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If the gravitational force were potentia...

If the gravitational force were potential to `1/r`, then a particle in a circular orbit under such a force would have its original speed:

A

Indepdent of r

B

`prop 1/r`

C

`prop 1/(r^(2))`

D

`prop r^(2)`

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A
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Knowledge Check

  • The gravitational force between two objects is proportional to 1//R (and not as 1//R^(2) ) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

    A
    `1/(R^(2))`
    B
    `R^(0)`
    C
    `R^(1)`
    D
    `1/R`

  • If the gravitational force between two objects were proportional to 1//R (and not as 1//R^(2) ), where R is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed v, proportional to

    A
    remains unchanged
    B
    `R_(0)` (independent of R)
    C
    `1//R^(2)`
    D
    `1//R`

  • Suppose that the gravitational force between two bodies separated by a distance R becomes inversely proportional to R (and not as (1)/(R^(2)) as given by Newton's law of gravitation). Then the speed of a particle moving in a circular orbit of radius R under such a force would be proportional to

    A
    `(1)/(R^(2))`
    B
    `R^(0)`
    C
    R
    D
    `(1)/(R )`

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