If the gravitional force between two objects were proportional to 1/R (and not as `1R^(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

Options

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

Answer

C

Explanation

Gravitational force provides necessary centripetal force
`therefore (GMm)/(R )=(mv^(2))/(R )`
`rArr v=sqrt(GM)`.
i.e. v is independent of R.
Thus correct choice is (c ).