Gravitational force increases as the mass increases and decreases as the distance between the bodies is increased.
The correct option is; The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B.Reasons:
The given parameters are;
The moons of the planet = Moon A and Moon B
Mass of Moon A = 2·M
Mass of moon B = M
The distance between Moon B and the planet = 2 × The distance between Moon A and the planet
Required:
Comparison (compare) of the force exerted from the planet on Moon A and Moon B.
Solution:
The force, F, exerted from the planet is the gravitational force which is given by Newton's Law of Gravitation as follows;
[tex]\displaystyle F = \mathbf{G \cdot \frac{M_{planet} \times M}{R^2}}[/tex]Where;
G = Universal gravitational constant
[tex]M_{planet}[/tex] = Mass of the planet
M = Mass of the Moon
R = The distance from the planet to the Moon
For Moon A, we have;
Mass = 2·M
Distance = R
Which gives;
[tex]\displaystyle F_A = G \cdot \frac{M_{planet} \times 2\cdot M}{R^2} = 2\cdotG \cdot \frac{M_{planet} \times M}{R^2} = \mathbf{2 \cdot F}[/tex]
With Moon B, we have;
Mass = M
Distance = 2·R
Therefore;
[tex]\displaystyle F_B = G \cdot \frac{M_{planet} \times M}{(2 \cdot R)^2} = G \cdot \frac{M_{planet} \times M}{4 \cdot R^2} = \frac{1}{4} \cdot G \cdot \frac{M_{planet} \times M}{R^2} = \mathbf{\frac{1}{4} \cdot F}[/tex]
Which gives;
[tex]\displaystyle \frac{F_A}{F_B} = \frac{2 \cdot F}{\frac{1}{4} \cdot F } =2 \times \frac{4}{1} = \mathbf{8}[/tex]
[tex]\displaystyle \frac{F_A}{F_B} = 8[/tex]
[tex]F_A = \mathbf{8 \times F_B}[/tex]
The force from the planet on Moon A, [tex]F_A[/tex], is 8 times the force from the planet on Moon B.
Therefore, whereby option B is;
The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B.The correct option is option B
Learn more about Newton's Law of gravitation here:
https://brainly.com/question/18670622
For two vectors A and B.A+B =A-B, if and only if??
Answer:
[tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex] if and only if [tex]\vec{B}[/tex] is a zero vector.
Explanation:
An equation is true if and only if adding the same value to both sides of the equation (the value needs to be compatible) gives an equation that is also true.
Start with the [tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex].
This equation is true if and only if [tex]\left(\vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B}[/tex] ([tex]\vec{B}[/tex] is added to both sides of the original equation.)
Vector addition and subtraction are associative. Therefore, [tex]\left(\vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B}[/tex] if and only if [tex]\vec{A} + \left(\vec{B} + \vec{B}\right) = \vec{A} + \left(- \vec{B} + \vec{B}\right)[/tex], which is equivalent to [tex]\vec{A} + 2\, \vec{B} = \vec{A}[/tex].
[tex]\vec{A} + 2\, \vec{B} = \vec{A}[/tex] if and only if [tex]\left(-\vec{A}\right) + \vec{A} + 2\, \vec{B} = \left(-\vec{A}\right) + \vec{A}[/tex] ([tex]\left(-\vec{A}\right)[/tex]is added to both sides of this equation,) which is equivalent to [tex]2\, \vec{B} = \vec{0}[/tex].
[tex]2\, \vec{B} = \vec{0}[/tex] if and only [tex]\displaystyle \frac{1}{2} \cdot \left(2\, \vec{B}\right) = \frac{1}{2} \cdot \vec{0}[/tex], which is equivalent to [tex]\vec{B} = \vec{0}[/tex]. That is: [tex]\vec{B}[/tex] is the zero vector.
