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

WILL GIVE BRAINLIEST
An object with mass m dropped from height H, after travelling a distance and emerged horizontally from the bottom of the track with a velocity v and height of h. what is The work done due to friction while traveling through the track. could someone also please explain the difference between h and H

Answers

Answer:

I think d

Explanation:

4. What is the density of a block with a mass of 36 g and a volume of 9 cm?
O A 45 g/cm3
O B.27 g/cm
O 0.4 g/cm
O D. 0.25 g/cm

Answers

Answer:

0.4 g/cm

Explanation:

density (g cm ³) = mass (g)

÷

volume (cm³)

Answer:

C. 4 g/cm

Explanation:

Use the formula:

density = mass ÷ volume

mass = 36volume = 9

Sub in the values:

density = 36 ÷ 9 = 4 g/cm

Answer = 4 g/cm

A flea can jump with an initial velocity of 2.2 m/s at an angle of 21° with respect to the
horizontal.

Answers

Answer:

Explanation:

If no one can see it because the lights were out. Did the flea really jump?

What do you want here?

Max height (2.2sin21)²/ 2(9.8) = 3.2 cm

Time of flight 2(2.2sin21)/ (9.8) = 0.16 s

distance of flight (2.2cos21)(0.16) = 33 cm

The pulley shown in the attached diagram has a diameter of 30 centimeters and a mass of 19 kilograms. The pulley is a solid disk with an axle through its center.

(a.) What is the moment of inertia of the pulley?

(b.) What is the magnitude of the net torque on the pulley about its axis

(c.) What is the direction of the net torque on the pulley?

(d.) What is the magnitude of the angular acceleration of the pulley?

(e.) What is direction of the angular acceleration?

Answers

Answer:

Explanation:

a) I = ½mR² = ½(19)(0.15²) = 0.21375 kg•m²

b) τ = Fnet(r) = (25 - 12)(0.15) = 1.95 N•m

c) CCW

d) a = τ/I = 1.95 / 0.21375 = 9.12280701... = 9.1 rad/s²

e) CCW

Two students were pushing a heavy sofa. One student pushed with a force of 200.0 N to the right, while the other pushed with a force of 150.0 N to the right. The floor exerted a frictional force of 100.0 N. If the sofa's mass is 91.0 kg, what is its acceleration? Round your answer to three significant figures.

Answers

Answer:

Explanation:

F = ma

a = F/m

a = (200.0 + 150.0 - 100.0) / 91.0

a = 250.0/91.0

a = 2.7472527...

a = 2.75 m/s²

Find the speed required to throw a ball straight up and it return 6 seconds later. Neglect air resistance

Answers

Answer:

the ball will go up 3s and down 3s

v=gt

where t=3s and g=9.8m/s^2

distance=v0(t)+(1/2)gt^2

where initial velocity (v0)=0

Explanation:

The speed required to throw a ball straight up and returns 6 seconds later would be 29.43 meters/seconds.

What are the three equations of motion?

There are three equations of motion given by Newton,

v = u + at

S = ut + 1/2×a×t²

v² - u² = 2×a×s

As given in the problem we have to find the speed required to throw a ball straight up and it returns 6 seconds later,

S = ut + 1/2*a*t²

0 = u×6 + 0.5×(-9.81)×6²

0 = 6u - 176.8

6u = 176.8

u = 176.8/6

u = 29.43 meters / seconds

Thus, the speed required to throw a ball straight up and returns 6 seconds later would be 29.43 meters/seconds.

To learn more about equations of motion here, refer to the link;

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A spring of spring constant k = 200 N m−1 is slowly extended from an extension of 3.0 cm to an extension of 5.0 cm. Calculate the work done by the extending force. 60

Answers

Answer:

31

Explanation:

No need

The correct answer is 31 I did it

define potential difference as used in electricity​

Answers

Potential difference is the difference in the amount of energy that charge carriers have between two points in a circuit.

Potential difference is the difference in the amount of energy that charge carriers have between two points in a circuit. ... The energy is transferred to the electrical components in a circuit when the charge carriers pass through them. We use a voltmeter to measure potential difference (or voltage).

When a straw with liquid is covered by a finger and raised, the liquid does not leak
from the straw. Explain this using ideas of pressure exerted by particles.

Answers

Answer:

lol I don't know think u could help me with my mathematics

can anyone heelp me pls

Answers

Answer:

Capsule : solid

Suspension : liquid

lotion : semisolid

Explanation:

Which statement describes friction?

Answers

Answer:

include the statements pls so i can choose wich one it is and tell you

Explanation:

A 23 g bullet traveling at 230 m/s penetrates a 2.0 kg block of wood and emerges cleanly at 170 m/s. If the block is stationary on a surface with a coefficient of kinetic friction of 0.15 when hit, how far does it move after the bullet emerges?

Answers

The distance traveled by the wood after the bullet emerges is 0.16 m.

