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Which formulas have been correctly rearranged to solve for radius? check all that apply. r = startfraction g times m subscript central baseline over v superscript 2 baseline endfraction. r = startfraction f subscript c baseline times m over v superscript 2 baseline endfraction. r = startfraction a subscript c baseline over v superscript 2 baseline endfraction r = startfraction v t over 2 pi endfraction r = startfraction a subscript c baseline times t over pi endfraction

Answer :

r = \frac{GM}{v^{2} } formulas have been correctly rearranged to solve for radius.

What is circular motion ?

  • An object moving in a circular motion is defined as rotating while doing so. There are two types of circular motion: uniform and non-uniform.
  • While the angular rate of rotation and speed are constant during uniform circular motion, they are not during non-uniform motion.

The problem is asking to find the radius of the orbit of a satellite around a planet, given the orbital speed of the satellite.

For a satellite in orbit around a planet, the gravitational force provides the required centripetal force to keep it in circular motion, therefore we can write:

[tex]\frac{GMm}{r^{2} } = m\frac{v^{2} }{r}[/tex]

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the satellite

r is the radius of the orbit

v is the speed of the satellite

Re-arranging the equation, we find

[tex]\frac{GM}{r} = v^{2}[/tex]

[tex]r = \frac{GM}{v^{2} }[/tex]

Learn more about circular motion

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