In other words:
[tex]\begin{aligned}& \vec{A} + \vec{B} = \vec{A} - \vec{B}\\ &\iff \left( \vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B} \\ &\iff \vec{A} + \left(\vec{B} + \vec{B}\right) = \vec{A} + \left(- \vec{B} + \vec{B}\right) \\ & \iff \vec{A} + 2\, \vec{B} = \vec{A} \\ & \iff \left(-\vec{A}\right) + \vec{A} + 2\, \vec{B} = \left(-\vec{A}\right) + \vec{A} \\ &\iff 2\, \vec{B} = \vec{0} \\ &\iff \frac{1}{2} \cdot 2\,\vec{B} = \frac{1}{2} \cdot \vec{0} \\ &\iff \vec{B} = \vec{0}\end{aligned}[/tex].
Hence, [tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex] if and only if [tex]\vec{B}[/tex] is the zero vector.
The oxygen side of a water molecule is
What is the equivalent resistance of the circuit?
Answer:
Option D. 5.45 Ω
Explanation:
From the question given above, the following data were obtained:
Resistance 1 (R₁) = 10 Ω
Resistance 2 (R₂) = 20 Ω
Resistance 3 (R₃) = 30 Ω
Voltage (V) = 120 V
Equivalent resistance (R) =?
The equivalent resistance can be obtained as follow:
1/R = 1/R₁ + 1/R₂ + 1/R₃
1/R = 1/10 + 1/20 + 1/30
Find the least common multiple (lcm) of 10, 20 and 30. The result is 60
Divide 60 by each of the denominators and multiply by their numerators respectively. We have:
1/R = (6 + 3 + 2)/60
1/R = 11/60
Invert
R = 60/11
R = 5.45 Ω
Thus, the equivalent resistance in the circuit is 5.45 Ω
Explain what ionisation is and why it is dangerous
Ionisation: the loss or gain of an electron
It is dangerous because cells that have been ionised can either die, or can mutate incorrectly, which might cause cancer.
The current of a circuit with a 3.0-volt battery and 1.0 ohm of resistance is __ amps
Answer:
3 amps
Explanation:
V = IR
I = [tex]\frac{V}{R}[/tex]
I =[tex]\frac{3}{1}[/tex]
I = 3 amps
Help please ASAP ONLY 1 question
A child squeezes a pillow over his ears during and thunderstorm. Which wave interaction helps decrease the sound of the thunder?
Answer:
Absorption
Explanation:
Scenario:
Two marbles role down a hill.
Marble 1 has a mass of 0.2g
Marble 2 has a mass of 1.2g
Marble 1 traveled 22cm in 0.8 seconds
Marble 2 traveled 26cm in 0.8 seconds
Determine the Kinetic Energy involved with each marble
Formulas you will need;
KE = (1/2)mv^2
v=d/t
Explanation:
K.E. of marble 1 = (1/2) × 0.2 × (22/0.8) ^2
= 0.1 × 756.25
= 75.625
K.E. of marble 2 = (1/2) × 1.2 × (26/0.8)^2
= 0.6 × 1056.25
= 633.75
What is the weight of an astronaut with a mass of 75 kg on the moon? The gravitational field strength on the moon is 1.6 Nkg-1.
okay this is kinda easy
What is the gravitational field strength on the moon?
The Moon has a gravitational field strength of 1.6 N/kg.
PLEASE HELPP I NEED TO PASS THIS !!
What are 4 physical properties for the bear
Answer:
A bear normally has a short, thick neck, a rounded head, a pointed muzzle, short ears, and small eyes. Some species have round faces. Bears have poor eyesight, and most have only fair hearing.
Explanation:
Modern Bears are characterized with large body and stocky legs, a long snout, shaggy hair, plantigrade paws with five non-retractile claws and a short tail.
Grizzly bears (Ursus arctos horribilis) have concave faces, a distinctive hump on their shoulders, and long claws about two to four inches long. Both the hump and the claws are traits associated with a grizzly bear's exceptional digging ability. Grizzlies are often dark brown, but can vary from blonde to nearly black.
The brown bear has a slight hump above its shoulder, round ears, a long snout and big paws with long, curved claws that it uses for digging. Unlike the black bear, it can't climb trees. It can weigh between 350-1,500 pounds. When standing on its hind legs it can be up to 5 feet tall.
Hope this helps :)
(I didn't know which type of bear so i did brown bear and grizzly bear)
PLEASEHELP THANK YOU SM
Answer:
I belive it would be the first answer choice.
