A planet moves around the sun. It is closest to sun to sun at a distance `d_(1)` and have velocity `v_(1)` At farthest distance `d_(2)` its speed will be

Options

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

Answer

C

Explanation

Since, Kepler's second law is same as the law of conservation of angular momentum
`d_(1)v_(1)=d_(2)v_(2)` (from conservation of angular momentum at these two points)
`:. V_(2) = (d_(1)v_(1))/(d_(2))`.