Answer: The gravitational force Fg exerted on the orbit by the planet is Fg = G 4/3πr3rhom/ (R1 + d+ R2)^2
Explanation:
Gravitational Force Fg = GMm/r2----1
Where G is gravitational constant
M Mass of the planet, m mass of the orbit and r is the distance between the masses.
Since the circular orbit move around the planet, it means they do not touch each other.
The distance between two points on the circumference of the two massesb is given by d, while the distance from the radius of each mass to the circumferences are R1 and R2 from the question.
Total distance r= (R1 + d + R2)^2---2
Recall, density rho =
Mass M/Volume V
Hence, mass of planet = rho × V
But volume of a sphere is 4/3πr3
Therefore,
Mass M of planet = rho × 4/3πr3
=4/3πr3rho in kg
From equation 1 and 2
Fg = G 4/3πr3rhom/ (R1 + d+ R2)^2
Answer:
Wavelength = 1.36 * 10^{-34} meters
Explanation:
Given the following data;
Mass = 0.113 kg
Velocity = 43 m/s
To find the wavelength, we would use the De Broglie's wave equation.
Mathematically, it is given by the formula;

Where;
h represents Planck’s constant.
m represents the mass of the particle.
v represents the velocity of the particle.
We know that Planck’s constant = 6.6262 * 10^{-34} Js
Substituting into the formula, we have;


Wavelength = 1.36 * 10^{-34} meters
Explanation:
The speed of a wave is given by :
......(1)
(i) Here, the wavelength of a sound wave in air reduces by a factor of 3. Equation (1) becomes :

Wavelength and frequency are inversely proportional to each other. So, if wavelength of a sound wave in air reduces by a factor of 3, then the frequency will increases by a factor of 3.
(ii) It remains the same.
It is the acceleration of an object in free fall
Explanation:
When an object is in free fall, it is subjected only to one force: the force of gravity, which pulls the object downward, with a magnitude (near the Earth's surface) which is given by

where
m is the mass of the object
is the acceleration due to gravity
We can apply Newton's second law to the object in free fall:

where
F is the net force on the object
a is the acceleration of the object
m is the mass
However, since there is only the force of gravity acting on the object, the net force is equal to the force of gravity: so we can equate the two equations, obtaining that

Which means that the acceleration of an object in free fall (acted upon the force of gravity only) is equal to the acceleration due to gravity,
.
Learn more about gravity:
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Since you already gave us the weight of the 2.5-kg box,
we don't even need to know what the distance is, just
as long as it doesn't change.
Look at the formula for the gravitational force:
F = G m₁ m₂ / R² .
If 'G', 'm₁' (mass of the Earth), and 'R' (distance from the Earth's center)
don't change, then the Force is proportional to m₂ ... mass of the box,
and you can write a simple proportion:
(6.1 N) / (2.5 kg) = (F) / (1 kg)
Cross-multiply: (6.1 N) (1 kg) = (F) (2.5 kg)
Divide each side by (2.5 kg): F = (6.1N) x (1 kg) / (2.5 kg) = 2.44 N .