The given parameters;

mass of the bullet, m = 23 g = 0.023 gspeed of the bullet, u = 230 m/smass of the wood, m = 2 kgfinal speed of the bullet, v = 170 m/scoefficient of friction, μ = 0.15

The final velocity of the wood after the bullet hits is calculated as follows;

[tex]m_1u_1 + m_2 u_2 = m_1v_1 + m_2v_2\\\\0.023(230) + 2(0) = 0.023(170) + 2v_2\\\\5.29 = 3.91 + 2v_2\\\\2v_2 = 1.38\\\\v_2 = \frac{1.38}{2} = 0.69 \ m/s[/tex]

The acceleration of the wood is calculated as follows;

[tex]\mu = \frac{a}{g} \\\\a = \mu g\\\\a = 0.15 \times 9.8\\\\a = 1.47 \ m/s^2[/tex]

The distance traveled by the wood after the bullet emerges is calculated as follows;

[tex]v^2 = v_0^2 + 2as\\\\v^2 = 0 + 2as\\\\v^2 = 2as\\\\s = \frac{v^2}{2a} \\\\s = \frac{(0.69)^2}{2(1.47)} \\\\s = 0.16 \ m[/tex]

Thus, the distance traveled by the wood after the bullet emerges is 0.16 m.

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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

What is the velocity of an object tht experiences 5.6m/s^2 and a radius of 3 meters?

Answers

The velocity of the object is 4.1 m/s. Recall that the centripetal acceleration is the acceleration of a body moving in a circular path.

Given that the centripetal acceleration is obtained using the formula;

ac = v^2/r

ac= centripetal acceleration

v = velocity

r = radius

v^2 = rac

v= √ rac

ac = 5.6m/s^2

r = 3 meters

Substituting values;

v = √3 × 5.6m/s^2

v = √16.8

v = 4.1 m/s

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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

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

dsfhfdskjhfdkshjkfdhskjdfhkjshjkfhsdkjf

Answers

Answer:

Abcdfeghijklmnopqrstuvwxyz

Explanation:

They are in order

how can I become a good science student ?​

Answers

Answer:

Study hard , focus on your studies and alyways ask questions .

Study, revise, write notes, listen in class, don't let yourself be distracted by others, and do the work in class...maybe join stem or science club if you wanna

Hope this helped you- have a good day bro cya)

A uniform string of length 0.50 m is fixed at both ends. Find the
wavelength of the fundamental mode of vibration. If the wave
speed is 300 mis, find the frequency of the fundamental and next
possible modes.

Answers

Answer:

configuration of string:

Node - Antinode - Node    or N-A-N

This is 1/2 wavelength since a full wavelength is N-A-N-A-N

f (fundamental) = V / wavelength

F0 = 300 m/s / 1 m = 100 / sec

F1 = 300 m/s / .5 m = 600 / sec

Each increase is a multiple of the fundamental since the wavelength

increases by 1/2 wavelength to keep nodes at both ends of the string

When converted to a household measurement, 9 kilograms is approximately equal to a

Answers

Ificicicucuivvicicicucucucu

Answer:

D) 19.8 lbs

Explanation:

1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.

1kg is also equal to 2.205 lbs. 9*2.205=19.8416

9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system

a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.

This leaves us with 19.8 lbs

A 940-g rock is whirled in a horizontal circle at the end of a 1.30-m-long string. (a) If the breaking strength of the string is 120 N, what’s the minimum angle the string can make with the horizontal? (b) At this minimum angle, what’s the rock’s speed?

Answers

(a) The minimum angle the string can make with the horizontal is 4.4 ⁰.

(b) The rocks speed at the minimum angle is 165.7 m/s.

The given parameters;

mass of the rock, m = 940 g = 0.94 kglength of the string, L = 1.3 mTension on the string, T = 120 N

The net force on the string is calculated as follows;

[tex]Tsin(\theta) = mg\\\\Tcos(\theta) = \frac{mv^2}{r} \\\\\frac{Tsin(\theta)}{Tcos(\theta)} = \frac{mg r}{mv^2} \\\\tan(\theta) = \frac{rg}{v^2} \\\\v^2 = \frac{rg}{tan (\theta)} \\\\v = \sqrt{\frac{rg}{tan (\theta)}}[/tex]

The minimum angle the string can make with the horizontal is calculated as follows;

[tex]Tsin(\theta) = mg\\\\sin(\theta) = \frac{mg}{T} \\\\sin(\theta) = \frac{0.94 \times 9.8}{120} \\\\sin(\theta) = 0.0767\\\\\theta = sin^{-1} (0.0767)\\\\\theta = 4.4 \ ^o[/tex]

The rocks speed at the minimum angle is calculated as follows;

[tex]v = \sqrt{\frac{rg}{tan(\theta)} } \\\\v = \sqrt{\frac{1.3 \times 9.8}{tan(4.4)} } \\\\v = 165.7 \ m/s[/tex]

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Adam and Bobby are twins who have the same weight. Adam drops to the ground from a tree at the same time that Bobby begins his descent down a frictionless slide. If they both start at the same height above the ground, how do their kinetic energies compare when they hit the ground

Answers

Answer:

They are the same.

Both have potential energy of M g H   and that is the energy that will be converted to kinetic energy for each twin,

A dry cell gives static electricity true or false?

