1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lions [1.4K]
3 years ago
14

Astronomers observe two separate solar systems each consisting of a planet orbiting a sun. The two orbits are circular and have

the same radius R. It is determined that the planets have angular momenta of the same magnitude L about their suns, and that the orbital periods are in the ratio of three to one; i.e., T1 = 3T2. The ratio m1/m2 of the masses of the two planets is
(A) 1
(C) (3)^1/2
(C) 2
(D) 3
(E) 9
Physics
1 answer:
Oxana [17]3 years ago
3 0

Answer:

(D) 3

Explanation:

The angular momentum is given by:

\vec{L}=\vec{r}\ X \ \vec{p}

Thus, the magnitude of the angular momenta of both solar systems are given by:

L_1=Rm_1v_1=Rm_1(\omega R)=R^2m_1(\frac{2\pi}{T_1})=2\pi R^2\frac{m_1}{T_1}\\\\L_2=Rm_2v_2=2\pi R^2\frac{m_2}{T_2}

where we have taken that both systems has the same radius.

By taking into account that T1=3T2, we have

L_1=2\pi R^2\frac{m_1}{3T_2}=\frac{1}{3}2\pi R^2\frac{1}{T_2}m_1=\frac{1}{3}\frac{L_2}{m_2}m_1

but L1=L2=L:

L=\frac{1}{3}L\frac{m_1}{m_2}\\\\\frac{m_1}{m_2}=3

Hence, the answer is (D) 3

HOPE THIS HELPS!!

You might be interested in
The distance between the centers of the wheels of a motorcycle is 156 cm. The center of mass of the motorcycle, including the ri
Drupady [299]

Answer:

a = 9.86 m/s²

Explanation:

given,

distance between the centers of wheel = 156 cm

center of mass of motorcycle including rider = 77.5 cm

horizontal acceleration of motor cycle = ?

now,

The moment created by the wheels must equal the moment created by gravity.

take moment about wheel as it touches the ground, here we will take horizontal distance between them.

then, take the moment around the center of mass. Since the force on the ground from the wheels is horizontal, we need the vertical distance.

now equating both the moment

m g d = F h

d is the horizontal distance

h is the vertical distance

m g d = m a h

term of mass get eliminated

g d = a h

so,

a = \dfrac{g\ d}{h}

a = \dfrac{9.8\times 0.78}{0.775}

a = 9.86 m/s²

4 0
3 years ago
What is a tool that measures the size of a force
MakcuM [25]
<span>this is a dynamometer</span>
3 0
3 years ago
Two identical conducting spheres, A and B, carry equal charge. They are stationary and are separated by a distance much larger t
podryga [215]

Answer:

8F_i = 3F_f

Explanation:

When two identical spheres are touched to each other, they equally share the total charge. Therefore, When neutral C is first touch to A, they share the initial charge of A equally.

Let us denote that the initial charge of A and B are Q. Then after C is touched to A, their respective charges are Q/2.

Then, C is touched to B, and they share the total charge of Q + Q/2 = 3Q/2. Their respective charges afterwards is 3Q/4 each.

The electrostatic force, Fi, in the initial configuration can be calculated as follows.

F_i = \frac{1}{4\pi\epsilon_0}\frac{q_Aq_B}{r^2} = \frac{1}{4\pi\epsilon_0}\frac{Q^2}{r^2}[/tex}The electrostatic force, Ff, in the final configuration is [tex]F_f = \frac{1}{4\pi\epsilon_0}\frac{q_Aq_B}{r^2} = \frac{1}{4\pi\epsilon_0}\frac{3Q^2/8}{r^2}[/tex}Therefore, the relation between Fi and Ff is as follows[tex]F_i = F_f\frac{3}{8}\\8F_i = 3F_f

7 0
3 years ago
Arigid body must rotate about an axis in order for it to have angular momentum about that axis. True False
kompoz [17]

Answer:

False

Explanation:

Let's consider the definition of the angular momentum,

\vec{L} = I \vec{\omega}

where I = \int\limits_m r^2 dm = \lim_{n \to \infty} \sum\limits_{i=1}^n m_i r_i^2 is the moment of inertia for a rigid body. Now, this moment of inertia could change if we change the axis of rotation, because "r" is defined as the distance between the puntual mass and the nearest point on the axis of rotation, but still it's going to have some value. On the other hand,

\vec{\omega} = \frac{\vec{r} \times \vec{v}}{r^2} so \vec{\omega} \neq 0 unless \vec{r} ║  \vec{v}.

In conclusion, a rigid body could rotate about certain axis, generating an angular momentum, but if you choose another axis, there could be some parts of the rigid body rotating around the new axis, especially if there is a projection of the old axis in the new one.

7 0
3 years ago
What mass of water will fill a tank that is 100.0 cm long, 50.0 cm wide, and 30.0 cm high? Express the answer in grams.
Bond [772]
calculate\ mass\ from\ formula\ for\ density:\\\\&#10;density=volume*mass\\&#10;mass=\frac{density}{volume}\\\\&#10;volume=width*length*height\\&#10;volume=100*50*30=150000cm^3=0,15m^3\\\\&#10;density\ of\ water=\ 999.9720 \frac{kg}{m^3} \\\\mass=0,15*999.9720=149,9958kg=149995,8grams\\\\ Answer\ is\ :\\water\ which\ weight\ is\ equal\ to\ 149995,8grams.&#10;
4 0
3 years ago
Other questions:
  • Briefly describe how the Sun produces energy. plz and thank you :)
    9·2 answers
  • Science Help ASAP please!!! 35 points what is the primary role of the respiratory system in humans.
    5·1 answer
  • Q 1. How does friction affect the mechanical energy of a system? Q 2. A roller coaster is at the stop of a hill and rolls to the
    12·1 answer
  • As energy transformations occur within a system, the total energy of the system it A)increases B) decreases C) remains constant
    13·1 answer
  • A small satellite being designed requires a nitrogen storage tank to store propellant for the cold gas thruster used to maintain
    14·1 answer
  • Airbags will deploy no matter from what angle your car is hit.
    7·2 answers
  • Please Hurry will mark Brainliest
    10·2 answers
  • These steps are followed when using the half-life of carbon-14 to determine the age of an object that contains carbon. what is t
    12·2 answers
  • A technician builds an RLC series circuit which includes an AC source that operates at a fixed frequency and voltage. At the ope
    8·1 answer
  • Differences between law of flotation and Archimedes's principle​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!