 909 N

We look for acceleration.        

        a = [tex]\frac{909 - 0.37 \ 79 \ 9.8 }{79}[/tex]  

        a = 7.88 m / S²

In conclusion using Newton's second law we can find the results for the acceleration of the blocks are:

         1) The acceleration is a = 559 m / s²

         2) The acceleration is a = 7.88 m / s²

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Does bouncing or sticking produce more impulse?

Answers

Answer:

yes

Explanation:

Bouncing is a way to increase impulse. Because an object that bounces changes directions the force of impulse must be absorbed then generated by the target object. (Impulse is nearly doubled.)

QUESTION 5 When 235U is bombarded with one neutron, fission occurs and the products are three neutrons, 94Kr and?

a. 139Ba
b. 141Ba
c. 139Ce
d. 139Xe​

Answers

The answer is of the question is A

You have a new goal of saving at least $4,500 over the course of the next year.

You already have $900 saved.

By how much would you need to increase your monthly net savings in order to meet this goal?

Answers

Answer:

You would need to save $300 every month to meet your savings goal.

Explanation:

4,500-900=3,600

3,600/12=300

Answer:

answer is 200

Explanation:

edge 2021

if you double the force an object what will hapen to the accelration

Answers

Explanation:

the acceleration will double because force is directly proportional to the acceleration

2. In these diagrams, the sunlight is coming from the left, as shown by the arrows. Which
diagram is accurate and why? (1)

a) A is accurate because the half of the Moon that is facing the sun is it by the sun, and the
other half is dark.

b) B is accurate because the whole Moon is bright as long as there are no shadows
covering parts of it.

c) C is accurate because the Moon is almost as close as it can be to the sun, and so the
Moon is almost fully lit by the sun.

d) All three diagrams are sometimes accurate because the Moon has some lighter-colored
rock and some darker-colored rock, and the half of the Moon with the lighter-colored
rock rotates to face different directions.

Answers

Answer:

Explanation:

a) A is accurate because the half of the Moon that is facing the sun is it by the sun, and the other half is dark.

The most accurate diagram of the Sun and Moon is: a. A is accurate because the half of the Moon that is facing the sun is it by the sun, and the other half is dark.

What is a Moon?

A Moon can be defined as the natural satellite of planet Earth that shines due to the Sun's reflected light (sunlight), as it revolves around the Earth from west to east in 29½ days.

The phases of the Moon.

Based on astronomical information, there are four (4) primary Moon phases and these are:

New MoonFirst QuarterFull MoonThird Quarter (Last Quarter)

In conclusion, diagram A is the most accurate because half of the Moon that faced the Sun is lit by the Sun while the other half is dark.

Read more on Moon here: brainly.com/question/1286910

An 80 kg box is accelerated to the right at a rate of 3 m/s2. What is the applied force?

Answers

As we know,

F= ma

Here,

applied force(f)= mass × acceleration

=80kg×3m/s2

=240kgm/s2

=240N

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