A planet is revolving around the Sun in an elliptical orbit. Its closest distance from the Sun is `r` and farthest distance is `R`. If the orbital velocity of the planet closest to the Sun is `v`, then what is the velocity at the farthest point?

Options

A. `(vr)/R`
B. `(vR)/r`
C. `vsqrt(r/R)`
D. `vsqrt(R/r)`

Answer

A

Explanation

As angular momentum is conserved, hence
`I_(1)omega_(1)=I_(2)omega_2`
or `MR_(1)^(2)omega_(1)=MR_(1)^(2)omega_(2)` or `MR_(1)v_(1)=MR_(2)v_(2)`
(`:'omega=v/R`)
`R_(1)v_(1)=R_(2)v_(2)=R_(2)v_(2)` or `VR=vr`
`:. V=(vr)/R`