1.

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

Answer»

`(vr)/(R )`
`(vR)/(r )`
`V((r )/(R ))^(1//2)`
`v ((R )/(r ))^(1//2)`

SOLUTION :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).


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