Explanation:
When the Mass is lower, the ball moves faster so it would have more kintetic energy
A circus performer wants to land in a net 5 meters to the right of where she will let go of the trapeze. If she is 10 meters above the net, how fast must she be moving horizontally when she lets go? Round your final answer to three significant figures.
Answer:
Assuming no air friction,
the time it takes to fall 10 m = t = √2h/g = √(20/9.8) = 1.43 s
horizontal distance = 5 m
horizontal speed = distance/time = 5/1.43 = 3.5 m/s ANS
Explanation:
i hope this helps!
A student has two identical sheets of paper. He crumples one up into a small ball. If he drops the sheet of paper and the ball of paper off a building at the same time, which of the following statements describes the result?
A. The sheet of paper because it is more affected by gravity.
B. The ball of paper hits the ground first because it is more affected by gravity
C. The sheet of paper and the ball of paper hit the ground at the same time.
D. The ball of paper hits the ground first because it has less surface area.
Answer:
B
Explanation:
basically, because the ball "weighs" more now, it will hit the ground quicker. so technically gravity is more affective towards it. the piece of paper kind of floats it's way down. gravity isn't pushing on one force more, but because because the ball weighs more, it technically would be said so. hope this helps!
Answer:
the ball of paper, because it has less surface area.
Explanation:
How much work (MJ) must a car produce to drive 125 miles if an average force of 306 N must be maintained to overcome friction?
Answer:
The right solution is "61.557 MJ". A further explanation is given below.
Explanation:
The given values are:
Force,
F = 306 N
Drive,
D = 125 miles,
i.e.,
= 201168
meters
As we know,
The work done will be:
= [tex]F\times S[/tex]
On substituting the given values, we get
= [tex]306\times 201168[/tex]
= [tex]61557408 \ J[/tex]
On converting it in "MJ", we get
= [tex]61.557\times 10^6 \ J[/tex]
= [tex]61.557 \ MJ[/tex]
Having some trouble with this one :/
An object has a kinetic energy of 50 J and a velocity of 5 m/s, what is the mass of the object?
Answer:
Mass, M = 4 kilograms.
Explanation:
Given the following data;
Kinetic energy = 50 J
Velocity = 5 m/s
To find the mass of the object;
Kinetic energy can be defined as an energy possessed by an object or body due to its motion.
Mathematically, kinetic energy is given by the formula;
[tex] K.E = \frac{1}{2}MV^{2}[/tex]
Where;
K.E represents kinetic energy measured in Joules.
M represents mass measured in kilograms.
V represents velocity measured in metres per seconds square.
Making mass the subject formula;
[tex] M = \frac{2K.E}{V^{2}}[/tex]
Substituting into the equation, we have;
[tex] M = \frac{2*50}{5^{2}}[/tex]
[tex] M = \frac{100}{25}[/tex]
Mass, M = 4 kg
A trampoline spring has a force constant k = 800 N/m and is stretched exactly 17.5cm. What is the energy required to do this?
Answer:
the energy required for the extension is 12.25 J
Explanation:
Given;
force constant of trampoline spring, k = 800 N/m
extension of trampoline spring, x = 17.5 cm = 0.175 m
The energy required for the extension is calculated as;
E = ¹/₂kx²
E = 0.5 x 800 x 0.175²
E = 12.25 J
Therefore, the energy required for the extension is 12.25 J
Which two planets have the closest average temperature?
Answer: The planets that have the closest average temperature is
1.) Mercury which is 800 degrees Fahrenheit
2.) Venus which is about 880 degrees Fahrenheit
Hope this helps :)
The planets Mercury and Venus has the closest average temperature
What are Planets?A planet is an astronomical object that orbits a star or stellar remnant that is large enough to be rounded by gravity, but not so large as to trigger thermonuclear fusion, and that is free of planetesimals in its locality
Planets are generally divided into two main types: large, low-density gas giants and smaller, rocky terrestrials.
