A planet is revolving round the sun in elliptical orbit. Its closest distance is r and farthest distance is R. If the orbital velocity closest to the sun is v, then velocity v at farthest point is :

Options

A. `(vr)/(R )`
B. `(vR)/(r )`
C. `v((r )/(R ))^(1//2)`
D. `v ((R )/(r ))^(1//2)`

Answer

A

Explanation

Here angular momentum is conserved.
`therefore I_(1)omega_(1)=I_(2)omega_(2) or MR_(1)^(2)omega_(1)=MR_(2)^(2)omega_(2)`
Now `omega_(1)=(v)/(r ) and omega_(2)=(V)/(R )`
`therefore r^(2)xx (v)/(r )=R^(2)xx(V)/(R ) or vr=V.R`
or `V=(vr)/(R )`.
Correct choice is (a).