Answers

Answer:

False

Explanation:

Which of the following happens when a substance melts?

Answers

Answer:

hola como estas hablas español

Explanation:

How much time does it take for a school bus traveling at 15 m/s north to get a distance of 600 meters north?

Possible answers:
40 seconds
9,000 seconds
615 seconds
0.025 seconds

Answers

Answer:

40s

Explanation:

Physical activities teaches an individual sense of responsibility and initiative.
True Or False

Answers

Answer:

true

Explanation:

Physical fitness is a personal responsibility so I would say true

the correct answer is true :)

Speed depends on how far something travels and

Answers

Answer:

Speed depends on how far something is travelling and the time taken for the object to travel that distance

Explanation:

(In reference to the speed formula)  Speed=[tex]\frac{Distance(m)}{Time(m/s)}[/tex]

Definition of speed:

Speed is the magnitude (unit) of the rate at which an object is moving.

(pls do correct me if I have any mistakes it makes a big difference to help each other out!)

A diffraction grating, ruled with 300 lines per mm, is illuminated with a white light source at normal incidence.
(i) What is the angular separation, in the third-order spectrum, between the 400 nm and 600 nm lines? [5]
(ii) Water (of refractive index 1.33) now fills the whole space between the grating and the screen. What is the angular separation, in the first-order spectrum, between the 400 nm and 600 nm lines? [5]​

Answers

the expression for diffraction grating allows to find the results for the questions for the angular separation are:

i) The third order is Δθ = 0.203 rad.

ii) The first order with water is Δθ = 0.046 rad.

The diffraction grating is a system formed by a large number of equally spaced lines whose diffraction is given by the expression.

          d sin θ = m λ

Where d is the distance between two lines, θ is the angle of diffraction, the order of diffraction and λ is the wavelength.

i) Let's start by looking for the separation between two lines

Let's use a rule of direct proportions. If there are 300 lines in 1 mm, what distance is there between two lines.

         d = 1 lines (1 mm / 300 lines) = 3,333 10⁻³ mm

         d = 3.333 10⁻⁶ m

Let's find the angle of diffraction for the third order (m = 3) for each wavelength.

λ₁ = 400 nm = 400 10⁻⁹ m

         sin θ₁ = [tex]\frac{m \ \lambda }{d}[/tex]m λ/ d

         sin θ₁ = [tex]\frac{3 \ 400 \ 10^{-9} }{3.333 \ 10^{-6} }[/tex]  

         θ₁ = sin⁻¹ 0.3600

         θ₁ = 0.368 rad

λ₂ = 600 nm = 600 10⁻⁹ m

         sin θ₂ = [tex]\frac{3 \ 600 \ 10^{-9} }{3.333 \ 10^{-6} }[/tex]  

         θ₂ = sin⁻¹ 0.5401

         θ₂ = 0.571 rad

The angular separation is

         Δθ = θ₂ - θ₁

         Δθ = 0.571 - 0.368

         Δθ = 0.203 rad

ii) In this case, the separation between the network and the observation screen is filled with water.

When the rays leave the network they undergo a refraction process, for which they must comply with the relationship.

           [tex]n_i \ sin \theta_1 = n_r \ sin \theta_r[/tex]

The incident side is in the air, therefore its refractive index is n_i = 1 and when it passes into the water with refractive index n_r = 1.33.

Let's start looking for the incident angles for the first order of diffraction.

      m = 1

λ₁ = 400 nm

         θ₁ = sin⁻¹  [tex]\frac{1 \ 400 \ 10^{-9}}{3.33 \ 10^{-6}}[/tex]

         θ₁ = 0.120 rad

λ₂ = 600 nm

        θ₂ = sin⁻¹¹ [tex]\frac{1 \ 600 \ 10^{-9} }{3.33 \ 10^{-6}}[/tex]

        θ₂ = 0.181 rad

we use the equation of refraction.

         [tex]\theta_r[/tex]  = sin⁻¹ ([tex]\frac{n_i}{n_r} \ sin \ \theta_i[/tex] )

λ₁ = 400 nm  

       θ₁ = sin¹ ([tex]\frac{1 sin 0.120}{1.33}[/tex]

       θ₁ = 0.090 rad

λ₂ = 600 nm

        θ₂ =sin⁻¹  [tex]\frac{1 sin 0.181}{1.33}[/tex]

        θ₂ = 0.1358 rad

The angular separation is

          Δθ = 0.1358 - 0.090

          Δθ = 0.046 rad.

In conclusion using the relation for the diffraction grating we can find the results for the questions about angular separation are:

       i) The third order is Δθ = 0.203 rad.

      ii) The first order with water is Δθ = 0.046 rad.

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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

A ball moving 2 ft/s rolls off a table (on earth) that is 32 inches high. How long will it take the ball to hit the floor answer

Answers

Answer:When the ball rolls off the edge of the table, it will continue moving forward at 2.0 m/s until it hits the floor.

Explanation:This is what I would say is the answer bc I had to do reasearch on a lot of this for my work this year so if its not im veery sorry

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