The earth moves around the Sun in an elliptical orbit as shown figure. The ratio OA/OB=x. The ratio of the speed of the earth at B to that at A is nearly

Options

A. `R^(-1)`
B. `sqrt(R)`
C. R
D. `R^(2//3)`

Answer

C

Explanation

In central force motion, the angular momentum of body remains conserved.
i.e., Angular momentum,
`L = r xx p = mvr`
[at minor and major axis, v and r are perpendicular]
So if `v_(1) and v_(2)` be the speed of earth at A and B, respectively.
Then, `mv_(1)r_(1)=mv_(2)r_(2)`
`rArr (v_(1))/(v_(2))=(r_(2))/(r_(1))=(OB)/(OA)rArr(v_(1))/(v_(2))=R`.