A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance `r`. The speed of the particle is

Options

A. Proportional to `r^(2)`
B. Independent of r
C. Proportional to r
D. Proportional to `1//r`

Answer

B

Explanation

Let .F. be the force.
Given `F prop alpha 1/r`
`= F = k/r`, where k is a constant.
Since, particle experiences centripetal force.
`(mv^(2))/r = k/r`
`=v = sqrt(k/m)` (independent of r)