The radii of circular orbits of two satellites A and B of the earth are 4R and R respectively. If the speed of satellite A is 3V, then the speed of satellite B will be A) 3V/4 B) 6V C) 12V D) 3V/3?

Question

Answer

F=GMm/R2,( it is R square)
now force of Gravitation provide centripetal force
therefore mv2/R=GMm/R2
v=[GM/R]1/2

Now, according to question
3v=[GM/4R]1/2
3v=1/2[GM/R]1/2 ----------(1)

and
let the velocity of the other planet be x,
x=[GM/R]1/2 -------------(2)

from (1) and (2)

3v=x/2,
x=6v

hence solved

Answer

Answer

The radii of the circular orbits
Satellite A is in a circular orbit with a radius of 4R, while satellite B is in a circular orbit with a radius of R. The radius of an orbit determines the distance of the satellite from the center of the Earth.

The speed of satellite A
The speed of satellite A is given as 3V. This means that satellite A is moving at a speed of 3 times the velocity V. The velocity of a satellite in orbit is determined by the gravitational force between the satellite and the Earth.

Relationship between velocity and radius
The velocity of a satellite in orbit is inversely proportional to the radius of its orbit. This means that as the radius of the orbit increases, the velocity of the satellite decreases, and vice versa. Mathematically, this relationship can be expressed as:

v ∝ 1/r

Where v is the velocity of the satellite and r is the radius of its orbit.

Determining the speed of satellite B
Since satellite B has a radius of R, which is one-fourth the radius of satellite A's orbit, we can determine its speed using the relationship between velocity and radius.

If the speed of satellite A is 3V, then the speed of satellite B can be calculated as follows:

vB = vA * (rA / rB)

Where vB is the speed of satellite B, vA is the speed of satellite A, rA is the radius of satellite A's orbit, and rB is the radius of satellite B's orbit.

Substituting the given values, we have:

vB = 3V * (4R / R)
vB = 3V * 4
vB = 12V

Therefore, the speed of satellite B is 12V.

Answer: C) 12V

In summary, the speed of satellite B is determined by the relationship between the velocities and radii of the two satellites. Since satellite B has a smaller radius than satellite A, its speed will be greater. Specifically, if the speed of satellite A is 3V, the speed of satellite B will be 12V.

Answer

The velocity of a satellite around the centre of its orbit is inversely proportional to its distance from the centre of the orbit which it follows.

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