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If the gravitational force between two o...

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`

Text Solution

Verified by Experts

The correct Answer is:
B
Centripetal force(F)`=(mv^(2))/(R )` and the gravitational force (F) `=(GMm)/(R^(2))=(GMm)/(R )`(where `R^(2) to R)`.
Since `(mv^(2))/(R )=(GMm)/(R )`, therefore `v=sqrt(GM)`.
Thus velocity v is independent of R.
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