A plenet moving along an elliptical orbit is closest to the sun at a distance `r_(1)` and farthest away at a distance of `r_(2)`. If `v_(1)` and `v_(2)` are the linear velocities at these points respectively, then the ratio `(v_(1))/(v_(2))` is

Options

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

Answer

A

Explanation

From the law of conservation of angular momentum
`mr_(1)v_(1)=m r_(2)v_(2)`
`r_(1)v_(1)=r_(2)v_(2) rarr (v_(1))/(v_(2))=(r_(2))/(r_(1))`