In order of increasing distance from the Sun, they are the four terrestrials, Mercury, Venus, Earth, and Mars, then the four gas giants, Jupiter, Saturn, Uranus, and Neptune
Given data ,
Let the first planet be represented as A
Let the second planet be represented as B
Now , the planets A and B have similar average temperature
where , the planets can have negative as well has very high temperatures
Now , when A = Mercury and B = Venus
Venus has 864 degrees Fahrenheit (462 degrees Celsius)
And , Mercury has 800 degrees Fahrenheit (430 degrees Celsius)
So , both Venus and Mercury has similar temperatures
Now , when A = Neptune and B = Uranus
Neptune has minus 353 degrees Fahrenheit (minus 214 degrees Celsius)
Uranus has minus 374 degrees Fahrenheit (minus 224 degrees Celsius)
So , both Neptune and Uranus has similar temperatures
Hence , the planets are Venus and Mercury
To learn more about planets click :
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WILL GIVE BRAINLIST QUICK!!! How does biodiversity support different varieties of species? (please put short answer)
A hot air balloon traveled 4 hours at a speed of 200 km/hr. What distance did it travel?
Which action has more power
describe what form of electromagnetic radiation does a radio use?
which type of thermometer is used to measure the temperature of a very hot object and why?
Answer:
Pyrometer, device for measuring relatively high temperatures, such as are encountered in furnaces. Most pyrometers work by measuring radiation from the body whose temperature is to be measured. Radiation devices have the advantage of not having to touch the material being measured.
Explanation:
An observer in the Northern Hemisphere watches the sky for several hours. Due to the motion of Earth, this observer notices that the stars near the north celestial pole appear to move An observer in the Northern Hemisphere watches the sky for several hours. Due to the motion of Earth, this observer notices that the stars near the north celestial pole appear to move from left to right. nearly vertically upward. counter-clockwise around the celestial pole. from right to left.
Answer:
counter clockwise
Explanation:
The observer in the Northern Hemisphere will notice that the stars near the NCP to move counter-clockwise
Counter - clockwise : The observer will observe this because the earth movement when viewed from the North pole is in a counterclockwise direction, hence the stars will appear to move in an ant-clockwise direction
A car starts at 25 m/s and then slows down at 13 m/s in 5 seconds. What is the acceleration of the car? What does the acceleration indicate?
Answer:
a=2.4m/s^2
Explanation:
Use V=vi+at
So, 13=25+a5
13-25=a5
[tex]\frac{-12}{5}[/tex]=a
a=2.4m/s^2
What are the independent and dependent variables in a circuit?
Answer:
Ideal independent sources can be batteries, DC generators or time-varying AC voltage supplies from alternators.
current dependable
Explanation:
Giving brainliest!! if you answer correctly :) (30pts)
Answer:
option A 4kg is your answer
Explanation:
given
mass(m)=?
velocity (v)=5m/s
we have
kinetic energy =50J
1/2 ×{m×v²)=50
m×5²=50×2
m=100/25=4 kg
A(n) _____ is an object that stops
electrons from completing the circuit.
answer this plsss
The range of human hearing is 20 Hz – 20 000 Hz.
Calculate the longest and shortest wavelengths we can hear.
Explanation:
the velocity of sound in air is 330m/s
and v=fh, where h is wavelength f is frequency,
h=v/f.......(1)
longer wavelength
h=330/20,h=16.5m
shorter wavelength
h=330/20000,h=1.65x10-²m
The lesser frequency was used for finding the longer wavelength since wavelength is inversely proportional to frequency,
thus an increase in frequency brings a decrease in wavelength.
and shorter wavelengths are more high and intense
hope this helps
the speed of an electric locomotive is 90kmh .express this speed in m/s with method
Answer:
24.3 m/s
Explanation:
1 kmh = 0.27 m/s, that makes a conversion ratio of 0.27/1kmh
[tex]\frac{90 kmh}{1}[/tex] x [tex]\frac{0.27 m/s}{1 kmh}[/tex]
The "kmh" n the top and bottom cancel out. And then you just multiply the top 90 x 0.27 and the bottom 1 x 1 to get
[tex]\frac{24.3 m/s}{1}[/tex]
and since its over 1 its just 24.3 m/s